The MEOW lunar project for education and science based on concurrent engineering approach

NASA Astrophysics Data System (ADS)

Roibás-Millán, E.; Sorribes-Palmer, F.; Chimeno-Manguán, M.

2018-07-01

The use of concurrent engineering in the design of space missions allows to take into account in an interrelated methodology the high level of coupling and iteration of mission subsystems in the preliminary conceptual phase. This work presents the result of applying concurrent engineering in a short time lapse to design the main elements of the preliminary design for a lunar exploration mission, developed within ESA Academy Concurrent Engineering Challenge 2017. During this program, students of the Master in Space Systems at Technical University of Madrid designed a low cost satellite to find water on the Moon south pole as prospect of a future human lunar base. The resulting mission, The Moon Explorer And Observer of Water/Ice (MEOW) compromises a 262 kg spacecraft to be launched into a Geostationary Transfer Orbit as a secondary payload in the 2023/2025 time frame. A three months Weak Stability Boundary transfer via the Sun-Earth L1 Lagrange point allows for a high launch timeframe flexibility. The different aspects of the mission (orbit analysis, spacecraft design and payload) and possibilities of concurrent engineering are described.

How to use the Sun-Earth Lagrange points for fundamental physics and navigation

NASA Astrophysics Data System (ADS)

Tartaglia, A.; Lorenzini, E. C.; Lucchesi, D.; Pucacco, G.; Ruggiero, M. L.; Valko, P.

2018-01-01

We illustrate the proposal, nicknamed LAGRANGE, to use spacecraft, located at the Sun-Earth Lagrange points, as a physical reference frame. Performing time of flight measurements of electromagnetic signals traveling on closed paths between the points, we show that it would be possible: (a) to refine gravitational time delay knowledge due both to the Sun and the Earth; (b) to detect the gravito-magnetic frame dragging of the Sun, so deducing information about the interior of the star; (c) to check the possible existence of a galactic gravitomagnetic field, which would imply a revision of the properties of a dark matter halo; (d) to set up a relativistic positioning and navigation system at the scale of the inner solar system. The paper presents estimated values for the relevant quantities and discusses the feasibility of the project analyzing the behavior of the space devices close to the Lagrange points.

Simple, Robust Cryogenic Propellant Depot for Near Term Applications

NASA Technical Reports Server (NTRS)

McLean, Christopher; Pitchford, Brian; Mustafi, Shuvo; Wollen, Mark; Walls, Laurie; Schmidt, Jeff

2011-01-01

The ability to refuel cryogenic propulsion stages on-orbit provides an innovative paradigm shift for space transportation supporting National Aeronautics and Space Administration s (NASA) Exploration program as well as deep space robotic, national security and commercial missions. Refueling enables large beyond low Earth orbit (LEO) missions without requiring super heavy lift vehicles that must continuously grow to support increasing mission demands as America s exploration transitions from early Lagrange point missions to near Earth objects (NEO), the lunar surface and eventually Mars. Earth-to-orbit launch can be optimized to provide competitive, cost-effective solutions that allow sustained exploration. This paper describes an experimental platform developed to demonstrate the major technologies required for fuel depot technology. This test bed is capable of transferring residual liquid hydrogen (LH2) or liquid oxygen (LO2) from a Centaur upper stage, and storage in a secondary tank for up to one year on-orbit. A dedicated, flight heritage spacecraft bus is attached to an Evolved Expendable Launch Vehicle (EELV) Secondary Payload Adapter (ESPA) ring supporting experiments and data collection. This platform can be deployed as early as Q1 2013. The propellant depot design described in this paper can be deployed affordably this decade supporting missions to Earth-Moon Lagrange points and lunar fly by. The same depot concept can be scaled up to support more demanding missions and launch capabilities. The enabling depot design features, technologies and concept of operations are described.

The Lagrange Points

ERIC Educational Resources Information Center

Lovell, M.S.

2007-01-01

This paper presents a derivation of all five Lagrange points by methods accessible to sixth-form students, and provides a further opportunity to match Newtonian gravity with centripetal force. The predictive powers of good scientific theories are also discussed with regard to the philosophy of science. Methods for calculating the positions of the…

Space Instrument Optimization by Implementing of Generic Three Bodies Circular Restricted Problem

NASA Astrophysics Data System (ADS)

Nejat, Cyrus

2011-01-01

In this study, the main discussion emphasizes on the spacecraft operation with a concentration on stationary points in space. To achieve these objectives, the circular restricted problem was solved for selected approaches. The equations of motion of three body restricted problem was demonstrated to apply in cases other than Lagrange's (1736-1813 A.D.) achievements, by means of the purposed CN (Cyrus Nejat) theorem along with appropriate comments. In addition to five Lagrange, two other points, CN1 and CN2 were found to be in unstable equilibrium points in a very large distance respect to Lagrange points, but stable at infinity. A very interesting simulation of Milky Way Galaxy and Andromeda Galaxy were created to find the Lagrange points, CN points (Cyrus Nejat Points), and CN lines (Cyrus Nejat Lines). The equations of motion were rearranged such a way that the transfer trajectory would be conical, by means of decoupling concept. The main objective was to make a halo orbit transfer about CN lines. The author purposes therefore that all of the corresponding sizing design that they must be developed by optimization techniques would be considered in future approaches. The optimization techniques are sufficient procedures to search for the most ideal response of a system.

NASA Human Spaceflight Architecture Team Lunar Destination Activities

NASA Technical Reports Server (NTRS)

Connolly, J. F.; Mueller, R. P.; Whitley, R. J.

2012-01-01

NASA's Human Spaceflight Architecture Team (HAT) Lunar Destination Team has been developing a number of "Design Reference Missions" (DRM) to inform exploration architecture development, transportation approaches, and destination elements and operations. There are four destinations being considered in the HAT studies: Cis-Lunar, Lunar, Near Earth Asteroids and Mars. The lunar destination includes all activities that occur on the moon itself, but not low lunar orbit operations or Earth Moon LaGrange points which are the responsibility of the HAT Cis-Lunar Team. This paper will review the various surface DRMs developed as representative scenarios that could occur in a human lunar return. The approaches have been divided into two broad categories: a seven day short stay mission with global capabilities and a longer extended duration stay of 28 days which is limited to the lunar poles as a landing zone. The surface elements, trade studies, traverses, concept of operations and other relevant issues and methodologies will be presented and discussed in the context and framework of the HAT ground rules and assumptions which are constrained by NASA's available transportation systems. An international collaborative effort based on the 2011 Global Exploration Roadmap (GER) will also be examined and evaluated.

Evolutionary Space Communications Architectures for Human/Robotic Exploration and Science Missions

NASA Technical Reports Server (NTRS)

Bhasin, Kul; Hayden, Jeffrey L.

2004-01-01

NASA enterprises have growing needs for an advanced, integrated, communications infrastructure that will satisfy the capabilities needed for multiple human, robotic and scientific missions beyond 2015. Furthermore, the reliable, multipoint infrastructure is required to provide continuous, maximum coverage of areas of concentrated activities, such as around Earth and in the vicinity of the Moon or Mars, with access made available on demand of the human or robotic user. As a first step, the definitions of NASA's future space communications and networking architectures are underway. Architectures that describe the communications and networking needed between the nodal regions consisting of Earth, Moon, Lagrange points, Mars, and the places of interest within the inner and outer solar system have been laid out. These architectures will need the modular flexibility that must be included in the communication and networking technologies to enable the infrastructure to grow in capability with time and to transform from supporting robotic missions in the solar system to supporting human ventures to Mars, Jupiter, Jupiter's moons, and beyond. The protocol-based networking capability seamlessly connects the backbone, access, inter-spacecraft and proximity network elements of the architectures employed in the infrastructure. In this paper, we present the summary of NASA's near and long term needs and capability requirements that were gathered by participative methods. We describe an integrated architecture concept and model that will enable communications for evolutionary robotic and human science missions. We then define the communication nodes, their requirements, and various options to connect them.

Evolutionary Space Communications Architectures for Human/Robotic Exploration and Science Missions

NASA Astrophysics Data System (ADS)

Bhasin, Kul; Hayden, Jeffrey L.

2004-02-01

NASA enterprises have growing needs for an advanced, integrated, communications infrastructure that will satisfy the capabilities needed for multiple human, robotic and scientific missions beyond 2015. Furthermore, the reliable, multipoint infrastructure is required to provide continuous, maximum coverage of areas of concentrated activities, such as around Earth and in the vicinity of the Moon or Mars, with access made available on demand of the human or robotic user. As a first step, the definitions of NASA's future space communications and networking architectures are underway. Architectures that describe the communications and networking needed between the nodal regions consisting of Earth, Moon, Lagrange points, Mars, and the places of interest within the inner and outer solar system have been laid out. These architectures will need the modular flexibility that must be included in the communication and networking technologies to enable the infrastructure to grow in capability with time and to transform from supporting robotic missions in the solar system to supporting human ventures to Mars, Jupiter, Jupiter's moons, and beyond. The protocol-based networking capability seamlessly connects the backbone, access, inter-spacecraft and proximity network elements of the architectures employed in the infrastructure. In this paper, we present the summary of NASA's near and long term needs and capability requirements that were gathered by participative methods. We describe an integrated architecture concept and model that will enable communications for evolutionary robotic and human science missions. We then define the communication nodes, their requirements, and various options to connect them.

Refueling with In-Situ Produced Propellants

NASA Technical Reports Server (NTRS)

Chato, David J.

2014-01-01

In-situ produced propellants have been identified in many architecture studies as key to implementing feasible chemical propulsion missions to destinations beyond lunar orbit. Some of the more noteworthy ones include: launching from Mars to return to Earth (either direct from the surface, or via an orbital rendezvous); using the Earth-Moon Lagrange point as a place to refuel Mars transfer stages with Lunar surface produced propellants; and using Mars Moon Phobos as a place to produce propellants for descent and ascent stages bound for the Mars surface. However successful implementation of these strategies require an ability to successfully transfer propellants from the in-situ production equipment into the propellant tankage of the rocket stage used to move to the desired location. In many circumstances the most desirable location for this transfer to occur is in the low-gravity environment of space. In support of low earth orbit propellant depot concepts, extensive studies have been conducted on transferring propellants in-space. Most of these propellant transfer techniques will be applicable to low gravity operations in other locations. Even ground-based transfer operations on the Moon, Mars, and especially Phobos could benefit from the propellant conserving techniques used for depot refueling. This paper will review the literature of in-situ propellants and refueling to: assess the performance benefits of the use in-situ propellants for mission concepts; review the parallels with propellant depot efforts; assess the progress of the techniques required; and provide recommendations for future research.

Concept Design of Cryogenic Propellant Storage and Transfer for Space Exploration

NASA Technical Reports Server (NTRS)

Free, James M.; Motil, Susan M.; Kortes, Trudy F.; Meyer, Michael L.; taylor, William J.

2012-01-01

NASA is in the planning and investigation process of developing innovative paths for human space exploration that strengthen the capability to extend human and robotic presence beyond low Earth orbit and throughout the solar system. NASA is establishing the foundations to enable humans to safely reach multiple potential destinations, including the Moon, asteroids, Lagrange points, and Mars and its environs through technology and capability development. To achieve access to these destinations within a reasonable flight time will require the use of high performance cryogenic propulsion systems. Therefore NASA is examining mission concepts for a Cryogenic Propellant Storage and Transfer (CPST) Flight Demonstration which will test and validate key capabilities and technologies required for future exploration elements such as large cryogenic propulsion stages and propellant depots. The CPST project will perform key ground testing in fiscal year 2012 and execute project formulation and implementation leading to a flight demonstration in 2017.

A Lagrange multiplier and Hopfield-type barrier function method for the traveling salesman problem.

PubMed

Dang, Chuangyin; Xu, Lei

2002-02-01

A Lagrange multiplier and Hopfield-type barrier function method is proposed for approximating a solution of the traveling salesman problem. The method is derived from applications of Lagrange multipliers and a Hopfield-type barrier function and attempts to produce a solution of high quality by generating a minimum point of a barrier problem for a sequence of descending values of the barrier parameter. For any given value of the barrier parameter, the method searches for a minimum point of the barrier problem in a feasible descent direction, which has a desired property that lower and upper bounds on variables are always satisfied automatically if the step length is a number between zero and one. At each iteration, the feasible descent direction is found by updating Lagrange multipliers with a globally convergent iterative procedure. For any given value of the barrier parameter, the method converges to a stationary point of the barrier problem without any condition on the objective function. Theoretical and numerical results show that the method seems more effective and efficient than the softassign algorithm.

A globally convergent Lagrange and barrier function iterative algorithm for the traveling salesman problem.

PubMed

Dang, C; Xu, L

2001-03-01

In this paper a globally convergent Lagrange and barrier function iterative algorithm is proposed for approximating a solution of the traveling salesman problem. The algorithm employs an entropy-type barrier function to deal with nonnegativity constraints and Lagrange multipliers to handle linear equality constraints, and attempts to produce a solution of high quality by generating a minimum point of a barrier problem for a sequence of descending values of the barrier parameter. For any given value of the barrier parameter, the algorithm searches for a minimum point of the barrier problem in a feasible descent direction, which has a desired property that the nonnegativity constraints are always satisfied automatically if the step length is a number between zero and one. At each iteration the feasible descent direction is found by updating Lagrange multipliers with a globally convergent iterative procedure. For any given value of the barrier parameter, the algorithm converges to a stationary point of the barrier problem without any condition on the objective function. Theoretical and numerical results show that the algorithm seems more effective and efficient than the softassign algorithm.

Project ECHO: Electronic Communications from Halo Orbit

NASA Technical Reports Server (NTRS)

Borrelli, Jason; Cooley, Bryan; Debole, Marcy; Hrivnak, Lance; Nielsen, Kenneth; Sangmeister, Gary; Wolfe, Matthew

1994-01-01

The design of a communications relay to provide constant access between the Earth and the far side of the Moon is presented. Placement of the relay in a halo orbit about the L2 Earth-Moon Lagrange point allows the satellite to maintain constant simultaneous communication between Earth and scientific payloads on the far side of the Moon. The requirements of NASA's Discovery-class missions adopted and modified for this design are: total project cost should not exceed $150 million excluding launch costs, launch must be provided by Delta-class vehicle, and the satellite should maintain an operational lifetime of 10 to 15 years. The spacecraft will follow a transfer trajectory to the L2 point, after launch by a Delta II 7925 vehicle in 1999. Low-level thrust is used for injection into a stationkeeping-free halo orbit once the spacecraft reaches the L2 point. The shape of this halo orbit is highly elliptical with the maximum excursion from the L2 point being 35000 km. A spun section and despun section connected through a bearing and power transfer assembly (BAPTA) compose the structure of the spacecraft. Communications equipment is placed on the despun section to provide for a stationary dual parabolic offset-feed array antenna system. The dual system is necessary to provide communications coverage during portions of maximum excursion on the halo orbit. Transmissions to the NASA Deep Space Network 34 m antenna include six channels (color video, two voice, scientific data from lunar payloads, satellite housekeeping and telemetry and uplinked commands) using the S- and X-bands. Four radioisotope thermoelectric generators (RTG's) provide a total of 1360 W to power onboard systems and any two of the four Hughes 13 cm ion thrusters at once. Output of the ion thrusters is approximately 17.8 mN each with xenon as the propellant. Presence of torques generated by solar pressure on the antenna dish require the addition of a 'skirt' extending from the spun section of the satellite for balance. Total mass of the satellite is approximately 900 kg at a cost of $130 million FY99.

Significance of specific force models in two applications: Solar sails to sun-earth L4/L5 and grail data analysis suggesting lava tubes and buried craters on the moon

NASA Astrophysics Data System (ADS)

Sood, Rohan

In the trajectory design process, gravitational interaction between the bodies of interest plays a key role in developing the over-arching force model. However, non-gravitational forces, such as solar radiation pressure (SRP), can significantly influence the motion of a spacecraft. Incorporating SRP within the dynamical model can assist in estimating the trajectory of a spacecraft with greater precision, in particular, for a spacecraft with a large area-to-mass ratio, i.e., solar sails. Subsequently, in the trajectory design process, solar radiation pressure can be leveraged to maneuver the sail-based spacecraft. First, to construct low energy transfers, the invariant manifolds are explored that form an important tool in the computation and design of complex trajectories. The focus is the investigation of trajectory design options, incorporating solar sail dynamics, from the Earth parking orbit to the vicinity of triangular Lagrange points. Thereafter, an optimization scheme assisted in investigating the ?V requirement to depart from the Earth parking orbit. Harnessing the solar radiation pressure, the spacecraft is delivered to the vicinity of the displaced Lagrange point and maintains a trajectory close to the artificial libration point with the help of the solar sail. However, these trajectories are converged in a model formulated as a three-body problem with additional acceleration from solar radiation pressure. Thus, the trajectories are transitioned to higher fidelity ephemeris model to account for additional perturbing accelerations that may dominate the sail-craft dynamics and improve upon the trajectory design process. Alternatively, precise knowledge of the motion of a spacecraft about a central body and the contribution of the SRP can assist in deriving a highly accurate gravity field model. The high resolution gravity data can potentially assist in exploring the surface and subsurface properties of a particular body. With the goal of expanding human presence beyond Earth, sub-surface empty lava tubes on other worlds form ideal candidates for creating a permanent habitation environment safe from cosmic radiation, micrometeorite impacts and temperature extremes. In addition, gravitational analysis has also revealed large buried craters under thick piles of mare basalt, shedding light on Moon's dynamic and hostile past. In this work, gravity mapping observations from NASA's Gravity Recovery and Interior Laboratory (GRAIL) are employed to detect the presence of potential empty lava tubes and large impact craters buried beneath the lunar maria.

Simulation of Shallow Water Jets with a Unified Element-based Continuous/Discontinuous Galerkin Model with Grid Flexibility on the Sphere

DTIC Science & Technology

2013-01-01

is the derivative of the N th-order Legendre polynomial . Given these definitions, the one-dimensional Lagrange polynomials hi(ξ) are hi(ξ) = − 1 N(N...2. Detail of one interface patch in the northern hemisphere. The high-order Legendre -Gauss-Lobatto (LGL) points are added to the linear grid by...smaller ones by a Lagrange polynomial of order nI . The number of quadrilateral elements and grid points of the final grid are then given by Np = 6(N

The Lagrange Points in a Binary Black Hole System: Applications to Electromagnetic Signatures

NASA Technical Reports Server (NTRS)

Schnittman, Jeremy

2010-01-01

We study the stability and evolution of the Lagrange points L_4 and L-5 in a black hole (BH) binary system, including gravitational radiation. We find that gas and stars can be shepherded in with the BH system until the final moments before merger, providing the fuel for a bright electromagnetic counterpart to a gravitational wave signal. Other astrophysical signatures include the ejection of hyper-velocity stars, gravitational collapse of globular clusters, and the periodic shift of narrow emission lines in AGN.

Plasmonic Roche lobe in metal-dielectric-metal structure

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shiu, Ruei-Cheng; Lan, Yung-Chiang

2013-07-15

This study investigates a plasmonic Roche lobe that is based on a metal-dielectric-metal (MDM) structure using finite-difference time-domain simulations and theoretical analyses. The effective refractive index of the MDM structure has two centers and is inversely proportional to the distance from the position of interest to the centers, in a manner that is analogous to the gravitational potential in a two-star system. The motion of surface plasmons (SPs) strongly depends on the ratio of permittivities at the two centers. The Lagrange point is an unstable equilibrium point for SPs that propagate in the system. After the SPs have passed throughmore » the Lagrange point, their spread drastically increases.« less

Investigating Trojan Asteroids at the L4/L5 Sun-Earth Lagrange Points

NASA Technical Reports Server (NTRS)

John, K. K.; Graham, L. D.; Abell, P. A.

2015-01-01

Investigations of Earth's Trojan asteroids will have benefits for science, exploration, and resource utilization. By sending a small spacecraft to the Sun-Earth L4 or L5 Lagrange points to investigate near-Earth objects, Earth's Trojan population can be better understood. This could lead to future missions for larger precursor spacecraft as well as human missions. The presence of objects in the Sun-Earth L4 and L5 Lagrange points has long been suspected, and in 2010 NASA's Wide-field Infrared Survey Explorer (WISE) detected a 300 m object. To investigate these Earth Trojan asteroid objects, it is both essential and feasible to send spacecraft to these regions. By exploring a wide field area, a small spacecraft equipped with an IR camera could hunt for Trojan asteroids and other Earth co-orbiting objects at the L4 or L5 Lagrange points in the near-term. By surveying the region, a zeroth-order approximation of the number of objects could be obtained with some rough constraints on their diameters, which may lead to the identification of potential candidates for further study. This would serve as a precursor for additional future robotic and human exploration targets. Depending on the inclination of these potential objects, they could be used as proving areas for future missions in the sense that the delta-V's to get to these targets are relatively low as compared to other rendezvous missions. They can serve as platforms for extended operations in deep space while interacting with a natural object in microgravity. Theoretically, such low inclination Earth Trojan asteroids exist. By sending a spacecraft to L4 or L5, these likely and potentially accessible targets could be identified.

Projection-based stabilization of interface Lagrange multipliers in immersogeometric fluid-thin structure interaction analysis, with application to heart valve modeling.

PubMed

Kamensky, David; Evans, John A; Hsu, Ming-Chen; Bazilevs, Yuri

2017-11-01

This paper discusses a method of stabilizing Lagrange multiplier fields used to couple thin immersed shell structures and surrounding fluids. The method retains essential conservation properties by stabilizing only the portion of the constraint orthogonal to a coarse multiplier space. This stabilization can easily be applied within iterative methods or semi-implicit time integrators that avoid directly solving a saddle point problem for the Lagrange multiplier field. Heart valve simulations demonstrate applicability of the proposed method to 3D unsteady simulations. An appendix sketches the relation between the proposed method and a high-order-accurate approach for simpler model problems.

DSCOVR/EPIC Images and Science: A New Way to View the Entire Sunlit Earth From A Sun-Earth Lagrange-1 Orbit

NASA Astrophysics Data System (ADS)

Herman, J. R.; Marshak, A.; Szabo, A.

2015-12-01

The DSCOVR mission was launched into a Sun-Earth Lagrange-1 orbit 1.5 million kilometers from earth in February 2015 onboard a SpaceX Falcon-9 rocket. The solar wind and earth science instruments were tested during the 4.5 month journey to L-1. The first data were obtained during the June-July commissioning phase, which included the first moderate resolution (10 km) color images of the entire sunlit earth, color images of the Moon, and scientific data from 10 narrow band filters (317.5, 325, 340, 388, 443, 551, 680, 687.75, 764, and 779.5 nm). Three of these filters were used to construct the color images (443, 551, 680 nm) based on the average eye response histogram of the sunlit earth. This talk will discuss some of the issues involved in deriving science quality data for global ozone, the aerosol index (dust, smoke, and volcanic ash), cloud amounts and reflectivity, and cloud height (measured from the O2 A- and B-bands). As with most new satellites, the science data are preliminary.

Cryogenic Propellant Storage and Transfer Technology Demonstration: Advancing Technologies for Future Mission Architectures Beyond Low Earth Orbit

NASA Technical Reports Server (NTRS)

Chojnacki, Kent T.; Crane, Deborah J.; Motil, Susan M.; Ginty, Carol A.; Tofil, Todd A.

2014-01-01

As part of U.S. National Space Policy, NASA is seeking an innovative path for human space exploration, which strengthens the capability to extend human and robotic presence throughout the solar system. NASA is laying the groundwork to enable humans to safely reach multiple potential destinations, including the Moon, asteroids, Lagrange points, and Mars and its environs. In support of this, NASA is embarking on the Technology Demonstration Mission Cryogenic Propellant Storage and Transfer (TDM CPST) Project to test and validate key cryogenic capabilities and technologies required for future exploration elements, opening up the architecture for large cryogenic propulsion stages and propellant depots. The TDM CPST will provide an on-orbit demonstration of the capability to store, transfer, and measure cryogenic propellants for a duration that enables long term human space exploration missions beyond low Earth orbit. This paper will present a summary of the cryogenic fluid management technology maturation effort, infusion of those technologies into flight hardware development, and a summary of the CPST preliminary design.

Does the Constellation Program Offer Opportunities to Achieve Space Science Goals in Space?

NASA Technical Reports Server (NTRS)

Thronson, Harley A.; Lester, Daniel F.; Dissel, Adam F.; Folta, David C.; Stevens, John; Budinoff, Jason G.

2008-01-01

Future space science missions developed to achieve the most ambitious goals are likely to be complex, large, publicly and professionally very important, and at the limit of affordability. Consequently, it may be valuable if such missions can be upgraded, repaired, and/or deployed in space, either with robots or with astronauts. In response to a Request for Information from the US National Research Council panel on Science Opportunities Enabled by NASA's Constellation System, we developed a concept for astronaut-based in-space servicing at the Earth-Moon L1,2 locations that may be implemented by using elements of NASA's Constellation architecture. This libration point jobsite could be of great value for major heliospheric and astronomy missions operating at Earth-Sun Lagrange points. We explored five alternative servicing options that plausibly would be available within about a decade. We highlight one that we believe is both the least costly and most efficiently uses Constellation hardware that appears to be available by mid-next decade: the Ares I launch vehicle, Orion/Crew Exploration Vehicle, Centaur vehicle, and an airlock/servicing node developed for lunar surface operations. Our concept may be considered similar to the Apollo 8 mission: a valuable exercise before descent by astronauts to the lunar surface.

Development and Evaluation of a Hydrostatic Dynamical Core Using the Spectral Element/Discontinuous Galerkin Methods

DTIC Science & Technology

2014-04-01

The CG and DG horizontal discretization employs high-order nodal basis functions associated with Lagrange polynomials based on Gauss-Lobatto- Legendre ...and DG horizontal discretization employs high-order nodal basis functions 29 associated with Lagrange polynomials based on Gauss-Lobatto- Legendre ...Inside 235 each element we build ( 1)N + Gauss-Lobatto- Legendre (GLL) quadrature points, where N 236 indicate the polynomial order of the basis

Synthesis of a controller for stabilizing the motion of a rigid body about a fixed point

NASA Astrophysics Data System (ADS)

Zabolotnov, Yu. M.; Lobanov, A. A.

2017-05-01

A method for the approximate design of an optimal controller for stabilizing the motion of a rigid body about a fixed point is considered. It is assumed that rigid body motion is nearly the motion in the classical Lagrange case. The method is based on the common use of the Bellman dynamic programming principle and the averagingmethod. The latter is used to solve theHamilton-Jacobi-Bellman equation approximately, which permits synthesizing the controller. The proposed method for controller design can be used in many problems close to the problem of motion of the Lagrange top (the motion of a rigid body in the atmosphere, the motion of a rigid body fastened to a cable in deployment of the orbital cable system, etc.).

A suggested trajectory for a Venus-sun, earth-sun Lagrange points mission, Vela

NASA Technical Reports Server (NTRS)

Bender, D. F.

1979-01-01

The possibility is suggested of investigating the existence of small, as-yet undiscovered, asteroids orbiting in the solar system near the earth-sun or Venus-sun stable Lagrange points by means of a spacecraft which traverses these regions. The type of trajectory suggested lies in the ecliptic plane and has a period of 5/6 years and a perihelion at the Venus orbital distance. The regions in which stable orbits associated with the earth and with Venus may lie are estimated to be a thin and tadpole-shaped area extending from 35 deg to 100 deg from the planet. Crossings of the regions by the trajectory are described, and the requirements for detecting the presence of 1 km sized asteroids are presented and shown to be attainable.

The Role of Cis-Lunar Space in Future Global Space Exploration

NASA Technical Reports Server (NTRS)

Bobskill, Marianne R.; Lupisella, Mark L.

2012-01-01

Cis-lunar space offers affordable near-term opportunities to help pave the way for future global human exploration of deep space, acting as a bridge between present missions and future deep space missions. While missions in cis-lunar space have value unto themselves, they can also play an important role in enabling and reducing risk for future human missions to the Moon, Near-Earth Asteroids (NEAs), Mars, and other deep space destinations. The Cis-Lunar Destination Team of NASA's Human Spaceflight Architecture Team (HAT) has been analyzing cis-lunar destination activities and developing notional missions (or "destination Design Reference Missions" [DRMs]) for cis-lunar locations to inform roadmap and architecture development, transportation and destination elements definition, operations, and strategic knowledge gaps. The cis-lunar domain is defined as that area of deep space under the gravitational influence of the earth-moon system. This includes a set of earth-centered orbital locations in low earth orbit (LEO), geosynchronous earth orbit (GEO), highly elliptical and high earth orbits (HEO), earth-moon libration or "Lagrange" points (E-ML1 through E-ML5, and in particular, E-ML1 and E-ML2), and low lunar orbit (LLO). To help explore this large possibility space, we developed a set of high level cis-lunar mission concepts in the form of a large mission tree, defined primarily by mission duration, pre-deployment, type of mission, and location. The mission tree has provided an overall analytical context and has helped in developing more detailed design reference missions that are then intended to inform capabilities, operations, and architectures. With the mission tree as context, we will describe two destination DRMs to LEO and GEO, based on present human space exploration architectural considerations, as well as our recent work on defining mission activities that could be conducted with an EML1 or EML2 facility, the latter of which will be an emphasis of this paper, motivated in part by recent interest expressed at the Global Exploration Roadmap Stakeholder meeting. This paper will also explore the links between this HAT Cis-Lunar Destination Team analysis and the recently released ISECG Global Exploration Roadmap and other potential international considerations, such as preventing harmful interference to radio astronomy observations in the shielded zone of the moon.

Space Transportation Infrastructure Supported By Propellant Depots

NASA Technical Reports Server (NTRS)

Smitherman, David; Woodcock, Gordon

2012-01-01

A space transportation infrastructure is described that utilizes propellant depot servicing platforms to support all foreseeable missions in the Earth-Moon vicinity and deep space out to Mars. The infrastructure utilizes current expendable launch vehicle (ELV) systems such as the Delta IV Heavy, Atlas V, and Falcon 9, for all crew, cargo, and propellant launches to orbit. Propellant launches are made to Low-Earth-Orbit (LEO) Depot and an Earth-Moon Lagrange Point 1 (L1) Depot to support a new reusable in-space transportation vehicles. The LEO Depot supports missions to Geosynchronous Earth Orbit (GEO) for satellite servicing and to L1 for L1 Depot missions. The L1 Depot supports Lunar, Earth-Sun L2 (ESL2), Asteroid and Mars Missions. New vehicle design concepts are presented that can be launched on current 5 meter diameter ELV systems. These new reusable vehicle concepts include a Crew Transfer Vehicle (CTV) for crew transportation between the LEO Depot, L1 Depot and missions beyond L1; a new reusable lunar lander for crew transportation between the L1 Depot and the lunar surface; and Mars orbital Depot are based on International Space Station (ISS) heritage hardware. Data provided includes the number of launches required for each mission utilizing current ELV systems (Delta IV Heavy or equivalent) and the approximate vehicle masses and propellant requirements. Also included is a discussion on affordability with ideas on technologies that could reduce the number of launches required and thoughts on how this infrastructure include competitive bidding for ELV flights and propellant services, developments of new reusable in-space vehicles and development of a multiuse infrastructure that can support many government and commercial missions simultaneously.

77 FR 9850 - Safety Zone; 2012 Mavericks Invitational, Half Moon Bay, CA

Federal Register 2010, 2011, 2012, 2013, 2014

2012-02-21

...-AA08 Safety Zone; 2012 Mavericks Invitational, Half Moon Bay, CA AGENCY: Coast Guard, DHS. ACTION... Pillar Point in the navigable waters of Half Moon Bay, California. The regulation will temporarily... the navigable waters of Half Moon Bay in vicinity of Pillar Point. The Coast Guard will enforce a...

The Gaia mission

NASA Astrophysics Data System (ADS)

Gaia Collaboration; Prusti, T.; de Bruijne, J. H. J.; Brown, A. G. A.; Vallenari, A.; Babusiaux, C.; Bailer-Jones, C. A. L.; Bastian, U.; Biermann, M.; Evans, D. W.; Eyer, L.; Jansen, F.; Jordi, C.; Klioner, S. A.; Lammers, U.; Lindegren, L.; Luri, X.; Mignard, F.; Milligan, D. J.; Panem, C.; Poinsignon, V.; Pourbaix, D.; Randich, S.; Sarri, G.; Sartoretti, P.; Siddiqui, H. I.; Soubiran, C.; Valette, V.; van Leeuwen, F.; Walton, N. A.; Aerts, C.; Arenou, F.; Cropper, M.; Drimmel, R.; Høg, E.; Katz, D.; Lattanzi, M. G.; O'Mullane, W.; Grebel, E. K.; Holland, A. D.; Huc, C.; Passot, X.; Bramante, L.; Cacciari, C.; Castañeda, J.; Chaoul, L.; Cheek, N.; De Angeli, F.; Fabricius, C.; Guerra, R.; Hernández, J.; Jean-Antoine-Piccolo, A.; Masana, E.; Messineo, R.; Mowlavi, N.; Nienartowicz, K.; Ordóñez-Blanco, D.; Panuzzo, P.; Portell, J.; Richards, P. J.; Riello, M.; Seabroke, G. M.; Tanga, P.; Thévenin, F.; Torra, J.; Els, S. G.; Gracia-Abril, G.; Comoretto, G.; Garcia-Reinaldos, M.; Lock, T.; Mercier, E.; Altmann, M.; Andrae, R.; Astraatmadja, T. L.; Bellas-Velidis, I.; Benson, K.; Berthier, J.; Blomme, R.; Busso, G.; Carry, B.; Cellino, A.; Clementini, G.; Cowell, S.; Creevey, O.; Cuypers, J.; Davidson, M.; De Ridder, J.; de Torres, A.; Delchambre, L.; Dell'Oro, A.; Ducourant, C.; Frémat, Y.; García-Torres, M.; Gosset, E.; Halbwachs, J.-L.; Hambly, N. C.; Harrison, D. L.; Hauser, M.; Hestroffer, D.; Hodgkin, S. T.; Huckle, H. E.; Hutton, A.; Jasniewicz, G.; Jordan, S.; Kontizas, M.; Korn, A. J.; Lanzafame, A. C.; Manteiga, M.; Moitinho, A.; Muinonen, K.; Osinde, J.; Pancino, E.; Pauwels, T.; Petit, J.-M.; Recio-Blanco, A.; Robin, A. C.; Sarro, L. M.; Siopis, C.; Smith, M.; Smith, K. W.; Sozzetti, A.; Thuillot, W.; van Reeven, W.; Viala, Y.; Abbas, U.; Abreu Aramburu, A.; Accart, S.; Aguado, J. J.; Allan, P. M.; Allasia, W.; Altavilla, G.; Álvarez, M. A.; Alves, J.; Anderson, R. I.; Andrei, A. H.; Anglada Varela, E.; Antiche, E.; Antoja, T.; Antón, S.; Arcay, B.; Atzei, A.; Ayache, L.; Bach, N.; Baker, S. G.; Balaguer-Núñez, L.; Barache, C.; Barata, C.; Barbier, A.; Barblan, F.; Baroni, M.; Barrado y Navascués, D.; Barros, M.; Barstow, M. A.; Becciani, U.; Bellazzini, M.; Bellei, G.; Bello García, A.; Belokurov, V.; Bendjoya, P.; Berihuete, A.; Bianchi, L.; Bienaymé, O.; Billebaud, F.; Blagorodnova, N.; Blanco-Cuaresma, S.; Boch, T.; Bombrun, A.; Borrachero, R.; Bouquillon, S.; Bourda, G.; Bouy, H.; Bragaglia, A.; Breddels, M. A.; Brouillet, N.; Brüsemeister, T.; Bucciarelli, B.; Budnik, F.; Burgess, P.; Burgon, R.; Burlacu, A.; Busonero, D.; Buzzi, R.; Caffau, E.; Cambras, J.; Campbell, H.; Cancelliere, R.; Cantat-Gaudin, T.; Carlucci, T.; Carrasco, J. M.; Castellani, M.; Charlot, P.; Charnas, J.; Charvet, P.; Chassat, F.; Chiavassa, A.; Clotet, M.; Cocozza, G.; Collins, R. S.; Collins, P.; Costigan, G.; Crifo, F.; Cross, N. J. G.; Crosta, M.; Crowley, C.; Dafonte, C.; Damerdji, Y.; Dapergolas, A.; David, P.; David, M.; De Cat, P.; de Felice, F.; de Laverny, P.; De Luise, F.; De March, R.; de Martino, D.; de Souza, R.; Debosscher, J.; del Pozo, E.; Delbo, M.; Delgado, A.; Delgado, H. E.; di Marco, F.; Di Matteo, P.; Diakite, S.; Distefano, E.; Dolding, C.; Dos Anjos, S.; Drazinos, P.; Durán, J.; Dzigan, Y.; Ecale, E.; Edvardsson, B.; Enke, H.; Erdmann, M.; Escolar, D.; Espina, M.; Evans, N. W.; Eynard Bontemps, G.; Fabre, C.; Fabrizio, M.; Faigler, S.; Falcão, A. J.; Farràs Casas, M.; Faye, F.; Federici, L.; Fedorets, G.; Fernández-Hernández, J.; Fernique, P.; Fienga, A.; Figueras, F.; Filippi, F.; Findeisen, K.; Fonti, A.; Fouesneau, M.; Fraile, E.; Fraser, M.; Fuchs, J.; Furnell, R.; Gai, M.; Galleti, S.; Galluccio, L.; Garabato, D.; García-Sedano, F.; Garé, P.; Garofalo, A.; Garralda, N.; Gavras, P.; Gerssen, J.; Geyer, R.; Gilmore, G.; Girona, S.; Giuffrida, G.; Gomes, M.; González-Marcos, A.; González-Núñez, J.; González-Vidal, J. J.; Granvik, M.; Guerrier, A.; Guillout, P.; Guiraud, J.; Gúrpide, A.; Gutiérrez-Sánchez, R.; Guy, L. P.; Haigron, R.; Hatzidimitriou, D.; Haywood, M.; Heiter, U.; Helmi, A.; Hobbs, D.; Hofmann, W.; Holl, B.; Holland, G.; Hunt, J. A. S.; Hypki, A.; Icardi, V.; Irwin, M.; Jevardat de Fombelle, G.; Jofré, P.; Jonker, P. G.; Jorissen, A.; Julbe, F.; Karampelas, A.; Kochoska, A.; Kohley, R.; Kolenberg, K.; Kontizas, E.; Koposov, S. E.; Kordopatis, G.; Koubsky, P.; Kowalczyk, A.; Krone-Martins, A.; Kudryashova, M.; Kull, I.; Bachchan, R. K.; Lacoste-Seris, F.; Lanza, A. F.; Lavigne, J.-B.; Le Poncin-Lafitte, C.; Lebreton, Y.; Lebzelter, T.; Leccia, S.; Leclerc, N.; Lecoeur-Taibi, I.; Lemaitre, V.; Lenhardt, H.; Leroux, F.; Liao, S.; Licata, E.; Lindstrøm, H. E. P.; Lister, T. A.; Livanou, E.; Lobel, A.; Löffler, W.; López, M.; Lopez-Lozano, A.; Lorenz, D.; Loureiro, T.; MacDonald, I.; Magalhães Fernandes, T.; Managau, S.; Mann, R. G.; Mantelet, G.; Marchal, O.; Marchant, J. M.; Marconi, M.; Marie, J.; Marinoni, S.; Marrese, P. M.; Marschalkó, G.; Marshall, D. J.; Martín-Fleitas, J. M.; Martino, M.; Mary, N.; Matijevič, G.; Mazeh, T.; McMillan, P. J.; Messina, S.; Mestre, A.; Michalik, D.; Millar, N. R.; Miranda, B. M. H.; Molina, D.; Molinaro, R.; Molinaro, M.; Molnár, L.; Moniez, M.; Montegriffo, P.; Monteiro, D.; Mor, R.; Mora, A.; Morbidelli, R.; Morel, T.; Morgenthaler, S.; Morley, T.; Morris, D.; Mulone, A. F.; Muraveva, T.; Musella, I.; Narbonne, J.; Nelemans, G.; Nicastro, L.; Noval, L.; Ordénovic, C.; Ordieres-Meré, J.; Osborne, P.; Pagani, C.; Pagano, I.; Pailler, F.; Palacin, H.; Palaversa, L.; Parsons, P.; Paulsen, T.; Pecoraro, M.; Pedrosa, R.; Pentikäinen, H.; Pereira, J.; Pichon, B.; Piersimoni, A. M.; Pineau, F.-X.; Plachy, E.; Plum, G.; Poujoulet, E.; Prša, A.; Pulone, L.; Ragaini, S.; Rago, S.; Rambaux, N.; Ramos-Lerate, M.; Ranalli, P.; Rauw, G.; Read, A.; Regibo, S.; Renk, F.; Reylé, C.; Ribeiro, R. A.; Rimoldini, L.; Ripepi, V.; Riva, A.; Rixon, G.; Roelens, M.; Romero-Gómez, M.; Rowell, N.; Royer, F.; Rudolph, A.; Ruiz-Dern, L.; Sadowski, G.; Sagristà Sellés, T.; Sahlmann, J.; Salgado, J.; Salguero, E.; Sarasso, M.; Savietto, H.; Schnorhk, A.; Schultheis, M.; Sciacca, E.; Segol, M.; Segovia, J. C.; Segransan, D.; Serpell, E.; Shih, I.-C.; Smareglia, R.; Smart, R. L.; Smith, C.; Solano, E.; Solitro, F.; Sordo, R.; Soria Nieto, S.; Souchay, J.; Spagna, A.; Spoto, F.; Stampa, U.; Steele, I. A.; Steidelmüller, H.; Stephenson, C. A.; Stoev, H.; Suess, F. F.; Süveges, M.; Surdej, J.; Szabados, L.; Szegedi-Elek, E.; Tapiador, D.; Taris, F.; Tauran, G.; Taylor, M. B.; Teixeira, R.; Terrett, D.; Tingley, B.; Trager, S. C.; Turon, C.; Ulla, A.; Utrilla, E.; Valentini, G.; van Elteren, A.; Van Hemelryck, E.; van Leeuwen, M.; Varadi, M.; Vecchiato, A.; Veljanoski, J.; Via, T.; Vicente, D.; Vogt, S.; Voss, H.; Votruba, V.; Voutsinas, S.; Walmsley, G.; Weiler, M.; Weingrill, K.; Werner, D.; Wevers, T.; Whitehead, G.; Wyrzykowski, Ł.; Yoldas, A.; Žerjal, M.; Zucker, S.; Zurbach, C.; Zwitter, T.; Alecu, A.; Allen, M.; Allende Prieto, C.; Amorim, A.; Anglada-Escudé, G.; Arsenijevic, V.; Azaz, S.; Balm, P.; Beck, M.; Bernstein, H.-H.; Bigot, L.; Bijaoui, A.; Blasco, C.; Bonfigli, M.; Bono, G.; Boudreault, S.; Bressan, A.; Brown, S.; Brunet, P.-M.; Bunclark, P.; Buonanno, R.; Butkevich, A. G.; Carret, C.; Carrion, C.; Chemin, L.; Chéreau, F.; Corcione, L.; Darmigny, E.; de Boer, K. S.; de Teodoro, P.; de Zeeuw, P. T.; Delle Luche, C.; Domingues, C. D.; Dubath, P.; Fodor, F.; Frézouls, B.; Fries, A.; Fustes, D.; Fyfe, D.; Gallardo, E.; Gallegos, J.; Gardiol, D.; Gebran, M.; Gomboc, A.; Gómez, A.; Grux, E.; Gueguen, A.; Heyrovsky, A.; Hoar, J.; Iannicola, G.; Isasi Parache, Y.; Janotto, A.-M.; Joliet, E.; Jonckheere, A.; Keil, R.; Kim, D.-W.; Klagyivik, P.; Klar, J.; Knude, J.; Kochukhov, O.; Kolka, I.; Kos, J.; Kutka, A.; Lainey, V.; LeBouquin, D.; Liu, C.; Loreggia, D.; Makarov, V. V.; Marseille, M. G.; Martayan, C.; Martinez-Rubi, O.; Massart, B.; Meynadier, F.; Mignot, S.; Munari, U.; Nguyen, A.-T.; Nordlander, T.; Ocvirk, P.; O'Flaherty, K. S.; Olias Sanz, A.; Ortiz, P.; Osorio, J.; Oszkiewicz, D.; Ouzounis, A.; Palmer, M.; Park, P.; Pasquato, E.; Peltzer, C.; Peralta, J.; Péturaud, F.; Pieniluoma, T.; Pigozzi, E.; Poels, J.; Prat, G.; Prod'homme, T.; Raison, F.; Rebordao, J. M.; Risquez, D.; Rocca-Volmerange, B.; Rosen, S.; Ruiz-Fuertes, M. I.; Russo, F.; Sembay, S.; Serraller Vizcaino, I.; Short, A.; Siebert, A.; Silva, H.; Sinachopoulos, D.; Slezak, E.; Soffel, M.; Sosnowska, D.; Straižys, V.; ter Linden, M.; Terrell, D.; Theil, S.; Tiede, C.; Troisi, L.; Tsalmantza, P.; Tur, D.; Vaccari, M.; Vachier, F.; Valles, P.; Van Hamme, W.; Veltz, L.; Virtanen, J.; Wallut, J.-M.; Wichmann, R.; Wilkinson, M. I.; Ziaeepour, H.; Zschocke, S.

2016-11-01

Gaia is a cornerstone mission in the science programme of the EuropeanSpace Agency (ESA). The spacecraft construction was approved in 2006, following a study in which the original interferometric concept was changed to a direct-imaging approach. Both the spacecraft and the payload were built by European industry. The involvement of the scientific community focusses on data processing for which the international Gaia Data Processing and Analysis Consortium (DPAC) was selected in 2007. Gaia was launched on 19 December 2013 and arrived at its operating point, the second Lagrange point of the Sun-Earth-Moon system, a few weeks later. The commissioning of the spacecraft and payload was completed on 19 July 2014. The nominal five-year mission started with four weeks of special, ecliptic-pole scanning and subsequently transferred into full-sky scanning mode. We recall the scientific goals of Gaia and give a description of the as-built spacecraft that is currently (mid-2016) being operated to achieve these goals. We pay special attention to the payload module, the performance of which is closely related to the scientific performance of the mission. We provide a summary of the commissioning activities and findings, followed by a description of the routine operational mode. We summarise scientific performance estimates on the basis of in-orbit operations. Several intermediate Gaia data releases are planned and the data can be retrieved from the Gaia Archive, which is available through the Gaia home page. http://www.cosmos.esa.int/gaia

Error estimates of Lagrange interpolation and orthonormal expansions for Freud weights

NASA Astrophysics Data System (ADS)

Kwon, K. H.; Lee, D. W.

2001-08-01

Let Sn[f] be the nth partial sum of the orthonormal polynomials expansion with respect to a Freud weight. Then we obtain sufficient conditions for the boundedness of Sn[f] and discuss the speed of the convergence of Sn[f] in weighted Lp space. We also find sufficient conditions for the boundedness of the Lagrange interpolation polynomial Ln[f], whose nodal points are the zeros of orthonormal polynomials with respect to a Freud weight. In particular, if W(x)=e-(1/2)x2 is the Hermite weight function, then we obtain sufficient conditions for the inequalities to hold:andwhere and k=0,1,2...,r.

Science Enabled by the Ares V: A Large Monolithic Telescope Placed at the Second Sun-Earth Lagrange Point

NASA Technical Reports Server (NTRS)

Hopkins, Randall C.; Stahl, H. Philip

2007-01-01

The payload mass and volume capabilities of the planned Ares V launch vehicle provide the science community with unprecedented opportunities to place large science payloads into low earth orbit and beyond. One example, the outcome of a recent study conducted at the NASA Marshall Space Flight Center, is a large, monolithic telescope with a primary mirror diameter of 6.2 meters placed into a halo orbit about the second Sun-Earth Lagrange point, or L2, approximately 1.5 million kin beyond Earth's orbit. Operating in the visible and ultraviolet regions of the electromagnetic spectrum, such a large telescope would allow astronomers to detect bio-signatures and characterize the atmospheres of transiting exoplanets, provide high resolution imaging three or more times better than the Hubble Space Telescope and the James Webb Space Telescope, and observe the ultraviolet light from warm baryonic matter.

Smoot Cosmology Group

Science.gov Websites

orbit around L2, the second Lagrange point of the Earth-Sun system, which is about 1.5 million orbits L2, it makes one rotation about the Sun per year. The spacecraft spin axis has to be rotated at the same rate in order to remain Sun pointed. This is achieved by making regular manoeuvres that will

Low Thrust Cis-Lunar Transfers Using a 40 kW-Class Solar Electric Propulsion Spacecraft

NASA Technical Reports Server (NTRS)

Mcguire, Melissa L.; Burke, Laura M.; Mccarty, Steven L.; Hack, Kurt J.; Whitley, Ryan J.; Davis, Diane C.; Ocampo, Cesar

2017-01-01

This paper captures trajectory analysis of a representative low thrust, high power Solar Electric Propulsion (SEP) vehicle to move a mass around cis-lunar space in the range of 20 to 40 kW power to the Electric Propulsion (EP) system. These cis-lunar transfers depart from a selected Near Rectilinear Halo Orbit (NRHO) and target other cis-lunar orbits. The NRHO cannot be characterized in the classical two-body dynamics more familiar in the human spaceflight community, and the use of low thrust orbit transfers provides unique analysis challenges. Among the target orbit destinations documented in this paper are transfers between a Southern and Northern NRHO, transfers between the NRHO and a Distant Retrograde Orbit (DRO) and a transfer between the NRHO and two different Earth Moon Lagrange Point 2 (EML2) Halo orbits. Because many different NRHOs and EML2 halo orbits exist, simplifying assumptions rely on previous analysis of orbits that meet current abort and communication requirements for human mission planning. Investigation is done into the sensitivities of these low thrust transfers to EP system power. Additionally, the impact of the Thrust to Weight ratio of these low thrust SEP systems and the ability to transit between these unique orbits are investigated.

Concept designs for NASA's Solar Electric Propulsion Technology Demonstration Mission

NASA Technical Reports Server (NTRS)

Mcguire, Melissa L.; Hack, Kurt J.; Manzella, David H.; Herman, Daniel A.

2014-01-01

Multiple Solar Electric Propulsion Technology Demonstration Mission were developed to assess vehicle performance and estimated mission cost. Concepts ranged from a 10,000 kilogram spacecraft capable of delivering 4000 kilogram of payload to one of the Earth Moon Lagrange points in support of future human-crewed outposts to a 180 kilogram spacecraft capable of performing an asteroid rendezvous mission after launched to a geostationary transfer orbit as a secondary payload. Low-cost and maximum Delta-V capability variants of a spacecraft concept based on utilizing a secondary payload adapter as the primary bus structure were developed as were concepts designed to be co-manifested with another spacecraft on a single launch vehicle. Each of the Solar Electric Propulsion Technology Demonstration Mission concepts developed included an estimated spacecraft cost. These data suggest estimated spacecraft costs of $200 million - $300 million if 30 kilowatt-class solar arrays and the corresponding electric propulsion system currently under development are used as the basis for sizing the mission concept regardless of launch vehicle costs. The most affordable mission concept developed based on subscale variants of the advanced solar arrays and electric propulsion technology currently under development by the NASA Space Technology Mission Directorate has an estimated cost of $50M and could provide a Delta-V capability comparable to much larger spacecraft concepts.

Transition in the Human Exploration of Space at NASA

NASA Technical Reports Server (NTRS)

Koch, Carla A.; Cabana, Robert

2011-01-01

NASA is taking the next step in human exploration, beyond low Earth orbit. We have been going to low Earth orbit for the past 50 years and are using this experience to work with commercial companies to perform this function. This will free NASA resources to develop the systems necessary to travel to a Near Earth Asteroid, the Moon, Lagrange Points, and eventually Mars. At KSC, we are positioning ourselves to become a multi-user launch complex and everything we are working on is bringing us closer to achieving this goal. A vibrant multi-use spaceport is to the 21st Century what the airport was to the 20th Century - an invaluable transportation hub that supports government needs while promoting economic development and commercial markets beyond Earth's atmosphere. This past year saw the end of Shuttle, but the announcements of NASA's crew module, Orion, and heavy-lift rocket, the SLS, as well as the establishment of the Commercial Crew Program. We have a busy, but very bright future ahead of us and KSC is looking forward to playing an integral part in the next era of human space exploration. The future is SLS, 21st Century Ground Systems Program, and the Commercial Crew Program; and the future is here.

CFDP: The Revised Standard and Some Handy Lab Tools

NASA Astrophysics Data System (ADS)

Montesinos, Juan Antonio; Valverde, Alberto; Taylor, Chris; Magistrati, Giorgio

2014-08-01

The original recommendation for the CCSDS File Delivery Protocol (CFDP) was published in 2002 and since then it has been adopted by many NASA missions for transferring files to and from the flight segment. Conversely, ESA missions have tended to rely on adaptation of the ECSS Packet Utilisation Standard. However, there are now ESA missions under design that will be using CFDP as the standard mechanism for file transfer. The first mission that is using CFDP as File Transfer Protocol is Euclid, to be launch in 2020 and destined to orbit the second Lagrange point (L2). The CFDP engine will be integrated in the Euclid mass memory, allowing the large data files produced by the scientific instruments to be directly downloaded on a KA band link. Moreover, it has also been proposed to be used in the JUICE mission, that will study the Jupiter moons. Due to the considerable distance from Earth, Juice has extremely challenging data transfer requirements but due to the flexibility of CFDP the requirements of both missions can be met.This report aims at presenting an overview of CFDP, the new modifications presently proposed to the standard and the tools that in the Data System division at ESTEC are using for simulation, testing and verification.

A Cryogenic Propellant Production Depot for Low Earth Orbit

NASA Technical Reports Server (NTRS)

Potter, Seth D.; Henley, Mark; Guitierrez, Sonia; Fikes, John; Carrington, Connie; Smitherman, David; Gerry, Mark; Sutherlin, Steve; Beason, Phil; Howell, Joe (Technical Monitor)

2001-01-01

The cost of access to space beyond low Earth orbit can be lowered if vehicles can refuel in orbit. The power requirements for a propellant depot that electrolyzes water and stores cryogenic oxygen and hydrogen can be met using technology developed for space solar power. A propellant depot is described that will be deployed in a 400 km circular equatorial orbit, receive tanks of water launched into a lower orbit from Earth by gun launch or reusable launch vehicle, convert the water to liquid hydrogen and oxygen, and store Lip to 500 metric tonnes of cryogenic propellants. The propellant stored in the depot can support transportation from low Earth orbit to geostationary Earth orbit, the Moon, LaGrange points, Mars, etc. The tanks are configured in an inline gravity-gradient configuration to minimize drag and settle the propellant. Temperatures can be maintained by body-mounted radiators; these will also provide some shielding against orbital debris. Power is supplied by a pair of solar arrays mounted perpendicular to the orbital plane, which rotate once per orbit to track the Sun. In the longer term, cryogenic propellant production technology can be applied to a larger LEO depot, as well as to the use of lunar water resources at a similar depot elsewhere.

Optimization Shield Materials Trade Study for Lunar/Gateway Mission

NASA Technical Reports Server (NTRS)

Tripathi, R. K.; Wilson, J. W.; Cucinotta, F. A.; Anderson, B. M.; Simonsen, L. C.

2002-01-01

The great cost of added radiation shielding is a potential limiting factor in many deep space missions. For this enabling technology, we are developing tools for optimized shield design over multi-segmented missions involving multiple work and living areas in the transport and duty phase of various space missions. The total shield mass over all pieces of equipment and habitats is optimized subject to career dose and dose rate constraints. Preliminary studies of deep space missions indicate that for long duration space missions, improved shield materials will be required. The details of this new method and its impact on space missions and other technologies will be discussed. This study will provide a vital tool for evaluating Gateway designs in their usage context. Providing protection against the hazards of space radiation is one of the challenges to the Gateway infrastructure designs. We will use the mission optimization software to scope the impact of Gateway operations on human exposures and the effectiveness of alternate shielding materials on Gateway infrastructure designs. It is being proposed to use Moon and the Lagrange points as the hub for deep space missions. This study will provide a guide to the effectiveness of multifunctional materials in preparation to more detailed geometry studies in progress.

Student Moon Observations and Spatial-Scientific Reasoning

NASA Astrophysics Data System (ADS)

Cole, Merryn; Wilhelm, Jennifer; Yang, Hongwei

2015-07-01

Relationships between sixth grade students' moon journaling and students' spatial-scientific reasoning after implementation of an Earth/Space unit were examined. Teachers used the project-based Realistic Explorations in Astronomical Learning curriculum. We used a regression model to analyze the relationship between the students' Lunar Phases Concept Inventory (LPCI) post-test score variables and several predictors, including moon journal score, number of moon journal entries, student gender, teacher experience, and pre-test score. The model shows that students who performed better on moon journals, both in terms of overall score and number of entries, tended to score higher on the LPCI. For every 1 point increase in the overall moon journal score, participants scored 0.18 points (out of 20) or nearly 1% point higher on the LPCI post-test when holding constant the effects of the other two predictors. Similarly, students who increased their scores by 1 point in the overall moon journal score scored approximately 1% higher in the Periodic Patterns (PP) and Geometric Spatial Visualization (GSV) domains of the LPCI. Also, student gender and teacher experience were shown to be significant predictors of post-GSV scores on the LPCI in addition to the pre-test scores, overall moon journal score, and number of entries that were also significant predictors on the LPCI overall score and the PP domain. This study is unique in the purposeful link created between student moon observations and spatial skills. The use of moon journals distinguishes this study further by fostering scientific observation along with skills from across science, technology, engineering, and mathematics disciplines.

76 FR 37641 - Safety Zone; Independence Day Fireworks Celebration for the City of Half Moon Bay, Half Moon Bay, CA

Federal Register 2010, 2011, 2012, 2013, 2014

2011-06-28

...-AA00 Safety Zone; Independence Day Fireworks Celebration for the City of Half Moon Bay, Half Moon Bay... temporary safety zone in the navigable waters of Half Moon Bay, off of Pillar Point Harbor beach, Half Moon Bay, CA in support of the Independence Day Fireworks Celebration for the City of Half Moon Bay...

Preliminary Design Considerations for Access and Operations in Earth-Moon L1/L2 Orbits

NASA Technical Reports Server (NTRS)

Folta, David C.; Pavlak, Thomas A.; Haapala, Amanda F.; Howell, Kathleen C.

2013-01-01

Within the context of manned spaceflight activities, Earth-Moon libration point orbits could support lunar surface operations and serve as staging areas for future missions to near-Earth asteroids and Mars. This investigation examines preliminary design considerations including Earth-Moon L1/L2 libration point orbit selection, transfers, and stationkeeping costs associated with maintaining a spacecraft in the vicinity of L1 or L2 for a specified duration. Existing tools in multi-body trajectory design, dynamical systems theory, and orbit maintenance are leveraged in this analysis to explore end-to-end concepts for manned missions to Earth-Moon libration points.

16QAM Blind Equalization via Maximum Entropy Density Approximation Technique and Nonlinear Lagrange Multipliers

PubMed Central

Mauda, R.; Pinchas, M.

2014-01-01

Recently a new blind equalization method was proposed for the 16QAM constellation input inspired by the maximum entropy density approximation technique with improved equalization performance compared to the maximum entropy approach, Godard's algorithm, and others. In addition, an approximated expression for the minimum mean square error (MSE) was obtained. The idea was to find those Lagrange multipliers that bring the approximated MSE to minimum. Since the derivation of the obtained MSE with respect to the Lagrange multipliers leads to a nonlinear equation for the Lagrange multipliers, the part in the MSE expression that caused the nonlinearity in the equation for the Lagrange multipliers was ignored. Thus, the obtained Lagrange multipliers were not those Lagrange multipliers that bring the approximated MSE to minimum. In this paper, we derive a new set of Lagrange multipliers based on the nonlinear expression for the Lagrange multipliers obtained from minimizing the approximated MSE with respect to the Lagrange multipliers. Simulation results indicate that for the high signal to noise ratio (SNR) case, a faster convergence rate is obtained for a channel causing a high initial intersymbol interference (ISI) while the same equalization performance is obtained for an easy channel (initial ISI low). PMID:24723813

Modified Interior Distance Functions (Theory and Methods)

NASA Technical Reports Server (NTRS)

Polyak, Roman A.

1995-01-01

In this paper we introduced and developed the theory of Modified Interior Distance Functions (MIDF's). The MIDF is a Classical Lagrangian (CL) for a constrained optimization problem which is equivalent to the initial one and can be obtained from the latter by monotone transformation both the objective function and constraints. In contrast to the Interior Distance Functions (IDF's), which played a fundamental role in Interior Point Methods (IPM's), the MIDF's are defined on an extended feasible set and along with center, have two extra tools, which control the computational process: the barrier parameter and the vector of Lagrange multipliers. The extra tools allow to attach to the MEDF's very important properties of Augmented Lagrangeans. One can consider the MIDFs as Interior Augmented Lagrangeans. It makes MIDF's similar in spirit to Modified Barrier Functions (MBF's), although there is a fundamental difference between them both in theory and methods. Based on MIDF's theory, Modified Center Methods (MCM's) have been developed and analyzed. The MCM's find an unconstrained minimizer in primal space and update the Lagrange multipliers, while both the center and the barrier parameter can be fixed or updated at each step. The MCM's convergence was investigated, and their rate of convergence was estimated. The extension of the feasible set and the special role of the Lagrange multipliers allow to develop MCM's, which produce, in case of nondegenerate constrained optimization, a primal and dual sequences that converge to the primal-dual solutions with linear rate, even when both the center and the barrier parameter are fixed. Moreover, every Lagrange multipliers update shrinks the distance to the primal dual solution by a factor 0 less than gamma less than 1 which can be made as small as one wants by choosing a fixed interior point as a 'center' and a fixed but large enough barrier parameter. The numericai realization of MCM leads to the Newton MCM (NMCM). The approximation for the primal minimizer one finds by Newton Method followed by the Lagrange multipliers update. Due to the MCM convergence, when both the center and the barrier parameter are fixed, the condition of the MDF Hessism and the neighborhood of the primal ninimizer where Newton method is 'well' defined remains stable. It contributes to both the complexity and the numerical stability of the NMCM.

Optimization of constrained density functional theory

NASA Astrophysics Data System (ADS)

O'Regan, David D.; Teobaldi, Gilberto

2016-07-01

Constrained density functional theory (cDFT) is a versatile electronic structure method that enables ground-state calculations to be performed subject to physical constraints. It thereby broadens their applicability and utility. Automated Lagrange multiplier optimization is necessary for multiple constraints to be applied efficiently in cDFT, for it to be used in tandem with geometry optimization, or with molecular dynamics. In order to facilitate this, we comprehensively develop the connection between cDFT energy derivatives and response functions, providing a rigorous assessment of the uniqueness and character of cDFT stationary points while accounting for electronic interactions and screening. In particular, we provide a nonperturbative proof that stable stationary points of linear density constraints occur only at energy maxima with respect to their Lagrange multipliers. We show that multiple solutions, hysteresis, and energy discontinuities may occur in cDFT. Expressions are derived, in terms of convenient by-products of cDFT optimization, for quantities such as the dielectric function and a condition number quantifying ill definition in multiple constraint cDFT.

Polestitters: Using Solar Sails for Constant Real-time Sensing of Earth's Polar Regions

NASA Astrophysics Data System (ADS)

Mulligan, P.; Diedrich, B. L.; Barnes, N.; Derbes, B.

2012-12-01

NASA has funded the Sunjammer mission - a near term demonstration of solar sail technology (2014/15). Sunjammer has the potential to demonstrate stationkeeping out of Earth's orbital plane. This is a first step in achieving "polesitter" orbits with year-round, real-time visibility of Earth's polar regions. Potential applications for such missions are illustrated. Solar sails have long been a concept for spacecraft propulsion that works by exchanging momentum with sunlight reflected by large, lightweight, mirrored sails. In addition to enabling propellantless propulsion throughout the solar system and beyond, their continuous thrust enables artificial Lagrange orbits (ALOs), some of which can be called "polesitter" orbits, with 24-hour, year-round visibility of Earth's polar regions. Several potential Earth remote sensing applications have been identified that address the limited temporal and spatial coverage from traditional polar and geostationary satellites. The Galileo spacecraft during its 1990 Earth flyby acquired imagery and radiometer data similar to the view from a polesitter. The Galileo imagery was used to derive aerosols and cloud variations used in atmospheric motion vector (AMV) derivations. Composites of satellite imagery over the South Pole is routinely used to derive atmospheric motion vectors like those performed regularly from geostationary satellites. The JAXA IKAROS mission flew a 14x14m solar sail past Venus in 2010. Sunjammer will demonstrate a state of the art 38x38m solar sail from Earth to an artificial Lagrange orbit located sunward and north of the sun-Earth L1 point. Traditional spacecraft can orbit naturally occurring Lagrange equilibrium points between the sun and Earth. The low, continuous thrust of solar sails can change where these points occur, creating new orbits with a variety of potential applications including polar remote sensing, space weather monitoring, and polar communications. This figure illustrates a selection of possible solar sail orbits around the sun-Earth L1 and L2 points.

27 CFR 9.75 - Central Coast.

Code of Federal Regulations, 2012 CFR

2012-04-01

... Mountain, California, scale 1:24,000, dated 1956, Photorevised 1980; (31) Half Moon Bay, California, scale..., Año Nuevo, Franklin Point, Pigeon Point, San Gregorio, Half Moon Bay, Montara Mountain and San...

27 CFR 9.75 - Central Coast.

Code of Federal Regulations, 2013 CFR

2013-04-01

... Mountain, California, scale 1:24,000, dated 1956, Photorevised 1980; (31) Half Moon Bay, California, scale..., Año Nuevo, Franklin Point, Pigeon Point, San Gregorio, Half Moon Bay, Montara Mountain and San...

27 CFR 9.75 - Central Coast.

Code of Federal Regulations, 2014 CFR

2014-04-01

... Mountain, California, scale 1:24,000, dated 1956, Photorevised 1980; (31) Half Moon Bay, California, scale..., Año Nuevo, Franklin Point, Pigeon Point, San Gregorio, Half Moon Bay, Montara Mountain and San...

Characterization of high order spatial discretizations and lumping techniques for discontinuous finite element SN transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maginot, P. G.; Ragusa, J. C.; Morel, J. E.

2013-07-01

We examine several possible methods of mass matrix lumping for discontinuous finite element discrete ordinates transport using a Lagrange interpolatory polynomial trial space. Though positive outflow angular flux is guaranteed with traditional mass matrix lumping in a purely absorbing 1-D slab cell for the linear discontinuous approximation, we show that when used with higher degree interpolatory polynomial trial spaces, traditional lumping does yield strictly positive outflows and does not increase in accuracy with an increase in trial space polynomial degree. As an alternative, we examine methods which are 'self-lumping'. Self-lumping methods yield diagonal mass matrices by using numerical quadrature restrictedmore » to the Lagrange interpolatory points. Using equally-spaced interpolatory points, self-lumping is achieved through the use of closed Newton-Cotes formulas, resulting in strictly positive outflows in pure absorbers for odd power polynomials in 1-D slab geometry. By changing interpolatory points from the traditional equally-spaced points to the quadrature points of the Gauss-Legendre or Lobatto-Gauss-Legendre quadratures, it is possible to generate solution representations with a diagonal mass matrix and a strictly positive outflow for any degree polynomial solution representation in a pure absorber medium in 1-D slab geometry. Further, there is no inherent limit to local truncation error order of accuracy when using interpolatory points that correspond to the quadrature points of high order accuracy numerical quadrature schemes. (authors)« less

The James Webb Space Telescope

NASA Technical Reports Server (NTRS)

Mather, John

2003-01-01

The James Webb Space Telescope (JWST) will extend the discoveries of the Hubble Space Telescope by deploying a large cooled infrared telescope at the Sun-Earth Lagrange point L2. It will have a 6 m aperture and three instruments covering the wavelength range from 0.6 to 28 microns.

Effect of Finite Particle Size on Convergence of Point Particle Models in Euler-Lagrange Multiphase Dispersed Flow

NASA Astrophysics Data System (ADS)

Nili, Samaun; Park, Chanyoung; Haftka, Raphael T.; Kim, Nam H.; Balachandar, S.

2017-11-01

Point particle methods are extensively used in simulating Euler-Lagrange multiphase dispersed flow. When particles are much smaller than the Eulerian grid the point particle model is on firm theoretical ground. However, this standard approach of evaluating the gas-particle coupling at the particle center fails to converge as the Eulerian grid is reduced below particle size. We present an approach to model the interaction between particles and fluid for finite size particles that permits convergence. We use the generalized Faxen form to compute the force on a particle and compare the results against traditional point particle method. We apportion the different force components on the particle to fluid cells based on the fraction of particle volume or surface in the cell. The application is to a one-dimensional model of shock propagation through a particle-laden field at moderate volume fraction, where the convergence is achieved for a well-formulated force model and back coupling for finite size particles. Comparison with 3D direct fully resolved numerical simulations will be used to check if the approach also improves accuracy compared to the point particle model. Work supported by the U.S. Department of Energy, National Nuclear Security Administration, Advanced Simulation and Computing Program, as a Cooperative Agreement under the Predictive Science Academic Alliance Program, under Contract No. DE-NA0002378.

State Machine Modeling of the Space Launch System Solid Rocket Boosters

NASA Technical Reports Server (NTRS)

Harris, Joshua A.; Patterson-Hine, Ann

2013-01-01

The Space Launch System is a Shuttle-derived heavy-lift vehicle currently in development to serve as NASA's premiere launch vehicle for space exploration. The Space Launch System is a multistage rocket with two Solid Rocket Boosters and multiple payloads, including the Multi-Purpose Crew Vehicle. Planned Space Launch System destinations include near-Earth asteroids, the Moon, Mars, and Lagrange points. The Space Launch System is a complex system with many subsystems, requiring considerable systems engineering and integration. To this end, state machine analysis offers a method to support engineering and operational e orts, identify and avert undesirable or potentially hazardous system states, and evaluate system requirements. Finite State Machines model a system as a finite number of states, with transitions between states controlled by state-based and event-based logic. State machines are a useful tool for understanding complex system behaviors and evaluating "what-if" scenarios. This work contributes to a state machine model of the Space Launch System developed at NASA Ames Research Center. The Space Launch System Solid Rocket Booster avionics and ignition subsystems are modeled using MATLAB/Stateflow software. This model is integrated into a larger model of Space Launch System avionics used for verification and validation of Space Launch System operating procedures and design requirements. This includes testing both nominal and o -nominal system states and command sequences.

Imaging Near-Earth Electron Densities Using Thomson Scattering

DTIC Science & Technology

2009-01-15

geocentric solar magnetospheric (GSM) coordinates1. TECs were initially computed from a viewing loca- tion at the Sun-Earth L1 Lagrange point2 for both...further find that an elliptical Earth orbit (apogee ~30 RE) is a suitable lower- cost option for a demonstration mission. 5. SIMULATED OBSERVATIONS We

Transfer to the Collinear Libration Point L3 in the Sun-Earth+Moon System

NASA Technical Reports Server (NTRS)

Hou, Xi-yun; Tang, Jing-shi; Liu, Lin

2007-01-01

The collinear libration point L3 of the sun-earth+moon system is an ideal place for some space missions. Although there has been a great amount of work concerning the applications of the other two collinear libration points L1 and L2, little work has been done about the point L3. In this paper, the dynamics of the libration points was briefly introduced first. Then a way to transfer the spacecraft to the collinear libration point L3 via the invariant manifolds of the other two collinear libration points was proposed. Theoretical works under the model of circular restricted three-body problem were done. For the sun-earth+moon system, this model is a good approximation. The results obtained are useful when a transfer trajectory under the real solar system is designed.

Direct and indirect capture of near-Earth asteroids in the Earth-Moon system

NASA Astrophysics Data System (ADS)

Tan, Minghu; McInnes, Colin; Ceriotti, Matteo

2017-09-01

Near-Earth asteroids have attracted attention for both scientific and commercial mission applications. Due to the fact that the Earth-Moon L1 and L2 points are candidates for gateway stations for lunar exploration, and an ideal location for space science, capturing asteroids and inserting them into periodic orbits around these points is of significant interest for the future. In this paper, we define a new type of lunar asteroid capture, termed direct capture. In this capture strategy, the candidate asteroid leaves its heliocentric orbit after an initial impulse, with its dynamics modeled using the Sun-Earth-Moon restricted four-body problem until its insertion, with a second impulse, onto the L2 stable manifold in the Earth-Moon circular restricted three-body problem. A Lambert arc in the Sun-asteroid two-body problem is used as an initial guess and a differential corrector used to generate the transfer trajectory from the asteroid's initial obit to the stable manifold associated with Earth-Moon L2 point. Results show that the direct asteroid capture strategy needs a shorter flight time compared to an indirect asteroid capture, which couples capture in the Sun-Earth circular restricted three-body problem and subsequent transfer to the Earth-Moon circular restricted three-body problem. Finally, the direct and indirect asteroid capture strategies are also applied to consider capture of asteroids at the triangular libration points in the Earth-Moon system.

Chaotic Dynamics in a Low-Energy Transfer Strategy to the Equilateral Equilibrium Points in the Earth-Moon System

NASA Astrophysics Data System (ADS)

Salazar, F. J. T.; Macau, E. E. N.; Winter, O. C.

In the frame of the equilateral equilibrium points exploration, numerous future space missions will require maximization of payload mass, simultaneously achieving reasonable transfer times. To fulfill this request, low-energy non-Keplerian orbits could be used to reach L4 and L5 in the Earth-Moon system instead of high energetic transfers. Previous studies have shown that chaos in physical systems like the restricted three-body Earth-Moon-particle problem can be used to direct a chaotic trajectory to a target that has been previously considered. In this work, we propose to transfer a spacecraft from a circular Earth Orbit in the chaotic region to the equilateral equilibrium points L4 and L5 in the Earth-Moon system, exploiting the chaotic region that connects the Earth with the Moon and changing the trajectory of the spacecraft (relative to the Earth) by using a gravity assist maneuver with the Moon. Choosing a sequence of small perturbations, the time of flight is reduced and the spacecraft is guided to a proper trajectory so that it uses the Moon's gravitational force to finally arrive at a desired target. In this study, the desired target will be an orbit about the Lagrangian equilibrium points L4 or L5. This strategy is not only more efficient with respect to thrust requirement, but also its time transfer is comparable to other known transfer techniques based on time optimization.

Alternative transfer to the Earth-Moon Lagrangian points L4 and L5 using lunar gravity assist

NASA Astrophysics Data System (ADS)

Salazar, F. J. T.; Macau, E. E. N.; Winter, O. C.

2014-02-01

Lagrangian points L4 and L5 lie at 60° ahead of and behind the Moon in its orbit with respect to the Earth. Each one of them is a third point of an equilateral triangle with the base of the line defined by those two bodies. These Lagrangian points are stable for the Earth-Moon mass ratio. As so, these Lagrangian points represent remarkable positions to host astronomical observatories or space stations. However, this same distance characteristic may be a challenge for periodic servicing mission. This paper studies elliptic trajectories from an Earth circular parking orbit to reach the Moon's sphere of influence and apply a swing-by maneuver in order to re-direct the path of a spacecraft to a vicinity of the Lagrangian points L4 and L5. Once the geocentric transfer orbit and the initial impulsive thrust have been determined, the goal is to establish the angle at which the geocentric trajectory crosses the lunar sphere of influence in such a way that when the spacecraft leaves the Moon's gravitational field, its trajectory and velocity with respect to the Earth change in order to the spacecraft arrives at L4 and L5. In this work, the planar Circular Restricted Three Body Problem approximation is used and in order to avoid solving a two boundary problem, the patched-conic approximation is considered.

Optical transmission for the James Webb Space Telescope

NASA Astrophysics Data System (ADS)

Lightsey, Paul A.; Gallagher, Benjamin B.; Nickles, Neal; Copp, Tracy

2012-09-01

The fabrication and coating of the mirrors for the James Webb Space Telescope has been completed. The spectral reflectivity of the protected gold coated beryllium mirrors has been measured. The predicted end-of-life transmission through the telescope builds from these values. The additional phenomena that have been analyzed are contamination effects and effects of the environment for the JWST operation about the Earth-Sun L2 Lagrange libration point. The L2 environment analysis has been based on radiation testing of mirror samples and hypervelocity testing to assess the micrometeoroid impact effects. The mirror showed no change in reflectance over the VIS-SWIR wavelengths after exposure to 6-9 Grad (Si) that simulated 6 years orbiting the L2 Lagrange point. The effects of hypervelocity particle impacts on the mirrors from test data has been extrapolated to the to the anticipated flux characteristics for micrometeoroids at the L2 environment. The results show that the micrometeoroid effects are orders of magnitude below the particulate contamination effects. The final end-of-life transmission for the mirrors including all of these phenomena will meet the performance requirements for JWST.

Alternative Transfer to the Earth-Moon Lagrangian Points L4 and L5 Using Lunar Gravity assist

NASA Astrophysics Data System (ADS)

Salazar, Francisco; Winter, Othon; Macau, Elbert; Bertachini de Almeida Prado, Antonio Fernando

2012-07-01

Lagrangian points L4 and L5 lie at 60 degrees ahead of and behind Moon in its orbit with respect to the Earth. Each one of them is a third point of an equilateral triangle with the base of the line defined by those two bodies. These Lagrangian points are stable for the Earth-Moon mass ratio. Because of their distance electromagnetic radiations from the Earth arrive on them substantially attenuated. As so, these Lagrangian points represent remarkable positions to host astronomical observatories. However, this same distance characteristic may be a challenge for periodic servicing mission. This paper studies transfer orbits in the planar restricted three-body problem. To avoid solving a two-boundary problem, the patched-conic approximation is used to find initial conditions to transfer a spacecraft between an Earth circular parking orbit and the Lagrangian points L4, L5 (in the Earth-Moon system), such that a swing-by maneuver is applied using the lunar gravity. We also found orbits that can be used to make a tour to the Lagrangian points L4, L5 based on the theorem of image trajectories. Keywords: Stable Lagrangian points, L4, L5, Three-Body problem, Patched Conic, Swing-by

76 FR 8651 - Special Local Regulation; Mavericks Surf Competition, Half Moon Bay, CA

Federal Register 2010, 2011, 2012, 2013, 2014

2011-02-15

...-AA08 Special Local Regulation; Mavericks Surf Competition, Half Moon Bay, CA AGENCY: Coast Guard, DHS... regulation on certain navigable waters of Half Moon Bay in support of the Mavericks Surf Competition. This...,000 yard radius of Pillar Point in Half Moon Bay. The Mavericks Surf Competition will occur in the...

Modeling the Global Coronal Field with Simulated Synoptic Magnetograms from Earth and the Lagrange Points L3, L4, and L5

NASA Astrophysics Data System (ADS)

Petrie, Gordon; Pevtsov, Alexei; Schwarz, Andrew; DeRosa, Marc

2018-06-01

The solar photospheric magnetic flux distribution is key to structuring the global solar corona and heliosphere. Regular full-disk photospheric magnetogram data are therefore essential to our ability to model and forecast heliospheric phenomena such as space weather. However, our spatio-temporal coverage of the photospheric field is currently limited by our single vantage point at/near Earth. In particular, the polar fields play a leading role in structuring the large-scale corona and heliosphere, but each pole is unobservable for {>} 6 months per year. Here we model the possible effect of full-disk magnetogram data from the Lagrange points L4 and L5, each extending longitude coverage by 60°. Adding data also from the more distant point L3 extends the longitudinal coverage much further. The additional vantage points also improve the visibility of the globally influential polar fields. Using a flux-transport model for the solar photospheric field, we model full-disk observations from Earth/L1, L3, L4, and L5 over a solar cycle, construct synoptic maps using a novel weighting scheme adapted for merging magnetogram data from multiple viewpoints, and compute potential-field models for the global coronal field. Each additional viewpoint brings the maps and models into closer agreement with the reference field from the flux-transport simulation, with particular improvement at polar latitudes, the main source of the fast solar wind.

The utility of polarized heliospheric imaging for space weather monitoring.

PubMed

DeForest, C E; Howard, T A; Webb, D F; Davies, J A

2016-01-01

A polarizing heliospheric imager is a critical next generation tool for space weather monitoring and prediction. Heliospheric imagers can track coronal mass ejections (CMEs) as they cross the solar system, using sunlight scattered by electrons in the CME. This tracking has been demonstrated to improve the forecasting of impact probability and arrival time for Earth-directed CMEs. Polarized imaging allows locating CMEs in three dimensions from a single vantage point. Recent advances in heliospheric imaging have demonstrated that a polarized imager is feasible with current component technology.Developing this technology to a high technology readiness level is critical for space weather relevant imaging from either a near-Earth or deep-space mission. In this primarily technical review, we developpreliminary hardware requirements for a space weather polarizing heliospheric imager system and outline possible ways to flight qualify and ultimately deploy the technology operationally on upcoming specific missions. We consider deployment as an instrument on NOAA's Deep Space Climate Observatory follow-on near the Sun-Earth L1 Lagrange point, as a stand-alone constellation of smallsats in low Earth orbit, or as an instrument located at the Sun-Earth L5 Lagrange point. The critical first step is the demonstration of the technology, in either a science or prototype operational mission context.

Grid Effect on Spherical Shallow Water Jets Using Continuous and Discontinuous Galerkin Methods

DTIC Science & Technology

2013-01-01

The high-order Legendre -Gauss-Lobatto (LGL) points are added to the linear grid by projecting the linear elements onto the auxiliary gnomonic space...mapping, the triangles are subdivided into smaller ones by a Lagrange polynomial of order nI . The number of quadrilateral elements and grid points of...of the acceleration of gravity and the vertical height of the fluid), ν∇2 is the artificial viscosity term of viscous coefficient ν = 1× 105 m2 s−1

Dynamic analysis and control PID path of a model type gantry crane

NASA Astrophysics Data System (ADS)

Ospina-Henao, P. A.; López-Suspes, Framsol

2017-06-01

This paper presents an alternate form for the dynamic modelling of a mechanical system that simulates in real life a gantry crane type, using Euler’s classical mechanics and Lagrange formalism, which allows find the equations of motion that our model describe. Moreover, it has a basic model design system using the SolidWorks software, based on the material and dimensions of the model provides some physical variables necessary for modelling. In order to verify the theoretical results obtained, a contrast was made between solutions obtained by simulation in SimMechanics-Matlab and Euler-Lagrange equations system, has been solved through Matlab libraries for solving equation’s systems of the type and order obtained. The force is determined, but not as exerted by the spring, as this will be the control variable. The objective is to bring the mass of the pendulum from one point to another with a specified distance without the oscillation from it, so that, the answer is overdamped. This article includes an analysis of PID control in which the equations of motion of Euler-Lagrange are rewritten in the state space, once there, they were implemented in Simulink to get the natural response of the system to a step input in F and then draw the desired trajectories.

Measuring the Orbital Period of the Moon Using a Digital Camera

ERIC Educational Resources Information Center

Hughes, Stephen W.

2006-01-01

A method of measuring the orbital velocity of the Moon around the Earth using a digital camera is described. Separate images of the Moon and stars taken 24 hours apart were loaded into Microsoft PowerPoint and the centre of the Moon marked on each image. Four stars common to both images were connected together to form a "home-made" constellation.…

Coherence Analysis of the Solar Wind Between l1 and the Lunar Orbit

NASA Astrophysics Data System (ADS)

Crane, S. O.; Fuqua, H.; Poppe, A. R.; Harada, Y.; Fatemi, S.; Delory, G. T.

2016-12-01

A cross correlation analysis of the lunar and solar wind interaction was performed to understand coherence length scales. This is mandatory for conducting tests in electromagnetic sounding of the moon with two measurement probes. Signal processing and data analysis methods encompass the study of the lunar electromagnetic plasma environment with properties of the solar wind at key positions outside of Earth's magnetosphere. Variations in solar activity detected by ACE, WIND, Kaguya and Lunar Prospector can be informative regarding how well correlated the magnetic properties of the solar wind are between the 1st Lagrange point (ACE & WIND orbits) and the lunar orbit (Kaguya & Lunar Prospector investigations). The analysis objective is to use cross correlation to understand the solar wind coherence between these positions. This requires mastering concrete analysis tools to filter and use data that yields high (>0.80) or intermediate (0.70-0.80) coherence values, while demonstrating an analysis of up to one month of data, and archiving poor (<0.50) cross correlation coefficients for effects of orbit position and downstream distance. We also consider the impact of high energy events such as Coronal Mass Ejections, Solar Flares, and shocks that may be recorded by `ACE's List of Disturbances and Transients' to the effect that, at the current level of analysis, various expected coefficients between 0.55 and 0.85 have been generated for up to 3 months of data, 2008-02-01 through 2008-05-03.

Solar Electric Propulsion Technologies Being Designed for Orbit Transfer Vehicle Applications

NASA Technical Reports Server (NTRS)

Sarver-Verhey, Timothy R.; Hoffman, David J.; Kerslake, Thomas W.; Oleson, Steven R.; Falck, Robert D.

2002-01-01

There is increasing interest in employing Solar Electric Propulsion (SEP) for new missions requiring transfer from low Earth orbit to the Earth-Moon Lagrange point, L1. Mission architecture plans place the Gateway Habitat at L1 in the 2011 to 2016 timeframe. The Gateway Habitat is envisioned to be used for Lunar exploration, space telescopes, and planetary mission staging. In these scenarios, an SEP stage, or "tug," is used to transport payloads to L1--such as the habitat module, lunar excursion and return vehicles, and chemical propellant for return crew trips. SEP tugs are attractive because they are able to efficiently transport large (less than 10,000 kg) payloads while minimizing propellant requirements. To meet the needs of these missions, a preliminary conceptual design for a general-purpose SEP tug was developed that incorporates several of the advanced space power and in-space propulsion technologies (such as high-power gridded ion and Hall thrusters, high-performance thin-film photovoltaics, lithium-ion batteries, and advanced high-voltage power processing) being developed at the NASA Glenn Research Center. A spreadsheet-based vehicle system model was developed for component sizing and is currently being used for mission planning. This model incorporates a low-thrust orbit transfer algorithm to make preliminary determinations of transfer times and propellant requirements. Results from this combined tug mass estimation and orbit transfer model will be used in a higher fidelity trajectory model to refine the analysis.

Access to Mars from Earth-Moon Libration Point Orbits:. [Manifold and Direct Options

NASA Technical Reports Server (NTRS)

Kakoi, Masaki; Howell, Kathleen C.; Folta, David

2014-01-01

This investigation is focused specifically on transfers from Earth-Moon L(sub 1)/L(sub 2) libration point orbits to Mars. Initially, the analysis is based in the circular restricted three-body problem to utilize the framework of the invariant manifolds. Various departure scenarios are compared, including arcs that leverage manifolds associated with the Sun-Earth L(sub 2) orbits as well as non-manifold trajectories. For the manifold options, ballistic transfers from Earth-Moon L(sub 2) libration point orbits to Sun-Earth L(sub 1)/L(sub 2) halo orbits are first computed. This autonomous procedure applies to both departure and arrival between the Earth-Moon and Sun-Earth systems. Departure times in the lunar cycle, amplitudes and types of libration point orbits, manifold selection, and the orientation/location of the surface of section all contribute to produce a variety of options. As the destination planet, the ephemeris position for Mars is employed throughout the analysis. The complete transfer is transitioned to the ephemeris model after the initial design phase. Results for multiple departure/arrival scenarios are compared.

A 3D Planetary Neocartographic Tool in Education: A Game on Virtual Moon and Mars Globes

NASA Astrophysics Data System (ADS)

Hargitai, H.; Simonné-Dombóvári, E.; Gede, M.

2012-03-01

The paper describes the educational use of online virtual globes of Mars and the Moon. The game uses topographic globes of Mars (MOLA) and the Moon (LRO DTM) that includes IAU nomenclature + informal names. Students have to position the points described.

Position Estimation Using Image Derivative

NASA Technical Reports Server (NTRS)

Mortari, Daniele; deDilectis, Francesco; Zanetti, Renato

2015-01-01

This paper describes an image processing algorithm to process Moon and/or Earth images. The theory presented is based on the fact that Moon hard edge points are characterized by the highest values of the image derivative. Outliers are eliminated by two sequential filters. Moon center and radius are then estimated by nonlinear least-squares using circular sigmoid functions. The proposed image processing has been applied and validated using real and synthetic Moon images.

Spacecraft Formation Flying near Sun-Earth L2 Lagrange Point: Trajectory Generation and Adaptive Full-State Feedback Control

NASA Technical Reports Server (NTRS)

Wong, Hong; Kapila, Vikram

2004-01-01

In this paper, we present a method for trajectory generation and adaptive full-state feedback control to facilitate spacecraft formation flying near the Sun-Earth L2 Lagrange point. Specifically, the dynamics of a spacecraft in the neighborhood of a Halo orbit reveals that there exist quasi-periodic orbits surrounding the Halo orbit. Thus, a spacecraft formation is created by placing a leader spacecraft on a desired Halo orbit and placing follower spacecraft on desired quasi-periodic orbits. To produce a formation maintenance controller, we first develop the nonlinear dynamics of a follower spacecraft relative to the leader spacecraft. We assume that the leader spacecraft is on a desired Halo orbit trajectory and the follower spacecraft is to track a desired quasi-periodic orbit surrounding the Halo orbit. Then, we design an adaptive, full-state feedback position tracking controller for the follower spacecraft providing an adaptive compensation for the unknown mass of the follower spacecraft. The proposed control law is simulated for the case of the leader and follower spacecraft pair and is shown to yield global, asymptotic convergence of the relative position tracking errors.

Dynamical evolution of a fictitious population of binary Neptune Trojans

NASA Astrophysics Data System (ADS)

Brunini, Adrián

2018-03-01

We present numerical simulations of the evolution of a synthetic population of Binary Neptune Trojans, under the influence of the solar perturbations and tidal friction (the so-called Kozai cycles and tidal friction evolution). Our model includes the dynamical influence of the four giant planets on the heliocentric orbit of the binary centre of mass. In this paper, we explore the evolution of initially tight binaries around the Neptune L4 Lagrange point. We found that the variation of the heliocentric orbital elements due to the libration around the Lagrange point introduces significant changes in the orbital evolution of the binaries. Collisional processes would not play a significant role in the dynamical evolution of Neptune Trojans. After 4.5 × 109 yr of evolution, ˜50 per cent of the synthetic systems end up separated as single objects, most of them with slow diurnal rotation rate. The final orbital distribution of the surviving binary systems is statistically similar to the one found for Kuiper Belt Binaries when collisional evolution is not included in the model. Systems composed by a primary and a small satellite are more fragile than the ones composed by components of similar sizes.

Transit detection of a `starshade' at the inner lagrange point of an exoplanet

NASA Astrophysics Data System (ADS)

Gaidos, E.

2017-08-01

All water-covered rocky planets in the inner habitable zones of solar-type stars will inevitably experience a catastrophic runaway climate due to increasing stellar luminosity and limits to outgoing infrared radiation from wet greenhouse atmospheres. Reflectors or scatterers placed near Earth's inner Lagrange point (L_1) have been proposed as a "geoengineering' solution to anthropogenic climate change and an advanced version of this could modulate incident irradiation over many Gyr or `rescue' a planet from the interior of the habitable zone. The distance of the starshade from the planet that minimizes its mass is 1.6 times the Earth-L_1 distance. Such a starshade would have to be similar in size to the planet and the mutual occultations during planetary transits could produce a characteristic maximum at mid-transit in the light curve. Because of a fortuitous ratio of densities, Earth-size planets around G dwarf stars present the best opportunity to detect such an artefact. The signal would be persistent and is potentially detectable by a future space photometry mission to characterize transiting planets. The signal could be distinguished from natural phenomenon, I.e. starspots or cometary dust clouds, by its shape, persistence and transmission spectrum.

Earth-Moon Libration Point Orbit Stationkeeping: Theory, Modeling and Operations

NASA Technical Reports Server (NTRS)

Folta, David C.; Pavlak, Thomas A.; Haapala, Amanda F.; Howell, Kathleen C.; Woodard, Mark A.

2013-01-01

Collinear Earth-Moon libration points have emerged as locations with immediate applications. These libration point orbits are inherently unstable and must be maintained regularly which constrains operations and maneuver locations. Stationkeeping is challenging due to relatively short time scales for divergence effects of large orbital eccentricity of the secondary body, and third-body perturbations. Using the Acceleration Reconnection and Turbulence and Electrodynamics of the Moon's Interaction with the Sun (ARTEMIS) mission orbit as a platform, the fundamental behavior of the trajectories is explored using Poincare maps in the circular restricted three-body problem. Operational stationkeeping results obtained using the Optimal Continuation Strategy are presented and compared to orbit stability information generated from mode analysis based in dynamical systems theory.

Orbital Maneuvers for Spacecrafts Travelling to/from the Lagrangian Points

NASA Astrophysics Data System (ADS)

Bertachini, A.

The well-known Lagrangian points that appear in the planar restricted three-body problem (Szebehely, 1967) are very important for astronautical applications. They are five points of equilibrium in the equations of motion, what means that a particle located at one of those points with zero velocity will remain there indefinitely. The collinear points (L1, L2 and L3) are always unstable and the triangular points (L4 and L5) are stable in the present case studied (Sun-Earth system). They are all very good points to locate a space-station, since they require a small amount of V (and fuel), the control to be used for station-keeping. The triangular points are specially good for this purpose, since they are stable equilibrium points. In this paper, the planar restricted three-body problem is regularized (using Lemaître regularization) and combined with numerical integration and gradient methods to solve the two point boundary value problem (the Lambert's three-body problem). This combination is applied to the search of families of transfer orbits between the Lagrangian points and the Earth, in the Sun-Earth system, with the minimum possible cost of the control used. So, the final goal of this paper is to find the magnitude and direction of the two impulses to be applied in the spacecraft to complete the transfer: the first one when leaving/arriving at the Lagrangian point and the second one when arriving/living at the Earth. This paper is a continuation of two previous papers that studied transfers in the Earth-Moon system: Broucke (1979), that studied transfer orbits between the Lagrangian points and the Moon and Prado (1996), that studied transfer orbits between the Lagrangian points and the Earth. So, the equations of motion are: whereis the pseudo-potential given by: To solve the TPBVP in the regularized variables the following steps are used: i) Guess a initial velocity Vi, so together with the initial prescribed position ri the complete initial state is known; ii) Guess a final regularized time f and integrate the regularized equations of motion from 0 = 0 until f; iii) Check the final position rf obtained from the numerical integration with the prescribed final position and the final real time with the specified time of flight. If there is an agreement (difference less than a specified error allowed) the solution is found and the process can stop here. If there is no agreement, an increment in the initial guessed velocity Vi and in the guessed final regularized time is made and the process goes back to step i). The method used to find the increment in the guessed variables is the standard gradient method, as described in Press et. al., 1989. The routines available in this reference are also used in this research with minor modifications. After that this algorithm is implemented, the Lambert's three-body problem between the Earth and the Lagrangian points is solved for several values of the time of flight. Since the regularized system is used to solve this problem, there is no need to specify the final position of M3 as lying in an primary's parking orbit (to avoid the singularity). Then, to make a comparison with previous papers (Broucke, 1979 and Prado, 1996) the centre of the primary is used as the final position for M3. The results are organized in plots of the energy and the initial flight path angle (the control to be used) in the rotating frame against the time of flight. The definition of the angle is such that the zero is in the "x" axis, (pointing to the positive direction) and it increases in the counter-clock-wise sense. This problem, as well as the Lambert's original version, has two solutions for a given transfer time: one in the counter-clock-wise direction and one in the clock-wise direction in the inertial frame. In this paper, emphasis is given in finding the families with the smallest possible energy (and velocity), although many other families do exist. Broucke, R., (1979) Travelling Between the Lagrange Points and the Moon, Journal of Guidance and Control, Vol. 2, Prado, A.F.B.A., (1969) Travelling Between the Lagrangian Points and the Earth, Acta Astronautica, Vol. 39, No. 7, pp. Press, W. H.; B. P. Flannery; S. A. Teukolsky and W. T. Vetterling (1989), Numerical Recipes, Cambridge University Szebehely, V., (1967), Theory of Orbits, Academic Press, New York.

Saturn: Origin and composition of its inner moons and rings

NASA Technical Reports Server (NTRS)

Prentice, A. J. R.

1980-01-01

The contraction of the primitive protosaturnian cloud, using ideas of supersonic turbulent convection was modeled. The model suggested that each of Saturn's inner moons, excepting Rhea, condensed above the ice-point of water and consists primarily of hydrous magnesium silicates. The satellite mean densities steadily increase towards the planet and the rocky moons are irregular in shape.

27 CFR 9.31 - Santa Cruz Mountains.

Code of Federal Regulations, 2011 CFR

2011-04-01

...—Santa Cruz County”; (7) “Franklin Point Quadrangle, California”; (8) “Half Moon Bay Quadrangle... 400-foot contour line intersect (Half Moon Bay Quadrangle), the boundary line follows Highway 92...

27 CFR 9.31 - Santa Cruz Mountains.

Code of Federal Regulations, 2010 CFR

2010-04-01

...—Santa Cruz County”; (7) “Franklin Point Quadrangle, California”; (8) “Half Moon Bay Quadrangle... 400-foot contour line intersect (Half Moon Bay Quadrangle), the boundary line follows Highway 92...

27 CFR 9.31 - Santa Cruz Mountains.

Code of Federal Regulations, 2012 CFR

2012-04-01

...—Santa Cruz County”; (7) “Franklin Point Quadrangle, California”; (8) “Half Moon Bay Quadrangle... 400-foot contour line intersect (Half Moon Bay Quadrangle), the boundary line follows Highway 92...

27 CFR 9.31 - Santa Cruz Mountains.

Code of Federal Regulations, 2014 CFR

2014-04-01

...”; (7) “Franklin Point Quadrangle, California”; (8) “Half Moon Bay Quadrangle, California—San Mateo... line intersect (Half Moon Bay Quadrangle), the boundary line follows Highway 92, beginning in a...

27 CFR 9.31 - Santa Cruz Mountains.

Code of Federal Regulations, 2013 CFR

2013-04-01

...—Santa Cruz County”; (7) “Franklin Point Quadrangle, California”; (8) “Half Moon Bay Quadrangle... 400-foot contour line intersect (Half Moon Bay Quadrangle), the boundary line follows Highway 92...

Searching for life with the Terrestrial Planet Finder: Lagrange point options for a formation flying interferometer

NASA Technical Reports Server (NTRS)

Beichman, C.; Gomez, G.; Lo, M.; Masdemont, J.; Romans, L.

2002-01-01

In this paper, we describe the mission design for TPF assuming a distributed spacecraft concept using formation flight around both a halo orbit around L2 as well as a heliocentric orbit. Although the mission architecture is still under study, the next two years will include study of four design cncepts and a downselect to two concepts around 2005.

Danish Passage Graves, "Spring/Summer/Fall full Moons" and Lunar Standstills

NASA Astrophysics Data System (ADS)

Clausen, Claus Jørgen

2015-05-01

The author proposes and discusses a model for azimuth distribution which involves the criterion of a 'spring full moon' (or a 'fall full moon') proposed by Marciano Da Silva (Da Silva 2004). The model is based on elements of the rising pattern of the summer full moon combined with directions pointing towards full moonrises which occur immediately prior to lunar standstill eclipses and directions aimed at the points at which these eclipses begin. An observed sample of 153 directions has been compared with the proposed model, which has been named the lunar 'season pointer'. Statistical tests show that the model fits well with the observed sample within the azimuth interval of 54.5° to 156.5°. The conclusion made is that at least the 'season pointer' section of the model used could very well explain the observed distribution.

Spinning Moons

NASA Image and Video Library

2015-11-10

Most inner moons in the solar system keep one face pointed toward their central planet; this frame from an animation by NASA New Horizons shows that certainly isnt the case with the small moons of Pluto, which behave like spinning tops. Pluto is shown at center with, in order, from smaller to wider orbit: Charon, Styx, Nix, Kerberos, Hydra. http://photojournal.jpl.nasa.gov/catalog/PIA20152

Modified Lagrange invariants and their role in determining transverse and axial imaging resolutions of self-interference incoherent holographic systems.

PubMed

Rosen, Joseph; Kelner, Roy

2014-11-17

The Lagrange invariant is a well-known law for optical imaging systems formulated in the frame of ray optics. In this study, we reformulate this law in terms of wave optics and relate it to the resolution limits of various imaging systems. Furthermore, this modified Lagrange invariant is generalized for imaging along the z axis, resulting with the axial Lagrange invariant which can be used to analyze the axial resolution of various imaging systems. To demonstrate the effectiveness of the theory, analysis of the lateral and the axial imaging resolutions is provided for Fresnel incoherent correlation holography (FINCH) systems.

Current Moon - June 15, 2011

NASA Image and Video Library

2017-12-08

Current moon as viewed on Wednesday, June 15, 2011, 19:00 UT (Phase 100%) This marks the first time that accurate shadows at this level of detail are possible in such a computer simulation. The shadows are based on the global elevation map being developed from measurements by the Lunar Orbiter Laser Altimeter (LOLA) aboard the Lunar Reconnaissance Orbiter (LRO). LOLA has already taken more than 10 times as many elevation measurements as all previous missions combined. The Moon always keeps the same face to us, but not exactly the same face. Because of the tilt and shape of its orbit, we see the Moon from slightly different angles over the course of a month. When a month is compressed into 12 seconds, as it is in this animation, our changing view of the Moon makes it look like it's wobbling. This wobble is called libration. The word comes from the Latin for "balance scale" (as does the name of the zodiac constellation Libra) and refers to the way such a scale tips up and down on alternating sides. The sub-Earth point gives the amount of libration in longitude and latitude. The sub-Earth point is also the apparent center of the Moon's disk and the location on the Moon where the Earth is directly overhead. The Moon is subject to other motions as well. It appears to roll back and forth around the sub-Earth point. The roll angle is given by the position angle of the axis, which is the angle of the Moon's north pole relative to celestial north. The Moon also approaches and recedes from us, appearing to grow and shrink. The two extremes, called perigee (near) and apogee (far), differ by more than 10%. The most noticed monthly variation in the Moon's appearance is the cycle of phases, caused by the changing angle of the Sun as the Moon orbits the Earth. The cycle begins with the waxing (growing) crescent Moon visible in the west just after sunset. By first quarter, the Moon is high in the sky at sunset and sets around midnight. The full Moon rises at sunset and is high in the sky at midnight. The third quarter Moon is often surprisingly conspicuous in the daylit western sky long after sunrise. Celestial north is up in these images, corresponding to the view from the northern hemisphere. The descriptions of the print resolution stills also assume a northern hemisphere orientation. To adjust for southern hemisphere views, rotate the images 180 degrees, and substitute "north" for "south" in the descriptions. Credit: NASA/Goddard Space Flight Center Scientific Visualization Studio NASA Goddard Space Flight Center enables NASA’s mission through four scientific endeavors: Earth Science, Heliophysics, Solar System Exploration, and Astrophysics. Goddard plays a leading role in NASA’s accomplishments by contributing compelling scientific knowledge to advance the Agency’s mission. Follow us on Twitter Join us on Facebook Find us on Instagram

Full Moon

NASA Image and Video Library

2017-12-08

Full Moon. Rises at sunset, high in the sky around midnight. Visible all night. This marks the first time that accurate shadows at this level of detail are possible in such a computer simulation. The shadows are based on the global elevation map being developed from measurements by the Lunar Orbiter Laser Altimeter (LOLA) aboard the Lunar Reconnaissance Orbiter (LRO). LOLA has already taken more than 10 times as many elevation measurements as all previous missions combined. The Moon always keeps the same face to us, but not exactly the same face. Because of the tilt and shape of its orbit, we see the Moon from slightly different angles over the course of a month. When a month is compressed into 12 seconds, as it is in this animation, our changing view of the Moon makes it look like it's wobbling. This wobble is called libration. The word comes from the Latin for "balance scale" (as does the name of the zodiac constellation Libra) and refers to the way such a scale tips up and down on alternating sides. The sub-Earth point gives the amount of libration in longitude and latitude. The sub-Earth point is also the apparent center of the Moon's disk and the location on the Moon where the Earth is directly overhead. The Moon is subject to other motions as well. It appears to roll back and forth around the sub-Earth point. The roll angle is given by the position angle of the axis, which is the angle of the Moon's north pole relative to celestial north. The Moon also approaches and recedes from us, appearing to grow and shrink. The two extremes, called perigee (near) and apogee (far), differ by more than 10%. The most noticed monthly variation in the Moon's appearance is the cycle of phases, caused by the changing angle of the Sun as the Moon orbits the Earth. The cycle begins with the waxing (growing) crescent Moon visible in the west just after sunset. By first quarter, the Moon is high in the sky at sunset and sets around midnight. The full Moon rises at sunset and is high in the sky at midnight. The third quarter Moon is often surprisingly conspicuous in the daylit western sky long after sunrise. Celestial north is up in these images, corresponding to the view from the northern hemisphere. The descriptions of the print resolution stills also assume a northern hemisphere orientation. To adjust for southern hemisphere views, rotate the images 180 degrees, and substitute "north" for "south" in the descriptions. Credit: NASA/Goddard Space Flight Center Scientific Visualization Studio NASA Goddard Space Flight Center enables NASA’s mission through four scientific endeavors: Earth Science, Heliophysics, Solar System Exploration, and Astrophysics. Goddard plays a leading role in NASA’s accomplishments by contributing compelling scientific knowledge to advance the Agency’s mission. Follow us on Twitter Join us on Facebook Find us on Instagram

New Moon

NASA Image and Video Library

2017-12-08

New Moon. By the modern definition, New Moon occurs when the Moon and Sun are at the same geocentric ecliptic longitude. The part of the Moon facing us is completely in shadow then. Pictured here is the traditional New Moon, the earliest visible waxing crescent, which signals the start of a new month in many lunar and lunisolar calendars. This marks the first time that accurate shadows at this level of detail are possible in such a computer simulation. The shadows are based on the global elevation map being developed from measurements by the Lunar Orbiter Laser Altimeter (LOLA) aboard the Lunar Reconnaissance Orbiter (LRO). LOLA has already taken more than 10 times as many elevation measurements as all previous missions combined. The Moon always keeps the same face to us, but not exactly the same face. Because of the tilt and shape of its orbit, we see the Moon from slightly different angles over the course of a month. When a month is compressed into 12 seconds, as it is in this animation, our changing view of the Moon makes it look like it's wobbling. This wobble is called libration. The word comes from the Latin for "balance scale" (as does the name of the zodiac constellation Libra) and refers to the way such a scale tips up and down on alternating sides. The sub-Earth point gives the amount of libration in longitude and latitude. The sub-Earth point is also the apparent center of the Moon's disk and the location on the Moon where the Earth is directly overhead. The Moon is subject to other motions as well. It appears to roll back and forth around the sub-Earth point. The roll angle is given by the position angle of the axis, which is the angle of the Moon's north pole relative to celestial north. The Moon also approaches and recedes from us, appearing to grow and shrink. The two extremes, called perigee (near) and apogee (far), differ by more than 10%. The most noticed monthly variation in the Moon's appearance is the cycle of phases, caused by the changing angle of the Sun as the Moon orbits the Earth. The cycle begins with the waxing (growing) crescent Moon visible in the west just after sunset. By first quarter, the Moon is high in the sky at sunset and sets around midnight. The full Moon rises at sunset and is high in the sky at midnight. The third quarter Moon is often surprisingly conspicuous in the daylit western sky long after sunrise. Celestial north is up in these images, corresponding to the view from the northern hemisphere. The descriptions of the print resolution stills also assume a northern hemisphere orientation. To adjust for southern hemisphere views, rotate the images 180 degrees, and substitute "north" for "south" in the descriptions. Credit: NASA/Goddard Space Flight Center Scientific Visualization Studio NASA Goddard Space Flight Center enables NASA’s mission through four scientific endeavors: Earth Science, Heliophysics, Solar System Exploration, and Astrophysics. Goddard plays a leading role in NASA’s accomplishments by contributing compelling scientific knowledge to advance the Agency’s mission. Follow us on Twitter Join us on Facebook Find us on Instagram

Corrections of the finite relativistic contributions to the synodic month period Earth-Moon range oscillations: Agreement between the geocentric and the solar-system barycentric inertial-frame calculations

NASA Astrophysics Data System (ADS)

Nordtvedt, Ken

1993-04-01

We have corrected our calculation of the finite general relativistic contribution to the synodic month period Earth-Moon range oscillation by including previously overlooked terms in the Moon's post-Newtonian equation of motion: the corrected result x(t)~=(3gSr2/c2) cos(ω-Ω)t agrees with the Shahid-Saless calculation which was performed in the geocentric frame. It is also pointed out that at the level of a few millimeters synodic month period amplitude, the Moon's orbit is polarized by the solar radiation pressure force on the Moon.

Phase-plane analysis to an “anisotropic” higher-order traffic flow model

NASA Astrophysics Data System (ADS)

Wu, Chun-Xiu

2018-04-01

The qualitative theory of differential equations is applied to investigate the traveling wave solution to an “anisotropic” higher-order viscous traffic flow model under the Lagrange coordinate system. The types and stabilities of the equilibrium points are discussed in the phase plane. Through the numerical simulation, the overall distribution structures of trajectories are drawn to analyze the relation between the phase diagram and the selected conservative solution variables, and the influences of the parameters on the system are studied. The limit-circle, limit circle-spiral point, saddle-spiral point and saddle-nodal point solutions are obtained. These steady-state solutions provide good explanation for the phenomena of the oscillatory and homogeneous congestions in real-world traffic.

FRESIP: A Discovery Mission Concept To Find Earth-Sized Planets Around Solar Like Stars

NASA Technical Reports Server (NTRS)

Borucki, William; Koch, D.; Dunham, E.; Cullers, D.; Webster, L.; Granados, A.; Ford, C.; Reitsema, H.; Cochran, W.; Bell, J.;

Revisiting the Tale of Hercules: How Stars Orbiting the Lagrange Points Visit the Sun

NASA Astrophysics Data System (ADS)

Pérez-Villegas, Angeles; Portail, Matthieu; Wegg, Christopher; Gerhard, Ortwin

2017-05-01

We propose a novel explanation for the Hercules stream consistent with recent measurements of the extent and pattern speed of the Galactic bar. We have adapted a made-to-measure dynamical model tailored for the Milky Way to investigate the kinematics of the solar neighborhood (SNd). The model matches the 3D density of the red clump giant stars (RCGs) in the bulge and bar as well as stellar kinematics in the inner Galaxy, with a pattern speed of 39 km s-1 kpc-1. Cross-matching this model with the Gaia DR1 TGAS data combined with RAVE and LAMOST radial velocities, we find that the model naturally predicts a bimodality in the U-V-velocity distribution for nearby stars which is in good agreement with the Hercules stream. In the model, the Hercules stream is made of stars orbiting the Lagrange points of the bar which move outward from the bar’s corotation radius to visit the SNd. While the model is not yet a quantitative fit of the velocity distribution, the new picture naturally predicts that the Hercules stream is more prominent inward from the Sun and nearly absent only a few 100 pc outward of the Sun, and plausibly explains that Hercules is prominent in old and metal-rich stars.

Free time minimizers for the three-body problem

NASA Astrophysics Data System (ADS)

Moeckel, Richard; Montgomery, Richard; Sánchez Morgado, Héctor

2018-03-01

Free time minimizers of the action (called "semi-static" solutions by Mañe in International congress on dynamical systems in Montevideo (a tribute to Ricardo Mañé), vol 362, pp 120-131, 1996) play a central role in the theory of weak KAM solutions to the Hamilton-Jacobi equation (Fathi in Weak KAM Theorem in Lagrangian Dynamics Preliminary Version Number 10, 2017). We prove that any solution to Newton's three-body problem which is asymptotic to Lagrange's parabolic homothetic solution is eventually a free time minimizer. Conversely, we prove that every free time minimizer tends to Lagrange's solution, provided the mass ratios lie in a certain large open set of mass ratios. We were inspired by the work of Da Luz and Maderna (Math Proc Camb Philos Soc 156:209-227, 1980) which showed that every free time minimizer for the N-body problem is parabolic and therefore must be asymptotic to the set of central configurations. We exclude being asymptotic to Euler's central configurations by a second variation argument. Central configurations correspond to rest points for the McGehee blown-up dynamics. The large open set of mass ratios are those for which the linearized dynamics at each Euler rest point has a complex eigenvalue.

Connection forces in deformable multibody dynamics

NASA Technical Reports Server (NTRS)

Shabana, A. A.; Chang, C. W.

1989-01-01

In the dynamic formulation of holonomic and nonholonomic systems based on D'Alembert-Lagrange equation, the forces of constraints are maintained in the dynamic equations by introducing auxiliary variables, called Lagrange multipliers. This approach introduces a set of generalized reaction forces associated with the system generalized coordinates. Different sets of variables can be used as generalized coordinates and accordingly, the generalized reactions associated with these generalized coordinates may not be the actual reaction forces at the joints. In rigid body dynamics, the generalized reaction forces and the actual reaction forces at the joints represent equipollent systems of forces since they produce the same total forces and moments at and about any point on the rigid body. This is not, however, the case in deformable body analyses wherein the generalized reaction forces depend on the system generalized reference and elastic coordinates. In this paper, a method for determining the actual reaction forces at the joints from the generalized reaction forces in deformable multibody systems is presented.

The Portrayal of the Medicean Moons in Early Astronomical Charts and Books

NASA Astrophysics Data System (ADS)

Mendillo, Michael

2014-06-01

Galileo’s talents in perspective and chiaroscuro drawing led to his images of the Moon being accepted as the portrayal of a truly natural physical place. The Moon was seen as a world—real but separate from Earth. In contrast to his resolved views of the Moon, Galileo saw the moons of Jupiter as only points of light, and thus in Sidereus Nuncius they appear as star-symbols. Within 50 years, in Cellarius’ Atlas Coelestis seu Harmonia Macrocosmica (1660), the Medicean moons continue to appear in multiple charts as star-shaped symbols—in most cases equidistant from Jupiter. They appear in the Cellarius charts as updates to the cosmological systems of Copernicus and Tycho Brahe, but not in the charts devoted to the Ptolemaic system. A quarter century later, Mallet did not include the moons of Jupiter in his Copernican chart in Description de l’Universe (1683). Around 1690, in Jaillot’s Four Systems of Cosmology, the Medicean moons appear as circular symbols in four distinct concentric orbits around Jupiter. Additional examples appear in a later edition of Mallet ((1690s), and in De Fer (1705), Dopplemayer (1720), and still later in Buy de Mornas (1761). As objects discussed in scientific book, symbolic representations of the Medicean moons appear in Marius (1614), Descartes (1644), Fontana (1646) and Hevelius (1647). A pictorial survey of antiquarian charts and books depicting the Medicean moons will be the focus of this presentation. As telescope sizes increased, the Galilean moons could be seen as extended objects, and thus the transition occurred from portraying the moons as points of light to disks with physically-meaningful details. Initially, these were done via drawings of glimpses of the disks of the four moons during moments of extremely good seeing (termed “lucky images” in the pre-adaptive optics period). This era of portraying surface characteristics of Io, Europa, Ganymede and Callisto by hand-drawn images from naked-eye observations ended in the 1970s when spaceflight missions to the outer planets returned photographic images.

The Sun-Earth saddle point: characterization and opportunities to test general relativity

NASA Astrophysics Data System (ADS)

Topputo, Francesco; Dei Tos, Diogene A.; Rasotto, Mirco; Nakamiya, Masaki

2018-04-01

The saddle points are locations where the net gravitational accelerations balance. These regions are gathering more attention within the astrophysics community. Regions about the saddle points present clean, close-to-zero background acceleration environments where possible deviations from General Relativity can be tested and quantified. Their location suggests that flying through a saddle point can be accomplished by leveraging highly nonlinear orbits. In this paper, the geometrical and dynamical properties of the Sun-Earth saddle point are characterized. A systematic approach is devised to find ballistic orbits that experience one or multiple passages through this point. A parametric analysis is performed to consider spacecraft initially on L_{1,2} Lagrange point orbits. Sun-Earth saddle point ballistic fly-through trajectories are evaluated and classified for potential use. Results indicate an abundance of short-duration, regular solutions with a variety of characteristics.

Sul moto del baricentro del sistema Terra-Luna intorno al Sole in assenza di perturbazioni planetarie

NASA Astrophysics Data System (ADS)

Sambo, Alberto

2003-09-01

The Sun, the Earth and the Moon are considered from the point of view of a dynamical problem of three point masses. In this setting, we are interested in investigating the motion of the barycentre C of the Earth/Moon system with respect to the Sun. The differential equation of the motion considered is obtained in vectorial form from the first principles. Its investigation allows to conclude that the motion of the barycentre C of the Earth/Moon system around the Sun is not keplerian, even in absence of planetary perturbations. The equation is derived without specific assumptions, and can thus be applied to any other "three body" system.

An Exploration Of Fuel Optimal Two-impulse Transfers To Cyclers in the Earth-Moon System

NASA Astrophysics Data System (ADS)

Hosseinisianaki, Saghar

2011-12-01

This research explores the optimum two-impulse transfers between a low Earth orbit and cycler orbits in the Earth-Moon circular restricted three-body framework, emphasizing the optimization strategy. Cyclers are those types of periodic orbits that meet both the Earth and the Moon periodically. A spacecraft on such trajectories are under the influence of both the Earth and the Moon gravitational fields. Cyclers have gained recent interest as baseline orbits for several Earth-Moon mission concepts, notably in relation to human exploration. In this thesis it is shown that a direct optimization starting from the classic lambert initial guess may not be adequate for these problems and propose a three-step optimization solver to improve the domain of convergence toward an optimal solution. The first step consists of finding feasible trajectories with a given transfer time. I employ Lambert's problem to provide initial guess to optimize the error in arrival position. This includes the analysis of the liability of Lambert's solution as an initial guess. Once a feasible trajectory is found, the velocity impulse is only a function of transfer time, departure, and arrival points' phases. The second step consists of the optimization of impulse over transfer time which results in the minimum impulse transfer for fixed end points. Finally, the third step is mapping the optimal solutions as the end points are varied.

An Exploration Of Fuel Optimal Two-impulse Transfers To Cyclers in the Earth-Moon System

NASA Astrophysics Data System (ADS)

Hosseinisianaki, Saghar

This research explores the optimum two-impulse transfers between a low Earth orbit and cycler orbits in the Earth-Moon circular restricted three-body framework, emphasizing the optimization strategy. Cyclers are those types of periodic orbits that meet both the Earth and the Moon periodically. A spacecraft on such trajectories are under the influence of both the Earth and the Moon gravitational fields. Cyclers have gained recent interest as baseline orbits for several Earth-Moon mission concepts, notably in relation to human exploration. In this thesis it is shown that a direct optimization starting from the classic lambert initial guess may not be adequate for these problems and propose a three-step optimization solver to improve the domain of convergence toward an optimal solution. The first step consists of finding feasible trajectories with a given transfer time. I employ Lambert's problem to provide initial guess to optimize the error in arrival position. This includes the analysis of the liability of Lambert's solution as an initial guess. Once a feasible trajectory is found, the velocity impulse is only a function of transfer time, departure, and arrival points' phases. The second step consists of the optimization of impulse over transfer time which results in the minimum impulse transfer for fixed end points. Finally, the third step is mapping the optimal solutions as the end points are varied.

Analysis of Roll Steering for Solar Electric Propulsion Missions

NASA Technical Reports Server (NTRS)

Pederson, Dylan, M.; Hojnicki, Jeffrey, S.

2012-01-01

Nothing is more vital to a spacecraft than power. Solar Electric Propulsion (SEP) uses that power to provide a safe, reliable, and, most importantly, fuel efficient means to propel a spacecraft to its destination. The power performance of an SEP vehicle s solar arrays and electrical power system (EPS) is largely influenced by the environment in which the spacecraft is operating. One of the most important factors that determines solar array power performance is how directly the arrays are pointed to the sun. To get the most power from the solar arrays, the obvious solution is to point them directly at the sun at all times. Doing so is not a problem in deep space, as the environment and pointing conditions that a spacecraft faces are fairly constant and are easy to accommodate, if necessary. However, large and sometimes rapid variations in environmental and pointing conditions are experienced by Earth orbiting spacecraft. SEP spacecraft also have the additional constraint of needing to keep the thrust vector aligned with the velocity vector. Thus, it is important to analyze solar array power performance for any vehicle that spends an extended amount of time orbiting the Earth, and to determine how much off-pointing can be tolerated to produce the required power for a given spacecraft. This paper documents the benefits and drawbacks of perfectly pointing the solar arrays of an SEP spacecraft spiraling from Earth orbit, and how this might be accomplished. Benefits and drawbacks are defined in terms of vehicle mass, power, volume, complexity, and cost. This paper will also look at the application of various solar array pointing methods to future missions. One such pointing method of interest is called roll steering . Roll steering involves rolling the entire vehicle twice each orbit. Roll steering, combined with solar array gimbal tracking, is used to point the solar arrays perfectly towards the sun at all points in the orbit, while keeping the vehicle thrusters aligned in the velocity direction. Roll steering is particularly attractive for a recently proposed mission that involves a spiral trajectory from low Earth orbit (LEO) to the Earth-Moon Lagrange Point 1 (E-M L1). During the spiral, the spacecraft will spend over 300 days experiencing the full spectrum of near-earth environments and solar array pointing conditions. An extensive study of the application of SEP (and roll steering) to this spiral mission is included, highlighting the ultimate goal of reduced vehicle cost and mass. Tools used for this analysis include the Systems Power Analysis for Capability Evaluation (Refs. 1 and 2) (SPACE) electrical power systems code, and SEP trajectory simulation tools developed at NASA Glenn Research Center.

Gallium isotopic evidence for extensive volatile loss from the Moon during its formation

PubMed Central

Kato, Chizu; Moynier, Frédéric

2017-01-01

The distribution and isotopic composition of volatile elements in planetary materials holds a key to the characterization of the early solar system and the Moon’s formation. The Moon and Earth are chemically and isotopically very similar. However, the Moon is highly depleted in volatile elements and the origin of this depletion is still debated. We present gallium isotopic and elemental measurements in a large set of lunar samples to constrain the origin of this volatile depletion. We show that while Ga has a geochemical behavior different from zinc, both elements show a systematic enrichment in the heavier isotopes in lunar mare basalts and Mg-suite rocks compared to the silicate Earth, pointing to a global-scale depletion event. On the other hand, the ferroan anorthosites are isotopically heterogeneous, suggesting a secondary distribution of Ga at the surface of the Moon by volatilization and condensation. The isotopic difference of Ga between Earth and the Moon and the isotopic heterogeneity of the crustal ferroan anorthosites suggest that the volatile depletion occurred following the giant impact and during the lunar magma ocean phase. These results point toward a Moon that has lost its volatile elements during a whole-scale evaporation event and that is now relatively dry compared to Earth. PMID:28782027

Observation in the MINOS far detector of the shadowing of cosmic rays by the sun and moon

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jaffe, D.E.; Bishai, M.; Diwan, M.V.

2010-10-10

The shadowing of cosmic ray primaries by the moon and sun was observed by the MINOS far detector at a depth of 2070 mwe using 83.54 million cosmic ray muons accumulated over 1857.91 live-days. The shadow of the moon was detected at the 5.6 {sigma} level and the shadow of the sun at the 3.8 {sigma} level using a log-likelihood search in celestial coordinates. The moon shadow was used to quantify the absolute astrophysical pointing of the detector to be 0.17 {+-} 0.12{sup o}. Hints of interplanetary magnetic field effects were observed in both the sun and moon shadow.

Observation in the MINOS far detector of the shadowing of cosmic rays by the sun and moon

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adamson, P.; /Fermilab; Andreopoulos, C.

2010-08-01

The shadowing of cosmic ray primaries by the the moon and sun was observed by the MINOS far detector at a depth of 2070 mwe using 83.54 million cosmic ray muons accumulated over 1857.91 live-days. The shadow of the moon was detected at the 5.6 {sigma} level and the shadow of the sun at the 3.8 {sigma} level using a log-likelihood search in celestial coordinates. The moon shadow was used to quantify the absolute astrophysical pointing of the detector to be 0.17 {+-} 0.12{sup o}. Hints of Interplanetary Magnetic Field effects were observed in both the sun and moon shadow.

Calibration View of Earth and the Moon by Mars Color Imager

NASA Image and Video Library

2005-08-22

Three days after the Mars Reconnaissance Orbiter Aug. 12, 2005, launch, the spacecraft was pointed toward Earth and the Mars Color Imager camera was powered up to acquire a suite of images of Earth and the Moon.

First Quarter

NASA Image and Video Library

2017-12-08

First quarter. Visible high in the southern sky in early evening. This marks the first time that accurate shadows at this level of detail are possible in such a computer simulation. The shadows are based on the global elevation map being developed from measurements by the Lunar Orbiter Laser Altimeter (LOLA) aboard the Lunar Reconnaissance Orbiter (LRO). LOLA has already taken more than 10 times as many elevation measurements as all previous missions combined. The Moon always keeps the same face to us, but not exactly the same face. Because of the tilt and shape of its orbit, we see the Moon from slightly different angles over the course of a month. When a month is compressed into 12 seconds, as it is in this animation, our changing view of the Moon makes it look like it's wobbling. This wobble is called libration. The word comes from the Latin for "balance scale" (as does the name of the zodiac constellation Libra) and refers to the way such a scale tips up and down on alternating sides. The sub-Earth point gives the amount of libration in longitude and latitude. The sub-Earth point is also the apparent center of the Moon's disk and the location on the Moon where the Earth is directly overhead. The Moon is subject to other motions as well. It appears to roll back and forth around the sub-Earth point. The roll angle is given by the position angle of the axis, which is the angle of the Moon's north pole relative to celestial north. The Moon also approaches and recedes from us, appearing to grow and shrink. The two extremes, called perigee (near) and apogee (far), differ by more than 10%. The most noticed monthly variation in the Moon's appearance is the cycle of phases, caused by the changing angle of the Sun as the Moon orbits the Earth. The cycle begins with the waxing (growing) crescent Moon visible in the west just after sunset. By first quarter, the Moon is high in the sky at sunset and sets around midnight. The full Moon rises at sunset and is high in the sky at midnight. The third quarter Moon is often surprisingly conspicuous in the daylit western sky long after sunrise. Celestial north is up in these images, corresponding to the view from the northern hemisphere. The descriptions of the print resolution stills also assume a northern hemisphere orientation. To adjust for southern hemisphere views, rotate the images 180 degrees, and substitute "north" for "south" in the descriptions. Credit: NASA/Goddard Space Flight Center Scientific Visualization Studio NASA Goddard Space Flight Center enables NASA’s mission through four scientific endeavors: Earth Science, Heliophysics, Solar System Exploration, and Astrophysics. Goddard plays a leading role in NASA’s accomplishments by contributing compelling scientific knowledge to advance the Agency’s mission. Follow us on Twitter Join us on Facebook Find us on Instagram

Waxing Gibbous

NASA Image and Video Library

2017-12-08

Waxing gibbous. Visible to the southeast in early evening, up for most of the night. This marks the first time that accurate shadows at this level of detail are possible in such a computer simulation. The shadows are based on the global elevation map being developed from measurements by the Lunar Orbiter Laser Altimeter (LOLA) aboard the Lunar Reconnaissance Orbiter (LRO). LOLA has already taken more than 10 times as many elevation measurements as all previous missions combined. The Moon always keeps the same face to us, but not exactly the same face. Because of the tilt and shape of its orbit, we see the Moon from slightly different angles over the course of a month. When a month is compressed into 12 seconds, as it is in this animation, our changing view of the Moon makes it look like it's wobbling. This wobble is called libration. The word comes from the Latin for "balance scale" (as does the name of the zodiac constellation Libra) and refers to the way such a scale tips up and down on alternating sides. The sub-Earth point gives the amount of libration in longitude and latitude. The sub-Earth point is also the apparent center of the Moon's disk and the location on the Moon where the Earth is directly overhead. The Moon is subject to other motions as well. It appears to roll back and forth around the sub-Earth point. The roll angle is given by the position angle of the axis, which is the angle of the Moon's north pole relative to celestial north. The Moon also approaches and recedes from us, appearing to grow and shrink. The two extremes, called perigee (near) and apogee (far), differ by more than 10%. The most noticed monthly variation in the Moon's appearance is the cycle of phases, caused by the changing angle of the Sun as the Moon orbits the Earth. The cycle begins with the waxing (growing) crescent Moon visible in the west just after sunset. By first quarter, the Moon is high in the sky at sunset and sets around midnight. The full Moon rises at sunset and is high in the sky at midnight. The third quarter Moon is often surprisingly conspicuous in the daylit western sky long after sunrise. Celestial north is up in these images, corresponding to the view from the northern hemisphere. The descriptions of the print resolution stills also assume a northern hemisphere orientation. To adjust for southern hemisphere views, rotate the images 180 degrees, and substitute "north" for "south" in the descriptions. Credit: NASA/Goddard Space Flight Center Scientific Visualization Studio NASA Goddard Space Flight Center enables NASA’s mission through four scientific endeavors: Earth Science, Heliophysics, Solar System Exploration, and Astrophysics. Goddard plays a leading role in NASA’s accomplishments by contributing compelling scientific knowledge to advance the Agency’s mission. Follow us on Twitter Join us on Facebook Find us on Instagram

Waning Crescent

NASA Image and Video Library

2017-12-08

Waning crescent. Low to the east before sunrise. This marks the first time that accurate shadows at this level of detail are possible in such a computer simulation. The shadows are based on the global elevation map being developed from measurements by the Lunar Orbiter Laser Altimeter (LOLA) aboard the Lunar Reconnaissance Orbiter (LRO). LOLA has already taken more than 10 times as many elevation measurements as all previous missions combined. The Moon always keeps the same face to us, but not exactly the same face. Because of the tilt and shape of its orbit, we see the Moon from slightly different angles over the course of a month. When a month is compressed into 12 seconds, as it is in this animation, our changing view of the Moon makes it look like it's wobbling. This wobble is called libration. The word comes from the Latin for "balance scale" (as does the name of the zodiac constellation Libra) and refers to the way such a scale tips up and down on alternating sides. The sub-Earth point gives the amount of libration in longitude and latitude. The sub-Earth point is also the apparent center of the Moon's disk and the location on the Moon where the Earth is directly overhead. The Moon is subject to other motions as well. It appears to roll back and forth around the sub-Earth point. The roll angle is given by the position angle of the axis, which is the angle of the Moon's north pole relative to celestial north. The Moon also approaches and recedes from us, appearing to grow and shrink. The two extremes, called perigee (near) and apogee (far), differ by more than 10%. The most noticed monthly variation in the Moon's appearance is the cycle of phases, caused by the changing angle of the Sun as the Moon orbits the Earth. The cycle begins with the waxing (growing) crescent Moon visible in the west just after sunset. By first quarter, the Moon is high in the sky at sunset and sets around midnight. The full Moon rises at sunset and is high in the sky at midnight. The third quarter Moon is often surprisingly conspicuous in the daylit western sky long after sunrise. Celestial north is up in these images, corresponding to the view from the northern hemisphere. The descriptions of the print resolution stills also assume a northern hemisphere orientation. To adjust for southern hemisphere views, rotate the images 180 degrees, and substitute "north" for "south" in the descriptions. Credit: NASA/Goddard Space Flight Center Scientific Visualization Studio NASA Goddard Space Flight Center enables NASA’s mission through four scientific endeavors: Earth Science, Heliophysics, Solar System Exploration, and Astrophysics. Goddard plays a leading role in NASA’s accomplishments by contributing compelling scientific knowledge to advance the Agency’s mission. Follow us on Twitter Join us on Facebook Find us on Instagram

Waning Gibbous

NASA Image and Video Library

2011-06-15

Waning gibbous. Rises after sunset, high in the sky after midnight, visible to the southwest after sunrise. This marks the first time that accurate shadows at this level of detail are possible in such a computer simulation. The shadows are based on the global elevation map being developed from measurements by the Lunar Orbiter Laser Altimeter (LOLA) aboard the Lunar Reconnaissance Orbiter (LRO). LOLA has already taken more than 10 times as many elevation measurements as all previous missions combined. The Moon always keeps the same face to us, but not exactly the same face. Because of the tilt and shape of its orbit, we see the Moon from slightly different angles over the course of a month. When a month is compressed into 12 seconds, as it is in this animation, our changing view of the Moon makes it look like it's wobbling. This wobble is called libration. The word comes from the Latin for "balance scale" (as does the name of the zodiac constellation Libra) and refers to the way such a scale tips up and down on alternating sides. The sub-Earth point gives the amount of libration in longitude and latitude. The sub-Earth point is also the apparent center of the Moon's disk and the location on the Moon where the Earth is directly overhead. The Moon is subject to other motions as well. It appears to roll back and forth around the sub-Earth point. The roll angle is given by the position angle of the axis, which is the angle of the Moon's north pole relative to celestial north. The Moon also approaches and recedes from us, appearing to grow and shrink. The two extremes, called perigee (near) and apogee (far), differ by more than 10%. The most noticed monthly variation in the Moon's appearance is the cycle of phases, caused by the changing angle of the Sun as the Moon orbits the Earth. The cycle begins with the waxing (growing) crescent Moon visible in the west just after sunset. By first quarter, the Moon is high in the sky at sunset and sets around midnight. The full Moon rises at sunset and is high in the sky at midnight. The third quarter Moon is often surprisingly conspicuous in the daylit western sky long after sunrise. Celestial north is up in these images, corresponding to the view from the northern hemisphere. The descriptions of the print resolution stills also assume a northern hemisphere orientation. To adjust for southern hemisphere views, rotate the images 180 degrees, and substitute "north" for "south" in the descriptions. Credit: NASA/Goddard Space Flight Center Scientific Visualization Studio NASA Goddard Space Flight Center enables NASA’s mission through four scientific endeavors: Earth Science, Heliophysics, Solar System Exploration, and Astrophysics. Goddard plays a leading role in NASA’s accomplishments by contributing compelling scientific knowledge to advance the Agency’s mission. Follow us on Twitter Join us on Facebook Find us on Instagram

Third Quarter

NASA Image and Video Library

2017-12-08

Third quarter. Rises around midnight, visible to the south after sunrise. This marks the first time that accurate shadows at this level of detail are possible in such a computer simulation. The shadows are based on the global elevation map being developed from measurements by the Lunar Orbiter Laser Altimeter (LOLA) aboard the Lunar Reconnaissance Orbiter (LRO). LOLA has already taken more than 10 times as many elevation measurements as all previous missions combined. The Moon always keeps the same face to us, but not exactly the same face. Because of the tilt and shape of its orbit, we see the Moon from slightly different angles over the course of a month. When a month is compressed into 12 seconds, as it is in this animation, our changing view of the Moon makes it look like it's wobbling. This wobble is called libration. The word comes from the Latin for "balance scale" (as does the name of the zodiac constellation Libra) and refers to the way such a scale tips up and down on alternating sides. The sub-Earth point gives the amount of libration in longitude and latitude. The sub-Earth point is also the apparent center of the Moon's disk and the location on the Moon where the Earth is directly overhead. The Moon is subject to other motions as well. It appears to roll back and forth around the sub-Earth point. The roll angle is given by the position angle of the axis, which is the angle of the Moon's north pole relative to celestial north. The Moon also approaches and recedes from us, appearing to grow and shrink. The two extremes, called perigee (near) and apogee (far), differ by more than 10%. The most noticed monthly variation in the Moon's appearance is the cycle of phases, caused by the changing angle of the Sun as the Moon orbits the Earth. The cycle begins with the waxing (growing) crescent Moon visible in the west just after sunset. By first quarter, the Moon is high in the sky at sunset and sets around midnight. The full Moon rises at sunset and is high in the sky at midnight. The third quarter Moon is often surprisingly conspicuous in the daylit western sky long after sunrise. Celestial north is up in these images, corresponding to the view from the northern hemisphere. The descriptions of the print resolution stills also assume a northern hemisphere orientation. To adjust for southern hemisphere views, rotate the images 180 degrees, and substitute "north" for "south" in the descriptions. Credit: NASA/Goddard Space Flight Center Scientific Visualization Studio NASA Goddard Space Flight Center enables NASA’s mission through four scientific endeavors: Earth Science, Heliophysics, Solar System Exploration, and Astrophysics. Goddard plays a leading role in NASA’s accomplishments by contributing compelling scientific knowledge to advance the Agency’s mission. Follow us on Twitter Join us on Facebook Find us on Instagram

Waxing crescent

NASA Image and Video Library

2017-12-08

Waxing crescent. Visible toward the southwest in early evening. This marks the first time that accurate shadows at this level of detail are possible in such a computer simulation. The shadows are based on the global elevation map being developed from measurements by the Lunar Orbiter Laser Altimeter (LOLA) aboard the Lunar Reconnaissance Orbiter (LRO). LOLA has already taken more than 10 times as many elevation measurements as all previous missions combined. The Moon always keeps the same face to us, but not exactly the same face. Because of the tilt and shape of its orbit, we see the Moon from slightly different angles over the course of a month. When a month is compressed into 12 seconds, as it is in this animation, our changing view of the Moon makes it look like it's wobbling. This wobble is called libration. The word comes from the Latin for "balance scale" (as does the name of the zodiac constellation Libra) and refers to the way such a scale tips up and down on alternating sides. The sub-Earth point gives the amount of libration in longitude and latitude. The sub-Earth point is also the apparent center of the Moon's disk and the location on the Moon where the Earth is directly overhead. The Moon is subject to other motions as well. It appears to roll back and forth around the sub-Earth point. The roll angle is given by the position angle of the axis, which is the angle of the Moon's north pole relative to celestial north. The Moon also approaches and recedes from us, appearing to grow and shrink. The two extremes, called perigee (near) and apogee (far), differ by more than 10%. The most noticed monthly variation in the Moon's appearance is the cycle of phases, caused by the changing angle of the Sun as the Moon orbits the Earth. The cycle begins with the waxing (growing) crescent Moon visible in the west just after sunset. By first quarter, the Moon is high in the sky at sunset and sets around midnight. The full Moon rises at sunset and is high in the sky at midnight. The third quarter Moon is often surprisingly conspicuous in the daylit western sky long after sunrise. Celestial north is up in these images, corresponding to the view from the northern hemisphere. The descriptions of the print resolution stills also assume a northern hemisphere orientation. To adjust for southern hemisphere views, rotate the images 180 degrees, and substitute "north" for "south" in the descriptions. Credit: NASA/Goddard Space Flight Center Scientific Visualization Studio NASA Goddard Space Flight Center enables NASA’s mission through four scientific endeavors: Earth Science, Heliophysics, Solar System Exploration, and Astrophysics. Goddard plays a leading role in NASA’s accomplishments by contributing compelling scientific knowledge to advance the Agency’s mission. Follow us on Twitter Join us on Facebook Find us on Instagram

Integración automatizada de las ecuaciones de Lagrange en el movimiento orbital.

NASA Astrophysics Data System (ADS)

Abad, A.; San Juan, J. F.

The new techniques of algebraic manipulation, especially the Poisson Series Processor, permit the analytical integration of the more and more complex problems of celestial mechanics. The authors are developing a new Poisson Series Processor, PSPC, and they use it to solve the Lagrange equation of the orbital motion. They integrate the Lagrange equation by using the stroboscopic method, and apply it to the main problem of the artificial satellite theory.

Positional control of space robot manipulator

NASA Astrophysics Data System (ADS)

Kurochkin, Vladislav; Shymanchuk, Dzmitry

2018-05-01

In this article the mathematical model of a planar space robot manipulator is under study. The space robot manipulator represents a solid body with attached manipulators. The system of equations of motion is determined using the Lagrange's equations. The control problem concerning moving the robot to a given point and return it to a given trajectory in the phase space is solved. Changes of generalized coordinates and necessary control actions are plotted for a specific model.

Town Hall Meeting Presentation

NASA Technical Reports Server (NTRS)

Mather, John C.

2002-01-01

The James Webb Space Telescope (JWST), formerly known as the Next Generation Space Telescope (NGST), will be the successor to the Hubble Space Telescope. It will carry 3 instruments to a deep space orbit around the Sun-Earth Lagrange point L2, and will cover the wavelength range from 0.6 to 28 microns. The design concepts and current status of the project will be summarized, including the telescope and observatory contract proposed by the new prime contractor, TRW.

Libration Point Navigation Concepts Supporting Exploration Vision

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell; Folta, David C.; Moreau, Michael C.; Gramling, Cheryl J.

2004-01-01

Farquhar described several libration point navigation concepts that would appear to support NASA s current exploration vision. One concept is a Lunar Relay Satellite operating in the vicinity of Earth-Moon L2, providing Earth-to-lunar far-side and long- range surface-to-surface navigation and communications capability. Reference [ 1] lists several advantages of such a system in comparison to a lunar orbiting relay satellite constellation. Among these are one or two vs. many satellites for coverage, simplified acquisition and tracking due to very low relative motion, much longer contact times, and simpler antenna pointing. An obvious additional advantage of such a system is that uninterrupted links to Earth avoid performing critical maneuvers "in the blind." Another concept described is the use of Earth-Moon L1 for lunar orbit rendezvous, rather than low lunar orbit as was done for Apollo. This rendezvous technique would avoid large plane change and high fuel cost associated with high latitude landing sites and long stay times. Earth-Moon L1 also offers unconstrained launch windows from the lunar surface. Farquhar claims this technique requires only slightly higher fuel cost than low lunar orbit rendezvous for short-stay equatorial landings. Farquhar also describes an Interplanetary Transportation System that would use libration points as terminals for an interplanetary shuttle. This approach would offer increased operational flexibility in terms of launch windows, rendezvous, aborts, etc. in comparison to elliptical orbit transfers. More recently, other works including Folta[3] and Howell[4] have shown that patching together unstable trajectories departing Earth-Moon libration points with stable trajectories approaching planetary libration points may also offer lower overall fuel costs than elliptical orbit transfers. Another concept Farquhar described was a Deep Space Relay at Earth-Moon IA and/or L5 that would serve as a high data rate optical navigation and communications relay satellite. The advantages in comparison to a geosynchronous relay are minimal Earth occultation, distance from large noise sources on Earth, easier pointing due to smaller relative velocity, and a large baseline for interferometry if both L4 and L5 are used.

Stationkeeping of the First Earth-Moon Libration Orbiters: The ARTEMIS Mission

NASA Technical Reports Server (NTRS)

Folta, David; Woodard, Mark; Cosgrove, D.

2011-01-01

Libration point orbits near collinear locations are inherently unstable and must be controlled. For Acceleration Reconnection and Turbulence and Electrodynamics of the Moon's Interaction with the Sun (ARTEMIS) Earth-Moon Lissajous orbit operations, stationkeeping is challenging because of short time scales, large orbital eccentricity of the secondary, and solar gravitational and radiation pressure perturbations. ARTEMIS is the first NASA mission continuously controlled at both Earth-Moon L1 and L2 locations and uses a balance of optimization, spacecraft implementation and constraints, and multi-body dynamics. Stationkeeping results are compared to pre-mission research including mode directions.

A free boundary approach to the Rosensweig instability of ferrofluids

NASA Astrophysics Data System (ADS)

Parini, Enea; Stylianou, Athanasios

2018-04-01

We establish the existence of saddle points for a free boundary problem describing the two-dimensional free surface of a ferrofluid undergoing normal field instability. The starting point is the ferrohydrostatic equations for the magnetic potentials in the ferrofluid and air, and the function describing their interface. These constitute the strong form for the Euler-Lagrange equations of a convex-concave functional, which we extend to include interfaces that are not necessarily graphs of functions. Saddle points are then found by iterating the direct method of the calculus of variations and applying classical results of convex analysis. For the existence part, we assume a general nonlinear magnetization law; for a linear law, we also show, via convex duality, that the saddle point is a constrained minimizer of the relevant energy functional.

Low-Latency Lunar Surface Telerobotics from Earth-Moon Libration Points

NASA Technical Reports Server (NTRS)

Lester, Daniel; Thronson, Harley

2011-01-01

Concepts for a long-duration habitat at Earth-Moon LI or L2 have been advanced for a number of purposes. We propose here that such a facility could also have an important role for low-latency telerobotic control of lunar surface equipment, both for lunar science and development. With distances of about 60,000 km from the lunar surface, such sites offer light-time limited two-way control latencies of order 400 ms, making telerobotic control for those sites close to real time as perceived by a human operator. We point out that even for transcontinental teleoperated surgical procedures, which require operational precision and highly dexterous manipulation, control latencies of this order are considered adequate. Terrestrial telerobots that are used routinely for mining and manufacturing also involve control latencies of order several hundred milliseconds. For this reason, an Earth-Moon LI or L2 control node could build on the technology and experience base of commercially proven terrestrial ventures. A lunar libration-point telerobotic node could demonstrate exploration strategies that would eventually be used on Mars, and many other less hospitable destinations in the solar system. Libration-point telepresence for the Moon contrasts with lunar telerobotic control from the Earth, for which two-way control latencies are at least six times longer. For control latencies that long, telerobotic control efforts are of the "move-and-wait" variety, which is cognitively inferior to near real-time control.

1. EXTERIOR VIEW OF 209 WARE STREET LOOKING SOUTH. THIS ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

1. EXTERIOR VIEW OF 209 WARE STREET LOOKING SOUTH. THIS STRUCTURE WAS ONE OF APPROXIMATELY SEVENTEEN DUPLEXES BUILT AS THE ORIGINAL WORKER HOUSING FOR THE LaGRANGE COTTON MILLS, LATER KNOWN AS CALUMET MILL. LaGRANGE MILLS (1888-89) WAS THE FIRST COTTON MILL IN LaGRANGE. NOTE THE GABLE-ON-HIP ROOF FORM AND TWO IDENTICAL STRUCTURES VISIBLE TO THE LEFT. - 209 Ware Street (House), 209 Ware Street, La Grange, Troup County, GA

Accuracy of Lagrange-sinc functions as a basis set for electronic structure calculations of atoms and molecules

DOE Office of Scientific and Technical Information (OSTI.GOV)

Choi, Sunghwan; Hong, Kwangwoo; Kim, Jaewook

2015-03-07

We developed a self-consistent field program based on Kohn-Sham density functional theory using Lagrange-sinc functions as a basis set and examined its numerical accuracy for atoms and molecules through comparison with the results of Gaussian basis sets. The result of the Kohn-Sham inversion formula from the Lagrange-sinc basis set manifests that the pseudopotential method is essential for cost-effective calculations. The Lagrange-sinc basis set shows faster convergence of the kinetic and correlation energies of benzene as its size increases than the finite difference method does, though both share the same uniform grid. Using a scaling factor smaller than or equal tomore » 0.226 bohr and pseudopotentials with nonlinear core correction, its accuracy for the atomization energies of the G2-1 set is comparable to all-electron complete basis set limits (mean absolute deviation ≤1 kcal/mol). The same basis set also shows small mean absolute deviations in the ionization energies, electron affinities, and static polarizabilities of atoms in the G2-1 set. In particular, the Lagrange-sinc basis set shows high accuracy with rapid convergence in describing density or orbital changes by an external electric field. Moreover, the Lagrange-sinc basis set can readily improve its accuracy toward a complete basis set limit by simply decreasing the scaling factor regardless of systems.« less

The squint Moon and the witch ball

NASA Astrophysics Data System (ADS)

Berry, M. V.

2015-06-01

A witch ball is a reflecting sphere of glass. Looking into the disk that it subtends, the whole sky can be seen at one glance. This feature can be exploited to see and photograph the squint Moon illusion, in which the direction normal to the illuminated face of the Moon—its ‘attitude vector’—does not appear to point towards the Sun. The images of the Sun and Moon in the disk, the geodesic connecting them, the Moon’s attitude, and the squint angle (distinct from the tilt), can be calculated and simulated, for all celestial configurations and viewing inclinations. The Moon direction antipodal to the Sun, corresponding to full Moon, is a singularity of the attitude vector field, with index +1. The main features of the witch ball images also occur in other ways of imaging the squint Moon.

Variational Integrators for Interconnected Lagrange-Dirac Systems

NASA Astrophysics Data System (ADS)

Parks, Helen; Leok, Melvin

2017-10-01

Interconnected systems are an important class of mathematical models, as they allow for the construction of complex, hierarchical, multiphysics, and multiscale models by the interconnection of simpler subsystems. Lagrange-Dirac mechanical systems provide a broad category of mathematical models that are closed under interconnection, and in this paper, we develop a framework for the interconnection of discrete Lagrange-Dirac mechanical systems, with a view toward constructing geometric structure-preserving discretizations of interconnected systems. This work builds on previous work on the interconnection of continuous Lagrange-Dirac systems (Jacobs and Yoshimura in J Geom Mech 6(1):67-98, 2014) and discrete Dirac variational integrators (Leok and Ohsawa in Found Comput Math 11(5), 529-562, 2011). We test our results by simulating some of the continuous examples given in Jacobs and Yoshimura (2014).

A possible space VLBI constellation utilizing the stable orbits around the TLPs in the Earth-Moon system.

NASA Astrophysics Data System (ADS)

Liu, Bin; Tang, Jingshi; Hou, Xiyun

2016-07-01

Current studies indicate that there are stable orbits around but far away from the triangular libration points .Two special quasi-periodic orbits around each triangular libration points L4 , L5 in the Earth-Moon sys-tem perturbed by Sun are gain , and the stable orbits discussed in this work are ideal places for space colonies because no orbit control is needed. These stable orbits can also be used as nominal orbits for space VLBI (Very Long Baseline Interferometry) stations. The two stations can also form baselines with stations on the Earth and the Moon, or with stations located around another TLP. Due to the long distance between the stations, the observation precision can be greatly enhanced compared with the VLBI stations on the Earth. Such a VLBI constellation not only can advance the radio astronomy, but also can be used as a navigation system for human activities in the Earth-Moon system and even in the solar system. This paper will focus on the navigation constellation coverage issues, and the orbit determination accuracy problems within the Earth-Moon sys-tem and interplanetary space.

The extreme ultraviolet albedos of the planet Mercury and of the moon

NASA Technical Reports Server (NTRS)

Wu, H. H.; Broadfoot, A. L.

1977-01-01

The albedo of the moon in the far UV was measured by Mariner 10 at a solar phase angle of 74 deg, and the geometric albedo of Mercury was measured in same wavelength range (584-1657 A) at solar phase angles ranging from 50 to 120 deg. For both the moon and Mercury there is a general increase in albedo for wavelengths decreasing from 1657 to 584 A. The ratio of the albedos of Mercury and the moon increases from about 0.6 to 0.8 in the range 600-1600 A. This merely points to a difference in the surfaces of the moon and Mercury, there being insufficient data to make any conclusions regarding the nature of the difference.

The Tethered Moon

NASA Technical Reports Server (NTRS)

Zahnle, Kevin; Lupu, Roxana Elena; Dubrovolskis, A. R.

2014-01-01

A reasonable initial condition on Earth after the Moonforming impact is that it begins as a hot global magma ocean1,2. We therefore begin our study with the mantle as a liquid ocean with a surface temperature on the order of 3000- 4000 K at a time some 100-1000 years after the impact, by which point we can hope that early transients have settled down. A 2nd initial condition is a substantial atmosphere, 100-1000 bars of H2O and CO2, supplemented by smaller amounts of CO, H2, N2, various sulfur-containing gases, and a suite of geochemical volatiles evaporated from the magma. Third, we start the Moon with its current mass at the relevant Roche limit. The 4th initial condition is the angular momentum of the Earth-Moon system. Canonical models hold this constant, whilst some recent models begin with considerably more angular momentum than is present today. Here we present a ruthlessly simplified model of Earth's cooling magmasphere based on a full-featured atmosphere and including tidal heating by the newborn Moon. Thermal blanketing by H2O-CO2 atmospheres slows cooling of a magma ocean. Geochemical volatiles - chiefly S, Na, and Cl - raise the opacity of the magma ocean's atmosphere and slow cooling still more. We assume a uniform mantle with a single internal (potential) temperature and a global viscosity. The important "freezing point" is the sharp rheological transition between a fluid carrying suspended crystals and a solid matrix through which fluids percolate. Most tidal heating takes place at this "freezing point" in a gel that is both pliable and viscous. Parameterized convection links the cooling rate to the temperature and heat generation inside the Earth. Tidal heating is a major effect. Tidal dissipation in the magma ocean is described by viscosity. The Moon is entwined with Earth by the negative feedback between thermal blanketing and tidal heating that comes from the temperature-dependent viscosity of the magma ocean. Because of this feedback, the rate that the Moon's orbit evolves is limited by the modest radiative cooling rate of Earth's atmosphere, which in effect tethers the Moon to the Earth. Consequently the Moon's orbit evolves orders of magnitude more slowly than in conventional models. Slow orbital evolution promotes capture by orbital resonances that may have been important in the Earth-Moon system

1. STREETSCAPE VIEW OF 208 VINE STREET (FIRST HOUSE ON ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

1. STREETSCAPE VIEW OF 208 VINE STREET (FIRST HOUSE ON RIGHT) LOOKING WEST. THIS STRUCTURE WAS ONE OF APPROXIMATELY SEVENTEEN DUPLEXES BUILT AS THE ORIGINAL WORKER HOUSING FOR THE LaGRANGE COTTON MILLS, LATER KNOWN AS CALUMET MILL. LaGRANGE MILLS (1888-89) WAS THE FIRST COTTON MILL IN LaGRANGE. NOTE THE GABLE-ON-HIP ROOF FORM AND IDENTICAL STRUCTURES FACING EACH OTHER ALONG BOTH SIDES OF THE NARROW STREET. - 208 Vine Street (House), 208 Vine Street, La Grange, Troup County, GA

Solar sail trajectory design in the Earth-Moon circular restricted three body problem

NASA Astrophysics Data System (ADS)

Das, Ashwati

The quest to explore the Moon has helped resolve scientific questions, has spurred leaps in technology development, and has revealed Earth's celestial companion to be a gateway to other destinations. With a renewed focus on returning to the Moon in this decade, alternatives to chemical propulsion systems are becoming attractive methods to efficiently use scarce resources and support extended mission durations. Thus, an investigation is conducted to develop a general framework, that facilitates propellant-free Earth-Moon transfers by exploiting sail dynamics in combination with advantageous transfer options offered in the Earth-Moon circular restricted multi-body dynamical model. Both periodic orbits in the vicinity of the Earth-Moon libration points, and lunar-centric long-term capture orbits are incorporated as target destinations to demonstrate the applicability of the general framework to varied design scanarios, each incorporating a variety of complexities and challenges. The transfers are comprised of three phases - a spiral Earth escape, a transit period, and, finally, the capture into a desirable orbit in the vicinity of the Moon. The Earth-escape phase consists of spiral trajectories constructed using three different sail steering strategies - locally optimal, on/off and velocity tangent. In the case of the Earth-libration point transfers, naturally occurring flow structures (e.g., invariant manifolds) arising from the mutual gravitational interaction of the Earth and Moon are exploited to link an Earth departure spiral with a destination orbit. In contrast, sail steering alone is employed to establish a link between the Earth-escape phase and capture orbits about the Moon due to a lack of applicable natural structures for the required connection. Metrics associated with the transfers including flight-time and the influence of operational constraints, such as occultation events, are investigated to determine the available capabilities for Earth-Moon transfers given current sail technology levels. Although the implemented steering laws suffice to generate baseline paths, infeasible turn rate demands placed on the sail are also investigated to explore the technical hurdles in designing Earth-Moon transfers. The methodologies are suitable for a variety of mission scenarios and sail configurations, rendering the resulting trajectories valuable for a diverse range of applications.

Spacecraft Conceptual Design for the 8-Meter Advanced Technology Large Aperture Space Telescope (ATLAST)

NASA Technical Reports Server (NTRS)

Hopkins, Randall C.; Capizzo, Peter; Fincher, Sharon; Hornsby, Linda S.; Jones, David

2010-01-01

The Advanced Concepts Office at Marshall Space Flight Center completed a brief spacecraft design study for the 8-meter monolithic Advanced Technology Large Aperture Space Telescope (ATLAST-8m). This spacecraft concept provides all power, communication, telemetry, avionics, guidance and control, and thermal control for the observatory, and inserts the observatory into a halo orbit about the second Sun-Earth Lagrange point. The multidisciplinary design team created a simple spacecraft design that enables component and science instrument servicing, employs articulating solar panels for help with momentum management, and provides precise pointing control while at the same time fast slewing for the observatory.

LAGRANGE: LAser GRavitational-wave ANtenna in GEodetic Orbit

NASA Astrophysics Data System (ADS)

Buchman, S.; Conklin, J. W.; Balakrishnan, K.; Aguero, V.; Alfauwaz, A.; Aljadaan, A.; Almajed, M.; Altwaijry, H.; Saud, T. A.; Byer, R. L.; Bower, K.; Costello, B.; Cutler, G. D.; DeBra, D. B.; Faied, D. M.; Foster, C.; Genova, A. L.; Hanson, J.; Hooper, K.; Hultgren, E.; Klavins, A.; Lantz, B.; Lipa, J. A.; Palmer, A.; Plante, B.; Sanchez, H. S.; Saraf, S.; Schaechter, D.; Shu, K.; Smith, E.; Tenerelli, D.; Vanbezooijen, R.; Vasudevan, G.; Williams, S. D.; Worden, S. P.; Zhou, J.; Zoellner, A.

2013-01-01

We describe a new space gravitational wave observatory design called LAG-RANGE that maintains all important LISA science at about half the cost and with reduced technical risk. It consists of three drag-free spacecraft in a geocentric formation. Fixed antennas allow continuous contact with the Earth, solving the problem of communications bandwidth and latency. A 70 mm diameter sphere with a 35 mm gap to its enclosure serves as the single inertial reference per spacecraft, operating in “true” drag-free mode (no test mass forcing). Other advantages are: a simple caging design based on the DISCOS 1972 drag-free mission, an all optical read-out with pm fine and nm coarse sensors, and the extensive technology heritage from the Honeywell gyroscopes, and the DISCOS and Gravity Probe B drag-free sensors. An Interferometric Measurement System, designed with reflective optics and a highly stabilized frequency standard, performs the ranging between test masses and requires a single optical bench with one laser per spacecraft. Two 20 cm diameter telescopes per spacecraft, each with infield pointing, incorporate novel technology developed for advanced optical systems by Lockheed Martin, who also designed the spacecraft based on a multi-flight proven bus structure. Additional technological advancements include updated drag-free propulsion, thermal control, charge management systems, and materials. LAGRANGE subsystems are designed to be scalable and modular, making them interchangeable with those of LISA or other gravitational science missions. We plan to space qualify critical technologies on small and nano satellite flights, with the first launch (UV-LED Sat) in 2013.

Americas from the Moon

NASA Image and Video Library

2010-09-15

The western hemisphere of our home planet Earth. North (upper left), Central, and South America (lower right) were nicely free of clouds when LRO pointed home on 9 August 2010 to acquire this beautiful view. LROC NAC E136013771. As LRO orbits the Moon every two hours sending down a stream of science data, it is easy to forget how close the Moon is to the Earth. The average distance between the two heavenly bodies is just 384,399 km (238,854 miles). Check your airline frequent flyer totals, perhaps you have already flown the distance to the Moon and back on a single airline. http://photojournal.jpl.nasa.gov/catalog/PIA13519

Space Transportation Infrastructure Supported By Propellant Depots

NASA Technical Reports Server (NTRS)

Smitherman, David; Woodcock, Gordon

2011-01-01

A space transportation infrastructure is described that utilizes propellant depots to support all foreseeable missions in the Earth-Moon vicinity and deep space out to Mars. The infrastructure utilizes current expendable launch vehicles such as the Delta IV Heavy, Atlas V, and Falcon 9, for all crew, cargo, and propellant launches to orbit. Propellant launches are made to a Low-Earth-Orbit (LEO) Depot and an Earth-Moon Lagrange Point 1 (L1) Depot to support new reusable in-space transportation vehicles. The LEO Depot supports missions to Geosynchronous Earth Orbit (GEO) for satellite servicing, and to L1 for L1 Depot missions. The L1 Depot supports Lunar, Earth-Sun L2 (ESL2), Asteroid, and Mars missions. A Mars Orbital Depot is also described to support ongoing Mars missions. New concepts for vehicle designs are presented that can be launched on current 5-meter diameter expendable launch vehicles. These new reusable vehicle concepts include a LEO Depot, L1 Depot, and Mars Orbital Depot based on International Space Station (ISS) heritage hardware. The high-energy depots at L1 and Mars orbit are compatible with, but do not require, electric propulsion tug use for propellant and/or cargo delivery. New reusable in-space crew transportation vehicles include a Crew Transfer Vehicle (CTV) for crew transportation between the LEO Depot and the L1 Depot, a new reusable Lunar Lander for crew transportation between the L1 Depot and the lunar surface, and a Deep Space Habitat (DSH) to support crew missions from the L1 Depot to ESL2, Asteroid, and Mars destinations. A 6 meter diameter Mars lander concept is presented that can be launched without a fairing based on the Delta IV heavy Payload Planners Guide, which indicates feasibility of a 6.5 meter fairing. This lander would evolve to re-usable operations when propellant production is established on Mars. Figure 1 provides a summary of the possible missions this infrastructure can support. Summary mission profiles are presented for each primary mission capability. These profiles are the basis for propellant loads, numbers of vehicles/stages and launches for each mission capability. Data includes the number of launches required for each mission utilizing current expendable launch vehicle systems, and concluding remarks include ideas for reducing the number of launches through incorporation of heavy-lift launch vehicles, solar electric propulsion, and other transportation support concepts.

Advanced Aero-Propulsive Mid-Lift-to-Drag Ratio Entry Vehicle for Future Exploration Missions

NASA Technical Reports Server (NTRS)

Campbell, C. H.; Stosaric, R. R; Cerimele, C. J.; Wong, K. A.; Valle, G. D.; Garcia, J. A.; Melton, J. E.; Munk, M. M.; Blades, E.; Kuruvila, G.;

Moon illusion simulated in complete darkness: planetarium experiment reexamined.

PubMed

Suzuki, K

1991-04-01

In 1962, Kaufman and Rock reported that the moon illusion did not occur in the darkness of a planetarium or in a completely dark room. The present study reexamined their findings. Two pairs of light points, separated by 3.5 degrees, were presented on the dome screen of a planetarium. Subjects compared the distance between the two light points presented in the horizontal direction with the distance between the two light points at the zenith. Three illumination conditions were used: The inside of the planetarium was completely dark, was lighted, or was projected with the silhouette of a city under a starry sky. The effect of eye elevation on the illusion was also examined. Contrary to Kaufman and Rock's results, a size discrepancy comparable to the moon illusion was obtained in the horizon-and-stars condition and even in the complete-darkness condition. Little or no illusion was obtained in the lighted-room condition. The results also showed that eye elevation affected the magnitude of the illusion.

Far Side of the Moon

NASA Image and Video Library

1996-02-08

This image of the moon was obtained by the Galileo Solid State imaging system on Dec. 8 at 7 p.m. PST as NASA Galileo spacecraft passed the Earth and was able to view the lunar surface from a vantage point not possible from the Earth. http://photojournal.jpl.nasa.gov/catalog/PIA00225

On the angle and wavelength dependencies of the radar backscatter from the icy Galilean moons of Jupiter

NASA Technical Reports Server (NTRS)

Gurrola, Eric M.; Eshleman, Von R.

1990-01-01

This paper reports new developments in the buried crater model that has proved successful in explaining the anomalous strengths and polarizations of the radar echoes from the icy Galilean moons of Jupiter (Europa, Ganymede, and Callisto). The theory is extended to make predictions of the radar cross sections at all points on the surface of the moon, to compute the shape and strength of the power spectra, and to model a wavelength dependence that has been observed.

Advanced propulsion for LEO-Moon transport. 3: Transportation model. M.S. Thesis - California Univ.

NASA Technical Reports Server (NTRS)

Henley, Mark W.

1992-01-01

A simplified computational model of low Earth orbit-Moon transportation system has been developed to provide insight into the benefits of new transportation technologies. A reference transportation infrastructure, based upon near-term technology developments, is used as a departure point for assessing other, more advanced alternatives. Comparison of the benefits of technology application, measured in terms of a mass payback ratio, suggests that several of the advanced technology alternatives could substantially improve the efficiency of low Earth orbit-Moon transportation.

The Numerical Simulation of the Shock Wave of Coal Gas Explosions in Gas Pipe*

NASA Astrophysics Data System (ADS)

Chen, Zhenxing; Hou, Kepeng; Chen, Longwei

2018-03-01

For the problem of large deformation and vortex, the method of Euler and Lagrange has both advantage and disadvantage. In this paper we adopt special fuzzy interface method(volume of fluid). Gas satisfies the conditions of conservation equations of mass, momentum, and energy. Based on explosion and three-dimension fluid dynamics theory, using unsteady, compressible, inviscid hydrodynamic equations and state equations, this paper considers pressure gradient’s effects to velocity, mass and energy in Lagrange steps by the finite difference method. To minimize transport errors of material, energy and volume in Finite Difference mesh, it also considers material transport in Euler steps. Programmed with Fortran PowerStation 4.0 and visualized with the software designed independently, we design the numerical simulation of gas explosion with specific pipeline structure, check the key points of the pressure change in the flow field, reproduce the gas explosion in pipeline of shock wave propagation, from the initial development, flame and accelerate the process of shock wave. This offers beneficial reference and experience to coal gas explosion accidents or safety precautions.

Calibration of the DSCOVR EPIC Visible and NIR Channels using MODIS Terra and Aqua Data and EPIC Lunar Observations

NASA Technical Reports Server (NTRS)

Geogdzhayev, Igor V.; Marshak, Alexander

2018-01-01

The unique position of the Deep Space Climate Observatory (DSCOVR) Earth Polychromatic Imaging Camera (EPIC) at the Lagrange 1 point makes an important addition to the data from currently operating low Earth orbit observing instruments. EPIC instrument does not have an onboard calibration facility. One approach to its calibration is to compare EPIC observations to the measurements from polar-orbiting radiometers. Moderate Resolution Imaging Spectroradiometer (MODIS) is a natural choice for such comparison due to its well-established calibration record and wide use in remote sensing. We use MODIS Aqua and Terra L1B 1km reflectances to infer calibration coefficients for four EPIC visible and NIR channels: 443, 551, 680 and 780 nm. MODIS and EPIC measurements made between June 2015 and 2016 are employed for comparison. We first identify favorable MODIS pixels with scattering angle matching temporarily collocated EPIC observations. Each EPIC pixel is then spatially collocated to a subset of the favorable MODIS pixels within 25 km radius. Standard deviation of the selected MODIS pixels as well as of the adjacent EPIC pixels is used to find the most homogeneous scenes. These scenes are then used to determine calibration coefficients using a linear regression between EPIC counts/sec and reflectances in the close MODIS spectral channels. We present thus inferred EPIC calibration coefficients and discuss sources of uncertainties. The lunar EPIC observations are used to calibrate EPIC O2 absorbing channels (688 and 764 nm), assuming that there is a small difference between moon reflectances separated by approx.10 nm in wavelength provided the calibration factors of the red (680 nm) and near-IR (780 nm) are known from comparison between EPIC and MODIS.

Planetary Defense From Space: Part 1-Keplerian Theory

NASA Astrophysics Data System (ADS)

Maccone, Claudio

A system of two space bases housing missiles is proposed to achieve the Planetary Defense of the Earth against dangerous asteroids and comets. We show that the layout of the Earth-Moon system with the five relevant Lagrangian (or libration) points in space leads naturally to only one, unmistakable location of these two space bases within the sphere of influence of the Earth. These locations are at the two Lagrangian points L1 (in between the Earth and the Moon) and L3 (in the direction opposite to the Moon from the Earth). We show that placing bases of missiles at L1 and L3 would cause those missiles to deflect the trajectory of asteroids by hitting them orthogonally to their impact trajectory toward the Earth, so as to maximize their deflection. We show that the confocal conics are the best class of trajectories fulfilling this orthogonal deflection requirement. An additional remark is that the theory developed in this paper is just a beginning of a larger set of future research work. In fact, while in this paper we only develop the Keplerian analytical theory of the Optimal Planetary Defense achievable from the Earth-Moon Lagrangian points L1 and L3, much more sophisticated analytical refinements would be needed to: Take into account many perturbation forces of all kinds acting on both the asteroids and missiles shot from L1 and L3; add more (non-optimal) trajectories of missiles shot from either the Lagrangian points L4 and L5 of the Earth-Moon system or from the surface of the Moon itself; encompass the full range of missiles currently available to the US (and possibly other countries) so as to really see "which asteroids could be diverted by which missiles", even in the very simplified scheme outlined here. Outlined for the first time in February 2002, our Confocal Planetary Defense concept is a Keplerian Theory that proved simple enough to catch the attention of scholars, representatives of the US Military and popular writers. These developments could possibly mark the beginning of an "all embracing" mathematical vision of Planetary Defense beyond all learned activities, dramatic movies and unknown military plans covered by secret.

Low-energy transfers to cislunar periodic orbits visiting triangular libration points

NASA Astrophysics Data System (ADS)

Lei, Hanlun; Xu, Bo

2018-01-01

This paper investigates the cislunar periodic orbits that pass through triangular libration points of the Earth-Moon system and studies the techniques on design low-energy transfer trajectories. In order to compute periodic orbits, families of impulsive transfers between triangular libration points are taken to generate the initial guesses of periodic orbits, and multiple shooting techniques are applied to solving the problem. Then, varieties of periodic orbits in cislunar space are obtained, and stability analysis shows that the majority of them are unstable. Among these periodic orbits, an unstable periodic orbit in near 3:2 resonance with the Moon is taken as the nominal orbit of an assumed mission. As the stable manifolds of the target orbit could approach the Moon, low-energy transfer trajectories can be designed by combining lunar gravity assist with the invariant manifold structure of the target orbit. In practice, both the natural and perturbed invariant manifolds are considered to obtain the low-energy transfers, which are further refined to the Sun-perturbed Earth-Moon system. Results indicate that (a) compared to the case of natural invariant manifolds, the optimal transfers using perturbed invariant manifolds could reduce flight time at least 50 days, (b) compared to the cheapest direct transfer, the optimal low-energy transfer obtained by combining lunar gravity assist and invariant manifolds could save on-board fuel consumption more than 200 m/s, and (c) by taking advantage of the gravitational perturbation of the Sun, the low-energy transfers could save more fuel consumption than the corresponding ones obtained in the Earth-Moon system.

Scale-Limited Lagrange Stability and Finite-Time Synchronization for Memristive Recurrent Neural Networks on Time Scales.

PubMed

Xiao, Qiang; Zeng, Zhigang

2017-10-01

The existed results of Lagrange stability and finite-time synchronization for memristive recurrent neural networks (MRNNs) are scale-free on time evolvement, and some restrictions appear naturally. In this paper, two novel scale-limited comparison principles are established by means of inequality techniques and induction principle on time scales. Then the results concerning Lagrange stability and global finite-time synchronization of MRNNs on time scales are obtained. Scaled-limited Lagrange stability criteria are derived, in detail, via nonsmooth analysis and theory of time scales. Moreover, novel criteria for achieving the global finite-time synchronization are acquired. In addition, the derived method can also be used to study global finite-time stabilization. The proposed results extend or improve the existed ones in the literatures. Two numerical examples are chosen to show the effectiveness of the obtained results.

Analytical Dynamics and Nonrigid Spacecraft Simulation

NASA Technical Reports Server (NTRS)

Likins, P. W.

1974-01-01

Application to the simulation of idealized spacecraft are considered both for multiple-rigid-body models and for models consisting of combination of rigid bodies and elastic bodies, with the elastic bodies being defined either as continua, as finite-element systems, or as a collection of given modal data. Several specific examples are developed in detail by alternative methods of analytical mechanics, and results are compared to a Newton-Euler formulation. The following methods are developed from d'Alembert's principle in vector form: (1) Lagrange's form of d'Alembert's principle for independent generalized coordinates; (2) Lagrange's form of d'Alembert's principle for simply constrained systems; (3) Kane's quasi-coordinate formulation of D'Alembert's principle; (4) Lagrange's equations for independent generalized coordinates; (5) Lagrange's equations for simply constrained systems; (6) Lagrangian quasi-coordinate equations (or the Boltzmann-Hamel equations); (7) Hamilton's equations for simply constrained systems; and (8) Hamilton's equations for independent generalized coordinates.

Impacts of Sigma Coordinates on the Euler and Navier-Stokes Equations using Continuous Galerkin Methods

DTIC Science & Technology

2009-03-01

the 1- D local basis functions. The 1-D Lagrange polynomial local basis function, using Legendre -Gauss-Lobatto interpolation points, was defined by...cases were run using 10th order polynomials , with contours from -0.05 to 0.525 K with an interval of 0.025 K...after 700 s for reso- lutions: (a) 20, (b) 10, and (c) 5 m. All cases were run using 10th order polynomials , with contours from -0.05 to 0.525 K

Advances in Highly Constrained Multi-Phase Trajectory Generation using the General Pseudospectral Optimization Software (GPOPS)

DTIC Science & Technology

2013-08-01

release; distribution unlimited. PA Number 412-TW-PA-13395 f generic function g acceleration due to gravity h altitude L aerodynamic lift force L Lagrange...cost m vehicle mass M Mach number n number of coefficients in polynomial regression p highest order of polynomial regression Q dynamic pressure R...Method (RPM); the collocation points are defined by the roots of Legendre -Gauss- Radau (LGR) functions.9 GPOPS also automatically refines the “mesh” by

The moon-Earth system...As a vacuum gravity energy machine? A Hint about the Nature of Universal Gravity that May Have Been Overlooked

NASA Astrophysics Data System (ADS)

Masters, Roy

2011-10-01

We revisit the theories describing the moon raising the tides by virtue of pull gravity combined with the moon's centripetal angular momentum. We show that if gravity is considered as the attractive interaction between individual bodies, then a laboring moon doing work would have fallen to earth eons ago. Isaac Newton's laws of motion cannot work with pull gravity, but they do with Einstein's gravity as a property of the universe, which produces a continuous infusion of energy. In other words, the moon-Earth system becomes the first observable vacuum gravity energy machine. In other words the dynamics of what appears to be a closed system has been producing energy that continues raising the tides into perpetuity along with the force needed for the moon to escape the Earth's gravitational pull 4cm per year. All this is in defiance of Newton's first law which says ``If no force is added to a body it cannot accelerate.'' In this theory, a flowing space-time curves with three dimensions of force. A (flowing) spatial fabric bends around mass and displaces the inverse square field vanishing point property of matter with the appearance of a push-force square of the distance. In other words, the immeasurable universal gravity field appears as measurable local gravitation, concentrating universal gravitational pressure with the square of the distance from the very point was supposed to have disappeared. Needless to say such ``gravity'' necessitates a different beginning.

Dynamics of tethered satellites in the vicinity of the Lagrangian point L2 of the Earth-Moon system

NASA Astrophysics Data System (ADS)

Baião, M. F.; Stuchi, T. J.

2017-08-01

This paper analyzes the dynamical evolution of satellites formed by two masses connected by a cable— tethered satellites. We derive the Lagrangian equations of motion in the neighborhood of the collinear equilibrium points, especially for the L2 , of the restricted problem of three bodies. The rigid body configuration is expanded in Legendre polynomials up to fourth degree. We present some numerical simulations of the influence of the parameters such as cable length, mass ratio and initial conditions in the behavior of the tethered satellites. The equation for the collinear equilibrium point is derived and numerically solved. The evolution of the equilibria with the variation of the cable length as a parameter is studied. We also present a discussion of the linear stability around these equilibria. Based on this analysis calculate some unstable Lyapunov orbits associated to these equilibrium points. We found periodic orbits in which the tether travels parallel to itself without involving the angular motion. The numerical applications are focused on the Earth-Moon system. However, the general character of the equations allows applications to the L1 equilibrium and obviously to systems other than the Earth-Moon.

Human Exploration of Earth's Neighborhood and Mars

NASA Technical Reports Server (NTRS)

Condon, Gerald

2003-01-01

The presentation examines Mars landing scenarios, Earth to Moon transfers comparing direct vs. via libration points. Lunar transfer/orbit diagrams, comparison of opposition class and conjunction class missions, and artificial gravity for human exploration missions. Slides related to Mars landing scenarios include: mission scenario; direct entry landing locations; 2005 opportunity - Type 1; Earth-mars superior conjunction; Lander latitude accessibility; Low thrust - Earth return phase; SEP Earth return sequence; Missions - 200, 2007, 2009; and Mission map. Slides related to Earth to Moon transfers (direct vs. via libration points (L1, L2) include libration point missions, expeditionary vs. evolutionary, Earth-Moon L1 - gateway for lunar surface operations, and Lunar mission libration point vs. lunar orbit rendezvous (LOR). Slides related to lunar transfer/orbit diagrams include: trans-lunar trajectory from ISS parking orbit, trans-Earth trajectories, parking orbit considerations, and landing latitude restrictions. Slides related to comparison of opposition class (short-stay) and conjunction class (long-stay) missions for human exploration of Mars include: Mars mission planning, Earth-Mars orbital characteristics, delta-V variations, and Mars mission duration comparison. Slides related to artificial gravity for human exploration missions include: current configuration, NEP thruster location trades, minor axis rotation, and example load paths.

TIME-DEPENDENT COROTATION RESONANCE IN BARRED GALAXIES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, Yu-Ting; Taam, Ronald E.; Pfenniger, Daniel, E-mail: ytwu@asiaa.sinica.edu.tw, E-mail: daniel.pfenniger@unige.ch, E-mail: taam@asiaa.sinica.edu.tw

2016-10-20

The effective potential neighboring the corotation resonance region in barred galaxies is shown to be strongly time-dependent in any rotating frame, due to the competition of nearby perturbations of similar strengths with differing rotation speeds. Contrary to the generally adopted assumption that in the bar rotating frame the corotation region should possess four stationary equilibrium points (Lagrange points), with high quality N -body simulations, we localize the instantaneous equilibrium points (EPs) and find that they circulate or oscillate broadly in azimuth with respect to the pattern speeds of the inner or outer perturbations. This implies that at the particle levelmore » the Jacobi integral is not well conserved around the corotation radius. That is, angular momentum exchanges decouple from energy exchanges, enhancing the chaotic diffusion of stars through the corotation region.« less

Variation of lunar sodium emission intensity with phase angle

NASA Technical Reports Server (NTRS)

Potter, A. E.; Morgan, T. H.

1994-01-01

We report new measurements of the sodium emission intensity seen in a line of sight just above the surface of the Moon. These data show a strong dependence on lunar phase. The emission intensity decreases from a maximum around first quarter (phase angle 90 deg) to very small values near full Moon (phase angle 0 deg). This suggests that the rate of sodium vapor production from the lunar surface is largest at the subsolar point and becomes small near the terminator. However, the sodium emission near full Moon falls below that which would be expected for solar photon-driven processes. Since the solar wind flux decreases substantially when the Moon enters the Earth's magnetotail near full Moon, while the global solar photon flux is undiminished, we suggest that solar wind sputtering is the dominant process for sodium production.

Spacecraft Maneuvering at the Sun/Earth-Moon L2 Libration Point

NASA Astrophysics Data System (ADS)

Shahid, Kamran

Spacecraft formation flying in the vicinity of the Sun/Earth-Moon libration points offers many promising possibilities for space exploration. The concept of formation flying involves the distribution of the functionality of a single spacecraft among several smaller, cooperative spacecraft. The libration points are locations relative to two large orbiting bodies where a third body with relatively small mass can remain stationary relative to the two larger bodies. The most significant perturbation experienced by a spacecraft at the libration point is effect of solar radiation pressure. This thesis presents the development of nonlinear control techniques for maneuvering control at the Sun-Earth/Moon L2 libration point. A new thruster based formation control technique is presented. We also consider a leader/follower formation architecture, and examine the station keeping control of the leader spacecraft and the formation control of the follower spacecraft using solar radiation pressure. Reference trajectories of the leader spacecraft, halo and Lissajous orbits, are determined using a numerical technique in order to take into account all major gravitational perturbations. The nonlinear controllers are developed based on Lyapunov analysis, including non-adaptive and adaptive designs. Thruster based and solar radiation pressure based control laws for spacecraft maneuvering at the Sun-Earth/Moon libration point are developed. Higher order sliding mode control is utilized to address the non-affine structure of the solar sail control inputs. The reduced input solar radiation pressure problem is properly addressed as an underactuated control problem. The development of adaptive control for solar sail equipped spacecraft is an innovation and represents and advancement in solar sailing control technology. Controller performance is evaluated in a high fidelity ephemeris model to reflect a realistic simulated space environment. The numerical results demonstrate the effectiveness of the proposed control techniques for spacecraft maneuvering using solar radiation pressure at the L2 libration point. Stationkeeping accuracies of 50m and formation maintenance accuracies of less than 1m are possible using solar radiation pressure at a sub-L2 libration point. The benefits of these control techniques include increasing libration point mission lifetimes and doubling payload mass fractions as compared to conventional propulsion methods.

GSFC_20180130_M12842_Supermoon

NASA Image and Video Library

2018-01-30

Get ready for the Super Blue Blood Moon! Our closest celestial neighbor is always a wondrous sight, but on the morning of Jan. 31, 2018, three special lunar events are all happening at the same time, providing an excellent excuse to go out and enjoy the nighttime sky. 1 - The full Moon is near the closest point of its orbit so it appears a little larger than usual, what many call a Supermoon. 2 - It’s the second full Moon of the month, what many call a Blue Moon, though the Moon is not literally blue. 3 - There’s a total lunar eclipse, what many call a Blood Moon, visible before sunrise for the western half of the U.S. and other countries near the Pacific. During a total lunar eclipse, the Moon crosses through the shadow of the Earth and LITERALLY appears red as it reflects all of Earth’s sunrises and sunsets. Join NASA scientists Michelle Thaller and Noah Petro live from the Goddard Space Flight Center as we discuss where, when, and how to view this lunar extravaganza and the latest Moon science brought to us by NASA’s Lunar Reconnaissance Orbiter.

TYCHO: Demonstrator and operational satellite mission to Earth-Moon-Libration point EML-4 for communication relay provision as a service

NASA Astrophysics Data System (ADS)

Hornig, Andreas; Homeister, Maren

2015-03-01

In the current wake of mission plans to the Moon and to Earth-Moon Libration points (EML) by several agencies and organizations, TYCHO identifies the key role of telecommunication provision for the future path of lunar exploration. It demonstrates an interesting extension to existing communication methods to the Moon and beyond by combining innovative technology with a next frontier location and the commercial space communication sector. It is evident that all communication systems will rely on direct communication to Earth ground stations. In case of EML-2 missions around HALO orbits or bases on the far side of the Moon, it has to be extended by communication links via relay stations. The innovative approach is that TYCHO provides this relay communication to those out-of-sight lunar missions as a service. TYCHO will establish a new infrastructure for future missions and even create a new market for add-on relay services. The TMA-0 satellite is TYCHO's first phase and a proposed demonstrator mission to the Earth-Moon Libration point EML-4. It demonstrates relay services needed for automated exploratory and manned missions (Moon bases) on the rim (>90°E and >90°W) and far side surface, to lunar orbits and even to EML-2 halo orbits (satellites and space stations). Its main advantage is the permanent availability of communication coverage. This will provide full access to scientific and telemetry data and furthermore to crucial medical monitoring and safety. The communication subsystem is a platform for conventional communication but also a test-bed for optical communication with high data-rate LASER links to serve the future needs of manned bases and periodic burst data-transfer from lunar poles. The operational TMA-1 satellite is a stand-alone mission integrated into existing space communication networks to provide open communication service to external lunar missions. Therefore the long-time stable libration points EML-4 and -5 are selected to guarantee an operation time of up to 10 years. It also enables measurements of the libration point environment with the scientific payloads. This includes sensors for space dust, solar and cosmic radiation activity for satellite lifetime estimation and lunar crew protection by providing early-warning systems. The paper describes the mission concept and the pre-design of the demonstrator satellite according to the operational mission requirements, advantages and benefits of this service. The concept was awarded with the Space Generation Advisory Council and OHB Scholarship in 2011 and the concept study is conducted at the Institute of Space Systems (IRS) [1] of the University of Stuttgart and OHB-System, Bremen [2].

Optimal trajectories from the Earth-Moon L1 and L3 points to deflect hazardous asteroids and comets.

PubMed

Maccone, Claudio

2004-05-01

Software code named asteroff was recently created by the author to simulate the deflection of hazardous asteroids off of their collision course with the Earth. This code was both copyrighted and patented to avoid unauthorized use of ideas that could possibly be vital to construct a planetary defense system in the vicinity of the Earth. Having so said, the basic ideas and equations underlying the asteroff simulation code are openly described in this paper. A system of two space bases housing missiles is proposed to achieve the planetary defense of the Earth against dangerous asteroids and comets, collectively called impactors herein. We show that the layout of the Earth-Moon system with the five relevant Lagrangian (or libration) points in space leads naturally to only one, unmistakable location of these two space bases within the sphere of influence of the Earth. These locations are at the two Lagrangian points L(1) (between the Earth and the Moon) and L(3) (in the direction opposite to the Moon from the Earth). We show that placing missile bases at L(1) and L(3) would enable those missiles to deflect the trajectory of impactors by hitting them orthogonally to their impact trajectory toward the Earth, so as to maximize their deflection. We show that confocal conics are the best class of trajectories fulfilling this orthogonal deflection requirement. One additional remark is that the theory developed in this paper is just a beginning for a wider set of future research. In fact, we only develop the Keplerian analytical theory for the optimal planetary defense achievable from the Earth-Moon Lagrangian points L(1) and L(3). Much more sophisticated analytical refinements would be needed to: (1) take into account many perturbation forces of all kinds acting on both the impactors and missiles shot from L(1) and L(3); (2) add more (non-optimal) trajectories of missiles shot from either the Lagrangian points L(4) and L(5) of the Earth-Moon System or from the surface of the Moon itself; and (3) encompass the full range of missiles currently available to the US (and possibly other countries) so as to really see which impactors could be diverted by which missiles, even in the very simplified scheme outlined here. Published for the first time in February 2002, our Keplerian planetary defense theory has proved, in just one year, to be simple enough to catch the attention of scholars, in addition to popular writers, and even of someone from the US Military. These recent developments might possibly mark the beginning of an all embracing vision in planetary defense beyond all learned congressional activities, dramatic movies, and unknown military plans covered by secrecy.

Influence of a weak gravitational wave on a bound system of two point-masses. [of binary stars

NASA Technical Reports Server (NTRS)

Turner, M. S.

1979-01-01

The problem of a weak gravitational wave impinging upon a nonrelativistic bound system of two point masses is considered. The geodesic equation for each mass is expanded in terms of two small parameters, v/c and dimensionless wave amplitude, in a manner similar to the post-Newtonian expansion; the geodesic equations are resolved into orbital and center-of-mass equations of motion. The effect of the wave on the orbit is determined by using Lagrange's planetary equations to calculate the time evolution of the orbital elements. The gauge properties of the solutions and, in particular, the gauge invariance of the secular effects are discussed.

Centrifuge Rotor Models: A Comparison of the Euler-Lagrange and the Bond Graph Modeling Approach

NASA Technical Reports Server (NTRS)

Granda, Jose J.; Ramakrishnan, Jayant; Nguyen, Louis H.

2006-01-01

A viewgraph presentation on centrifuge rotor models with a comparison using Euler-Lagrange and bond graph methods is shown. The topics include: 1) Objectives; 2) MOdeling Approach Comparisons; 3) Model Structures; and 4) Application.

On the commutator of C^{\\infty}} -symmetries and the reduction of Euler-Lagrange equations

NASA Astrophysics Data System (ADS)

Ruiz, A.; Muriel, C.; Olver, P. J.

2018-04-01

A novel procedure to reduce by four the order of Euler-Lagrange equations associated to nth order variational problems involving single variable integrals is presented. In preparation, a new formula for the commutator of two \

Dirac structures in vakonomic mechanics

NASA Astrophysics Data System (ADS)

Jiménez, Fernando; Yoshimura, Hiroaki

2015-08-01

In this paper, we explore dynamics of the nonholonomic system called vakonomic mechanics in the context of Lagrange-Dirac dynamical systems using a Dirac structure and its associated Hamilton-Pontryagin variational principle. We first show the link between vakonomic mechanics and nonholonomic mechanics from the viewpoints of Dirac structures as well as Lagrangian submanifolds. Namely, we clarify that Lagrangian submanifold theory cannot represent nonholonomic mechanics properly, but vakonomic mechanics instead. Second, in order to represent vakonomic mechanics, we employ the space TQ ×V∗, where a vakonomic Lagrangian is defined from a given Lagrangian (possibly degenerate) subject to nonholonomic constraints. Then, we show how implicit vakonomic Euler-Lagrange equations can be formulated by the Hamilton-Pontryagin variational principle for the vakonomic Lagrangian on the extended Pontryagin bundle (TQ ⊕T∗ Q) ×V∗. Associated with this variational principle, we establish a Dirac structure on (TQ ⊕T∗ Q) ×V∗ in order to define an intrinsic vakonomic Lagrange-Dirac system. Furthermore, we also establish another construction for the vakonomic Lagrange-Dirac system using a Dirac structure on T∗ Q ×V∗, where we introduce a vakonomic Dirac differential. Finally, we illustrate our theory of vakonomic Lagrange-Dirac systems by some examples such as the vakonomic skate and the vertical rolling coin.

Variational Ridging in Sea Ice Models

NASA Astrophysics Data System (ADS)

Roberts, A.; Hunke, E. C.; Lipscomb, W. H.; Maslowski, W.; Kamal, S.

2017-12-01

This work presents the results of a new development to make basin-scale sea ice models aware of the shape, porosity and extent of individual ridges within the pack. We have derived an analytic solution for the Euler-Lagrange equation of individual ridges that accounts for non-conservative forces, and therefore the compressive strength of individual ridges. Because a region of the pack is simply a collection of paths of individual ridges, we are able to solve the Euler-Lagrange equation for a large-scale sea ice field also, and therefore the compressive strength of a region of the pack that explicitly accounts for the macro-porosity of ridged debris. We make a number of assumptions that have simplified the problem, such as treating sea ice as a granular material in ridges, and assuming that bending moments associated with ridging are perturbations around an isostatic state. Regardless of these simplifications, the ridge model is remarkably predictive of macro-porosity and ridge shape, and, because our equations are analytic, they do not require costly computations to solve the Euler-Lagrange equation of ridges on the large scale. The new ridge model is therefore applicable to large-scale sea ice models. We present results from this theoretical development, as well as plans to apply it to the Regional Arctic System Model and a community sea ice code. Most importantly, the new ridging model is particularly useful for pinpointing gaps in our observational record of sea ice ridges, and points to the need for improved measurements of the evolution of porosity of deformed ice in the Arctic and Antarctic. Such knowledge is not only useful for improving models, but also for improving estimates of sea ice volume derived from altimetric measurements of sea ice freeboard.

A composite experimental dynamic substructuring method based on partitioned algorithms and localized Lagrange multipliers

NASA Astrophysics Data System (ADS)

Abbiati, Giuseppe; La Salandra, Vincenzo; Bursi, Oreste S.; Caracoglia, Luca

2018-02-01

Successful online hybrid (numerical/physical) dynamic substructuring simulations have shown their potential in enabling realistic dynamic analysis of almost any type of non-linear structural system (e.g., an as-built/isolated viaduct, a petrochemical piping system subjected to non-stationary seismic loading, etc.). Moreover, owing to faster and more accurate testing equipment, a number of different offline experimental substructuring methods, operating both in time (e.g. the impulse-based substructuring) and frequency domains (i.e. the Lagrange multiplier frequency-based substructuring), have been employed in mechanical engineering to examine dynamic substructure coupling. Numerous studies have dealt with the above-mentioned methods and with consequent uncertainty propagation issues, either associated with experimental errors or modelling assumptions. Nonetheless, a limited number of publications have systematically cross-examined the performance of the various Experimental Dynamic Substructuring (EDS) methods and the possibility of their exploitation in a complementary way to expedite a hybrid experiment/numerical simulation. From this perspective, this paper performs a comparative uncertainty propagation analysis of three EDS algorithms for coupling physical and numerical subdomains with a dual assembly approach based on localized Lagrange multipliers. The main results and comparisons are based on a series of Monte Carlo simulations carried out on a five-DoF linear/non-linear chain-like systems that include typical aleatoric uncertainties emerging from measurement errors and excitation loads. In addition, we propose a new Composite-EDS (C-EDS) method to fuse both online and offline algorithms into a unique simulator. Capitalizing from the results of a more complex case study composed of a coupled isolated tank-piping system, we provide a feasible way to employ the C-EDS method when nonlinearities and multi-point constraints are present in the emulated system.

78 FR 43821 - Final Flood Elevation Determinations

Federal Register 2010, 2011, 2012, 2013, 2014

2013-07-22

............ +902 Unincorporated Areas of LaGrange County. Big Long Lake Entire shoreline......... +957 Unincorporated Areas of LaGrange County. Big Turkey Lake Entire shoreline within +932 Unincorporated Areas of... Vertical Datum. + North American Vertical Datum. Depth in feet above ground. [caret] Mean Sea Level...

Quantitative Tomography for Continuous Variable Quantum Systems

NASA Astrophysics Data System (ADS)

Landon-Cardinal, Olivier; Govia, Luke C. G.; Clerk, Aashish A.

2018-03-01

We present a continuous variable tomography scheme that reconstructs the Husimi Q function (Wigner function) by Lagrange interpolation, using measurements of the Q function (Wigner function) at the Padua points, conjectured to be optimal sampling points for two dimensional reconstruction. Our approach drastically reduces the number of measurements required compared to using equidistant points on a regular grid, although reanalysis of such experiments is possible. The reconstruction algorithm produces a reconstructed function with exponentially decreasing error and quasilinear runtime in the number of Padua points. Moreover, using the interpolating polynomial of the Q function, we present a technique to directly estimate the density matrix elements of the continuous variable state, with only a linear propagation of input measurement error. Furthermore, we derive a state-independent analytical bound on this error, such that our estimate of the density matrix is accompanied by a measure of its uncertainty.

An operational theory of laser-radar selenodesy

USGS Publications Warehouse

Wildey, R.L.; Schlier, R.E.; Hull, J.A.; Larson, G.

1967-01-01

A theory of the utilization of laser techniques for ranging from the Earth to the Moon for the purpose of providing control points on the lunar surface at which the figure of the Moon is measured to an accuracy at least an order of magnitude better than that of the present astrometric measurements is presented. This, in turn, increases the accuracy of the horizontal selenocentric coordinates of topographical features measured by present astrometric methods. The improvement in the vertical and horizontal coordinates of control points in the Apollo landing zone will aid in the analysis of Unmanned Lunar Orbiter photographs for the selection of Apollo landing sites. The present discussion proposes the means of obtaining the ground control upon which the Orbiter photogrammetry is to be fastened. In addition, a technique of combining Goldstone tracking data to show where the resulting lunar figure is positioned relative to the Moon's center of mass is presented. If corner reflectors are placed on the lunar surface, as suggested by many members of the scientific community, or on a lunar orbiting vehicle, one or more Earth-based laser ranging systems are essential. These reflectors will give enough enhancement in return signal to allow for an additional increase in range accuracy of one to two orders of magnitude. In addition to the primary data on the figure of the Moon, a number of other measurements of scientific importance are then readily obtainable. As far as the measurement of control points is concerned, however, the use of corner reflectors is not essential for the success of this project. Questions regarding the influence on the present shape of the Moon of the frozen tide, isostasy, and past impacts of large asteroids appear in large part answerable through the data which are indicated to be obtainable under the present theory. ?? 1967.

Mars Odyssey Observes Martian Moons

NASA Image and Video Library

2018-02-22

Phobos and Deimos, the moons of Mars, are seen by the Mars Odyssey orbiter's Thermal Emission Imaging System, or THEMIS, camera. The images were taken in visible-wavelength light. THEMIS also recorded thermal-infrared imagery in the same scan. The apparent motion is due to progression of the camera's pointing during the 17-second span of the February 15, 2018, observation, not from motion of the two moons. This was the second observation of Phobos by Mars Odyssey; the first was on September 29, 2017. Researchers have been using THEMIS to examine Mars since early 2002, but the maneuver turning the orbiter around to point the camera at Phobos was developed only recently. The distance to Phobos from Odyssey during the observation was about 3,489 miles (5,615 kilometers). The distance to Deimos from Odyssey during the observation was about 12,222 miles (19,670 kilometers). An animation is available at https://photojournal.jpl.nasa.gov/catalog/PIA22248

Mars Odyssey Observes Deimos

NASA Image and Video Library

2018-02-22

Colors in this image of the Martian moon Deimos indicate a range of surface temperatures detected by observing the moon on February 15, 2018, with the Thermal Emission Imaging System (THEMIS) camera on NASA's Mars Odyssey orbiter. The left edge of the small moon is in darkness, and the right edge in sunlight. Temperature information was derived from thermal-infrared imaging such as the grayscale image shown smaller at lower left with the moon in the same orientation. The color-coding merges information from THEMIS observations made in 10 thermal-infrared wavelength bands. This was the first observation of Deimos by Mars Odyssey; the spacecraft first imaged Mars' other moon, Phobos, on September 29, 2017. Researchers have been using THEMIS to examine Mars since early 2002, but the maneuver turning the orbiter around to point the camera at Phobos was developed only recently. https://photojournal.jpl.nasa.gov/catalog/PIA22250

The economics of mining the Martian moons

NASA Technical Reports Server (NTRS)

Leonard, Raymond S.; Blacic, James D.; Vaniman, David T.

1987-01-01

The costs for extracting and shipping volatiles such as water, carbon, and nitrogen that might be found on Phobos and Deimos are estimated. The costs are compared to the cost of shipping the same volatiles from earth, assuming the use of nuclear powered mining facilities and freighters. Mineral resources and possible products from the Martian moons, possible markets for these products, and the costs of transporting these resources to LEO or GEO or to transportation nodal points are examined. Most of the technology needed to mine the moons has already been developed. The need for extraterrestrial sources of propellants for ion propulsion systems and ways in which the mining of the moons would reduce the cost of space operations near earth are discussed. It is concluded that it would be commercially viable to mine the Martian moons, making a profit of at least a 10 percent return on capital.

Impact of Utilizing Photos and Deimos as Waypoints for Mars Human Surface Missions

NASA Technical Reports Server (NTRS)

Cianciolo, Alicia D.; Brown, Kendall

2015-01-01

Phobos and Deimos, the moons of Mars, are interesting exploration destinations that offer extensibility of the Asteroid Redirect Mission (ARM) technologies. Solar Electric Propulsion (SEP), asteroid rendezvous and docking, and surface operations can be used to land on and explore the moons of Mars. The close Mars vicinity of Phobos and Deimos warrant examining them as waypoints, or intermediate staging orbits, for Mars surface missions. This paper outlines the analysis performed to determine the mass impact of using the moons of Mars both as an intermediate staging point for exploration as well as for in-situ recourse utilization, namely propellant, to determine if the moons are viable options to include in the broader Mars surface exploration architecture.

ARC-1979-AC79-7014

NASA Image and Video Library

1979-03-04

2:30 pm Photographer : JPL Range : 2.6 million km. ( 1.6 million miles ) Ganymede is Jupiter's largest satellite ( or moon ) With a radius of about 2600 km., about 1.5 times that of our moon, Ganymede has a bulk density of about 2.0 g/cc, almost half that of our moon, and is probably composed of rock and ice. The large dark regions, in the northeast quadrant, and the white spots, resemble features found on the moon, mare and impact respectively. The long white filaments resemble rays associated with impacts on the lunar surface. The various colors, other than the several blue, green, & orange dots, which are markings on the camera used for pointing determinations and are not physical markings, probably represent differing surface materials.

Magnetism and the history of the moon

NASA Technical Reports Server (NTRS)

Strangway, D. W.; Gose, W. A.; Pearce, G. W.; Carnes, J. G.

1973-01-01

All lunar samples measured to date contain a weak but stable remanent magnetization of lunar origin. The magnetization is carried by metallic iron and is considered to be caused by cooling from above the Curie point in the presence of a magnetic field. Although at present the moon does not have a global field, the remanent magnetization of the rock samples and the presence of magnetic anomalies, both on the near and far side of the moon, imply that the moon experienced a magnetic field during some portion of its history. The field could have been generated in a liquid iron core sustaining a self-exciting dynamo, but there are some basic thermal and geochemical objections that need to be resolved.

Initial Results of a Survey of Earth's L4 Point for Possible Earth Trojan Asteroids

NASA Astrophysics Data System (ADS)

Connors, M.; Veillet, C.; Wiegert, P.; Innanen, K.; Mikkola, S.

2000-10-01

Using the Canada-France-Hawaii 3.6 m telescope and the new CFH12k wide-field CCD imager, a survey of the region near Earth's L4 (morning) Lagrange Point was conducted in May and July/August 2000, in hopes of finding asteroids at or near this point. This survey was motivated by the dynamical interest of a possible Earth Trojan asteroid (ETA) population and by the fact that they would be the easiest asteroids to access from Earth. Recent calculations (Wiegert, Innanen and Mikkola, 2000, Icarus v. 145, 33-43) indicate stability of objects in ETA orbits over a million year timescale and that their on-sky density would be greatest roughly five degrees sunward of the L4 position. An optimized search technique was used, with tracking at the anticipated rate of the target bodies, near real-time scanning of images, and duplication of fields to aid in detection and permit followup. Limited time is available on any given night to search near the Lagrange points, and operations must be conducted at large air mass. Approximately 9 square degrees were efficiently searched and two interesting asteroids were found, NEA 2000 PM8 and our provisionally named CFZ001. CFZ001 cannot be excluded from being an Earth Trojan although that is not the optimal solution for the short arc we observed. This object, of R magnitude 22, was easily detected, suggesting that our search technique worked well. This survey supports the earlier conclusion of Whitely and Tholen (1998, Icarus v. 136, 154-167) that a large population of several hundred meter diameter ETAs does not exist. However, our effective search technique and the discovery of two interesting asteroids suggest the value of completing the survey with approximately 10 more square degrees to be searched near L4 and a comparable search to be done at L5. Funding from Canada's NSERC and HIA and the Academic Research Fund of Athabasca University is gratefully acknowledged.

Planetary Defense Architecture for Mitigating Short-Term Warning Cosmic Threats: READI Project

NASA Technical Reports Server (NTRS)

Nambiar, Shrrirup; Hussein, Alaa; Silva-Martinez, Jackelynne; Reinert, Jessica; Gonzalez, Fernando

2016-01-01

Earth is being constantly bombarded by a large variety of celestial bodies and has been since its formation 4.5 billion years ago. Among those bodies, mainly asteroids and comets, there are those that have the potential to create large scale destruction upon impact. The only extinction-level impact recorded to date was 65 million years ago, during the era of dinosaurs. The probability of another extinction-level, or even city-killer, impact may be negligible, but the consequences can be severe for the biosphere and for our species. Therefore it is highly imperative for us to be prepared for such a devastating impact in the near future, especially since humanity is at the threshold of wielding technologies that allow us to do so. Majority of scientists, engineers, and policymakers have focused on long-term strategies and warning periods for Earth orbit crossing Near-Earth Objects (NEOs), and have suggested methods and policies to tackle such problems. However, less attention has been paid to short warning period NEO threats. Such NEOs test current technological and international cooperation capabilities in protecting ourselves, and can create unpredictable devastation ranging from local to global scale. The most recent example is the Chelyabinsk incident in Russia. This event has provided a wakeup call for space agencies and governments around the world towards establishing a Planetary Defense Program. The Roadmap for EArth Defense Initiative (READI) is a project by a team of international, intercultural, and interdisciplinary participants of the International Space University's Space Studies Program 2015 hosted by Ohio University, Athens, OH proposing a roadmap for space agencies, governments, and the general public to tackle NEOs with a short warning before impact. Taking READI as a baseline, this paper presents a technical description of methodologies proposed for detection and impact mitigation of a medium-sized comet (up to 800m across) with a short-warning period of two years on a collision course with Earth. The hypothetical comet is on a highly-inclined orbit having a high probability for Earth impact after its perihelion. For detection, we propose a space-based infrared detection system consisting of two satellites located at the Earth-Moon Lagrange points L1 and L2 coupled with space observatories, like the James Webb telescope and the Centennial telescope. These telescopes are supported by ground-based telescopes, like the Arecibo and Green Bank telescope, in the search for NEOs. Upon detection, the comet is tracked constantly using space- and ground-based telescopes. The deflection system is two-pronged, firstly involving the use of a high energy Directed Energy Laser Terminals (DELT) placed at Sun-Earth Lagrange points L4 and L5 so as to initiate and increase the ablation rate of the comet and deviate it from its collision trajectory, and secondly by the Hypervelocity Comet Intercept Vehicle (HCIV), a space-borne system combining a kinetic impactor with a thermonuclear device. The policy and international collaboration aspects to implement these methods are also outlined in the paper. The techniques mentioned could also be applied to mitigate medium-to-large sized asteroids (up to 2km across).

Architecture for Mitigating Short-Term Warning Cosmic Threats: READI Project

NASA Technical Reports Server (NTRS)

Nambiar, Shrrirup P.; Hussein, Alaa; Silva-Martinez, Jackelynne; Reinert, Jessica; Gonzalez, Fernando

2016-01-01

Earth is being constantly bombarded by a large variety of celestial bodies and has been since its formation 4.5 billion years ago. Among those bodies, mainly asteroids and comets, there are those that have the potential to create large scale destruction upon impact. The only extinction-level impact recorded to date was 65 million years ago, during the era of dinosaurs. The probability of another extinction-level, or even city-killer, impact may be negligible, but the consequences can be severe for the biosphere and for our species. Therefore it is highly imperative for us to be prepared for such a devastating impact in the near future, especially since humanity is at the threshold of wielding technologies that allow us to do so. Majority of scientists, engineers, and policymakers have focused on long-term strategies and warning periods for Earth orbit crossing Near-Earth Objects (NEOs), and have suggested methods and policies to tackle such problems. However, less attention has been paid to short warning period NEO threats. Such NEOs test current technological and international cooperation capabilities in protecting ourselves, and can create unpredictable devastation ranging from local to global scale. The most recent example is the Chelyabinsk incident in Russia. This event has provided a wakeup call for space agencies and governments around the world towards establishing a Planetary Defense Program. The Roadmap for EArth Defense Initiative (READI) is a project by a team of international, intercultural, and interdisciplinary participants of the International Space University's Space Studies Program 2015 hosted by Ohio University, Athens, OH proposing a roadmap for space agencies, governments, and the general public to tackle NEOs with a short warning before impact. Taking READI as a baseline, this paper presents a technical description of methodologies proposed for detection and impact mitigation of a medium-sized comet (up to 800m across) with a short-warning period of two years on a collision course with Earth. The hypothetical comet is on a highly-inclined orbit having a high probability for Earth impact after its perihelion. For detection, we propose a space-based infrared detection system consisting of two satellites located at the Earth-Moon Lagrange points L1 and L2 coupled with space observatories, like the James Webb telescope and the Centennial telescope. These telescopes are supported by ground-based telescopes, like the Arecibo and Green Bank telescope, in the search for NEOs. Upon detection, the comet is tracked constantly using space- and ground-based telescopes. The deflection system is two-pronged, firstly involving the use of a high energy Directed Energy Laser Terminals (DELT) placed at Sun-Earth Lagrange points L4 and L5 so as to initiate and increase the ablation rate of the comet and deviate it from its collision trajectory, and secondly by the Hypervelocity Comet Intercept Vehicle (HCIV), a space-borne system combining a kinetic impactor with a thermonuclear device. The policy and international collaboration aspects to implement these methods are also outlined in the paper. The techniques mentioned could also be applied to mitigate medium-to-large sized asteroids (up to 2km across).

JPL-19671111-SURVEYf-0001-AVC2002083 Surveyor 6 Lands on Moon

NASA Image and Video Library

1967-11-11

After its soft landing, Surveyor 6 was the first spacecraft to be launched from the surface of the moon. It lifted itself to about 3 meters altitude and flew about 2.5 meters from its initial landing point to further validate Surveyor 5's finding that the lunar soil is basaltic, an important detail for Apollo mission planners.

Learning Mediated by an Educational Hypermedia

NASA Astrophysics Data System (ADS)

Fagundes, Adriano Luiz; da Silva, Tatiana; Barroso, Marta Feijó

2015-12-01

The phases of the Moon is a learning subject composed of smaller units here elaborated by adopting the theory of cognitive load, including aspects related to visualization in science education and taking into account learning difficulties documented in the research literature on science/astronomy teaching as theoretical guiding. The complete research process involved 77 students attending an undergraduate physics course and included data collection instruments to investigate technical aspects of the material, quality of contents and learning. This work focused on learning mediated by a hypermedia digital resource. The instruments used at this stage were pre-testing and learning evaluation allowing a qualitative and quantitative assessment. The questions pointed to the knowledge of the Moon as a body without its own light, to representations of schematic diagrams with sequences of lunar phases and the possibility of observing the Sun and the Moon according to the time of the day, an explanation and a representation of the dynamics of synchronous rotation motion of the Moon. The result provided an overall average increase of 33% in learning. We point out the features of the material that may have contributed to a highest quality as a learning tool.

Modeling Lunar Phases in the Classroom: A Hands-On Interactive Lesson

NASA Astrophysics Data System (ADS)

Sarrazine, Angela R.

2007-12-01

Using Power-Point technology and hands-on materials, a 45 minute lesson has been created to allow students to explore the cause of lunar phases. Students work in cooperative pairs to model the different phases of the moon. In addition, this lesson does not require a bright light source. Using a partially painted Styrofoam ball, a small cup of Play-dough, a simple, protractor, and a data collection sheet, students observe the lunar phases and measure the angle between the sun and the moon. Students place the moon model in eight different positions simulating its orbit around the earth and record the observed changes. The Power-Point presentation contains three segments. The first section allows the teacher to determine the students’ level of prior knowledge about the moon and to uncover possible misconceptions. The second section facilitates the students’ learning by displaying the proper alignment of the model and the proper viewing position for the students. Finally, the presentation culminates in a review of what the students have just observed. This lesson has been created to meet Georgia Performance Standards (GPS) for 4th grade science regarding the cause of lunar phases. Teacher and student responses to this lesson have been extremely positive.

Passage through the Ring Plane

NASA Image and Video Library

2004-06-03

The path that lies ahead for the Cassini-Huygens mission is indicated in this image which illustrates where the spacecraft will be just 27 days from now, when it arrives at Saturn and crosses the ring plane 33 minutes before performing its critical orbital insertion maneuver. The X indicates the point where Cassini will pierce the ring plane on June 30, 2004, going from south to north of the ring plane, 33 minutes before the main engine fires to begin orbital insertion. The indicated point is between the narrow F-ring on the left and Saturn's tenuous G-ring which is too faint to be seen in this exposure. The image was taken on May 11, 2004 when the spacecraft was 26.3 million kilometers (16.3 million miles) from Saturn. Image scale is 158 kilometers (98 miles) per pixel. Moons visible in this image: Janus (181 kilometers or 113 miles across), one of the co-orbital moons; Pandora (84 kilometers or 52 miles across), one of the F ring shepherding moons; and Enceladus (499 kilometers or 310 miles across), a moon which may be heated from within and thus have a liquid sub-surface ocean. http://photojournal.jpl.nasa.gov/catalog/PIA06061

Effect of electromagnetic field on Kordylewski clouds formation

NASA Astrophysics Data System (ADS)

Salnikova, Tatiana; Stepanov, Sergey

2018-05-01

In previous papers the authors suggest a clarification of the phenomenon of appearance-disappearance of Kordylewski clouds - accumulation of cosmic dust mass in the vicinity of the triangle libration points of the Earth-Moon system. Under gravi-tational and light perturbation of the Sun the triangle libration points aren't the points of relative equilibrium. However, there exist the stable periodic motion of the particles, surrounding every of the triangle libration points. Due to this fact we can consider a probabilistic model of the dust clouds formation. These clouds move along the periodical orbits in small vicinity of the point of periodical orbit. To continue this research we suggest a mathematical model to investigate also the electromagnetic influences, arising under consideration of the charged dust particles in the vicinity of the triangle libration points of the Earth-Moon system. In this model we take under consideration the self-unduced force field within the set of charged particles, the probability distribution density evolves according to the Vlasov equation.

Size illusion, distance illusion, and terrestrial passage: comment on reed.

PubMed

Loftus, G R

1985-03-01

Two assumptions of Reed's (1984) terrestrial passage theory are questioned. First, Reed assumes that the moon's failure to increase in visual subtense while elevating is accounted for strictly by perceptual distancing. This allows a formal account of the moon distance illusion, but at the expense of a compelling explanation of the moon size illusion. Second, in order to explain the distance illusion, Reed assumes that all objects, regardless of their perceived altitude, are perceived to start from a common point at the horizon. Several alternative application of Reed's terrestrial-passage foundation to the actual illusions are suggested.

Two former faces of the moon

USGS Publications Warehouse

Wilhelms, D.E.; Davis, D.E.

1971-01-01

Systematic geologic mapping of the lunar near side has resulted in the assignment of relative ages to most visible features. As a derivative of this work, geologic and artistic interpretations have been combined to produce reconstructions of the Moon's appearance at two significant points in its history. The reconstructions, although generalized, show the Moon (1) as it probably appeared about 3.3 billion years ago after most of the mare materials had accumulated, and (2) about 4.0 billion years ago after formation of the youngest of the large multiringed basins, but prior to appreciable flooding by mare material.

Contact solution algorithms

NASA Technical Reports Server (NTRS)

Tielking, John T.

1989-01-01

Two algorithms for obtaining static contact solutions are described in this presentation. Although they were derived for contact problems involving specific structures (a tire and a solid rubber cylinder), they are sufficiently general to be applied to other shell-of-revolution and solid-body contact problems. The shell-of-revolution contact algorithm is a method of obtaining a point load influence coefficient matrix for the portion of shell surface that is expected to carry a contact load. If the shell is sufficiently linear with respect to contact loading, a single influence coefficient matrix can be used to obtain a good approximation of the contact pressure distribution. Otherwise, the matrix will be updated to reflect nonlinear load-deflection behavior. The solid-body contact algorithm utilizes a Lagrange multiplier to include the contact constraint in a potential energy functional. The solution is found by applying the principle of minimum potential energy. The Lagrange multiplier is identified as the contact load resultant for a specific deflection. At present, only frictionless contact solutions have been obtained with these algorithms. A sliding tread element has been developed to calculate friction shear force in the contact region of the rolling shell-of-revolution tire model.

An Unstable Arch Model of a Solar Flare

DTIC Science & Technology

1976-08-10

where the Euler-Lagrange equation becomes singular. We now expand f(r) and g(r) around the singular point r. Thus k JA + - p x, (3.20) m where x...current layer, etc.) can result only from convection. The equations we will use are ()B E 2 - VX(vXB)- _ VX(1TV XB), (4.8) E+ vX B=77j (4.9) C and curl (P...d- curl (J ( curl B) X B+pg . (4.10) Since the treatment is principally concerned with resistive instabilities whose growth times are long compared to

The Next Generation Space Telescope

NASA Technical Reports Server (NTRS)

Mather, John C.; Seery, Bernard (Technical Monitor)

2001-01-01

The Next Generation Space Telescope NGST is an 6-7 m class radiatively cooled telescope, planned for launch to the Lagrange point L2 in 2009, to be built by a partnership of NASA, ESA, and CSA. The NGST science program calls for three core instruments: 1) Near IR camera, 0.6 - 5 micrometer; 2) Near IR multiobject spectrometer, 1 - 5 micrometer, and 3) Mid IR camera and spectrometer, 5 - 28 micrometers. I will report on the scientific goals, project status, and the recent reduction in aperture from the target of 8 m.

Seeking a Human Spaceflight Program Worthy of a Great Nation. Review of U.S. Human Spaceflight Plans Committee

DTIC Science & Technology

2009-10-01

human spaceflight plan is its affordability. In the way of background , Fig- ures 1-4, 1- 5 and 1-6 present the overall NASA bud- get trend over time...build upon the experience gained from prior ones. All as- sume a first flight to lunar orbit, and then to the Lagrange points, and then to near-Earth...and a description of the scenarios considered for inclusion in the integrated options presented in this report. 4.1.1 Background . The Space

Lagrange formula for differential operators on a tree-graph and the resolvents of well-posed restrictions of operator

NASA Astrophysics Data System (ADS)

Koshkarbayev, Nurbol; Kanguzhin, Baltabek

2017-09-01

In this paper we study the question on the full description of well-posed restrictions of given maximal differential operator on a tree-graph. Lagrange formula for differential operator on a tree with Kirchhoff conditions at its internal vertices is presented.

ARTEMIS: The First Mission to the Lunar Libration Orbits

NASA Technical Reports Server (NTRS)

Woodward, Mark; Folta, David; Woodfork, Dennis

2009-01-01

The ARTEMIS mission will be the first to navigate to and perform stationkeeping operations around the Earth-Moon L1 and L2 Lagrangian points. The NASA Goddard Space Flight Center (GSFC) has previous mission experience flying in the Sun-Earth L1 (SOHO, ACE, WIND, ISEE-3) and L2 regimes (WMAP) and have maintained these spacecraft in libration point orbits by performing regular orbit stationkeeping maneuvers. The ARTEMIS mission will build on these experiences, but stationkeeping in Earth-Moon libration orbits presents new challenges since the libration point orbit period is on the order of two weeks rather than six months. As a result, stationkeeping maneuvers to maintain the Lissajous orbit will need to be performed frequently, and the orbit determination solutions between maneuvers will need to be quite accurate. The ARTEMIS mission is a collaborative effort between NASA GSFC, the University of California at Berkeley (UCB), and the Jet Propulsion Laboratory (JPL). The ARTEMIS mission is part of the THEMIS extended mission. ARTEMIS comprises two of the five THEMIS spacecraft that will be maneuvered from near-Earth orbits into lunar libration orbits using a sequence of designed orbital maneuvers and Moon & Earth gravity assists. In July 2009, a series of orbit-raising maneuvers began the proper orbit phasing of the two spacecraft for the first lunar flybys. Over subsequent months, additional propulsive maneuvers and gravity assists will be performed to move each spacecraft though the Sun-Earth weak stability regions and eventually into Earth-Moon libration point orbits. We will present the overall orbit designs for the two ARTEMIS spacecraft and provide analysis results of the 3/4-body dynamics, and the sensitivities of the trajectory design to both · maneuver errors and orbit determination errors. We will present results from the. initial orbit-raising maneuvers.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jimenez, Bienvenido; Novo, Vicente

We provide second-order necessary and sufficient conditions for a point to be an efficient element of a set with respect to a cone in a normed space, so that there is only a small gap between necessary and sufficient conditions. To this aim, we use the common second-order tangent set and the asymptotic second-order cone utilized by Penot. As an application we establish second-order necessary conditions for a point to be a solution of a vector optimization problem with an arbitrary feasible set and a twice Frechet differentiable objective function between two normed spaces. We also establish second-order sufficient conditionsmore » when the initial space is finite-dimensional so that there is no gap with necessary conditions. Lagrange multiplier rules are also given.« less

Bounded state variables and the calculus of variations

NASA Technical Reports Server (NTRS)

Hanafy, L. M.

1972-01-01

An optimal control problem with bounded state variables is transformed into a Lagrange problem by means of differentiable mappings which take some Euclidean space onto the control and state regions. Whereas all such mappings lead to a Lagrange problem, it is shown that only those which are defined as acceptable pairs of transformations are suitable in the sense that solutions to the transformed Lagrange problem will lead to solutions to the original bounded state problem and vice versa. In particular, an acceptable pair of transformations is exhibited for the case when the control and state regions are right parallelepipeds. Finally, a description of the necessary conditions for the bounded state problem which were obtained by this method is given.

Technique to eliminate computational instability in multibody simulations employing the Lagrange multiplier

NASA Technical Reports Server (NTRS)

Watts, G.

1992-01-01

A programming technique to eliminate computational instability in multibody simulations that use the Lagrange multiplier is presented. The computational instability occurs when the attached bodies drift apart and violate the constraints. The programming technique uses the constraint equation, instead of integration, to determine the coordinates that are not independent. Although the equations of motion are unchanged, a complete derivation of the incorporation of the Lagrange multiplier into the equation of motion for two bodies is presented. A listing of a digital computer program which uses the programming technique to eliminate computational instability is also presented. The computer program simulates a solid rocket booster and parachute connected by a frictionless swivel.

Towards a Moon Village: Young Lunar Explorers Report

NASA Astrophysics Data System (ADS)

Kamps, Oscar; Foing, Bernard; Batenburg, Peter

2016-04-01

Introduction: The Moon Village Workshop at ESTEC on the 14th December 2015 was organized by ILEWG/ESTEC in conjunction with the Moon 2020-2030 Symposium. It gathered a multi-disciplinary group of professionals from all around the world to discuss their ideas about the concept of a Moon Village, the vision of ESA's Director General (DG) Jan Woerner of a permanent lunar base within the next decades [1]. The workshop participants split in three working groups focusing on Moon Habitat Design, science and technology potentials of the Moon Village, and engaging stakeholders [2-3]. Their results and recommendations are presented in this abstract. The Moon Habitat Design group identified that the lunar base design is strongly driven by the lunar environment, which is characterized by high radiation, meteoroids, abrasive dust particles, low gravity and vacu-um. The base location is recommended to be near the poles to provide optimized illumination conditions for power generation, permanent communication to Earth, moderate temperature gradients at the surface and interesting subjects to scientific investigations. The abundance of nearby available resources, especially ice at the dark bottoms of craters, can be exploited in terms of In-Situ Resources Utilization (ISRU). The identified infrastructural requirements include a navigation, data- & commlink network, storage facilities and sustainable use of resources. This involves a high degree of recycling, closed-loop life support and use of 3D-printing technology, which are all technologies with great potential for terrestrial spin-off applications. For the site planning of the Moon Village, proven ideas from urban planning on Earth should be taken into account. A couple of principles, which could improve the quality of a long-term living milieu on the Moon, are creating spacious environments, visibility between interior and exterior spaces, areas with flora, such as gardens and greenhouses, establishing a sustainable community and creating social places for astronauts to interact and relax. The proposed establishment of the lunar base can be divided into 4 steps. First the primary base infrastructure is laid out through robotic missions, assisted by human tele-operations from Earth, from the lunar orbit, or via a human-tended gateway station in one of the Earth-Moon Lagrange points (EML-1/2). During the second phase, the first manned habitation module will be deployed. This module contains a bare minimum of functionality to support a small crew for a couple of months. During the third phase, additional modules with more dedicated functions will be sent to the Moon, in order to enhance functionality and to provide astronauts with more space and comfort for long-term missions. In the final phase of the lunar village, a new set of modules will be sent to the base in order to accommodate new arriving crew members. To ensure crew safety, the landing site for supply vessels shall be located in safe distance to the base. Extensive utilization of autonomous or tele-operated robots further minimizes the risk for the crew. From the very beginning, quickly accessible emergency escape vehicles, as well as a heavily shielded 'safe haven' module to protect the crew from solar flares, shall be available. Sustainable moon village development would require explorers to fully utilize and process in-situ resources, in order to manufacture necessary equipment and create new infrastructure. Mining activities would be performed by autonomous robotic systems and managed by colonists from the command center. Building upon the heritage of commercial mining activities on Earth the production would be divided into six stages: geological exploration and mapping, mine preparation, extraction of raw resources, processing of raw resources, separation of minerals, storage and utilization. Additional manufacturing techniques, such as forging, would also need to be explored so as not to limit the production capabilities. To facilitate the progress of the Moon Village initiative it is necessary to attract private industry investments. Potential sources range from technology testing in the moon environment and private R&D funding from science and academia fields, to space tourism, and more ambitious endeavors such as building a prototype launcher site as a ground segment for debris de-orbiting and satellite recycling activities. The Science and Technology team has identified key technologies and possible major scientific disciplines for a Moon Village and ranked them by importance and by Technology Readiness Level (TRL). In terms of basic technologies and objectives, rover exploration, life support systems, navigation and surveying technologies resulted to have the highest importance and readiness. Technologies for the development of the habitats (materials, modules connections, power supply, alternative energy technologies and energy storage) ended up on having high importance with medium-low technology readiness. Technologies intended to help the astronauts or improve techniques had low-medium importance together with low-medium TRL (e.g. space lift to transfer resources, bio cybernetic augmentation "Exoskeleton", jumping rover, telescope). After brainstorming for required technologies, the fo-cus was shifted to what kinds of science can be ex-pected to be performed, once a functional and usable habitat would be available. The group has categorized studies of planetary formation and the Solar System as a highly important scientific discipline with a medi-um-high TRL. Scientific areas with high-medium im-portance, but low technological readiness, were found to be ISRU, psychological effects, adaptations of life to low gravity and plant cultivation. The physiological effects of low-gravity on the body were considered of medium importance and readiness. The Engaging Stakeholders working group started by identifying the main stakeholders and groups that play a role or that could play a role towards the Moon Village project. These stakeholders were classified on their influence towards the program and their attitude towards it. Complex system innovations like the Moon Village initiative often encounter stiff resistance from intended beneficiaries and stakeholders, because they disrupt existing behaviors, organizational structures and business models. However, if this large-scale change is rather approached as two simultaneous and parallel challenges - the design of the artifact in ques-tion and the design of the intervention that brings it to life - the chances that it will take hold will increase. Finally, the group recommended actions to be taken by the ESA DG to engage the most direct stakeholders: The general public should be addressed on an emotional level, human centered design thinking and social movement design should be used to engage the civic society. When engaging with the Moon Village stakeholders, the emotional resonance of Moon Village's value proposition should be taken into account as much as its scientific and technical requirements. This involves (social) media, art and humanities and, for the long term, also investments on education. In this way, a social excitement similar as for the Apollo program might be triggered, which can be used by the member states to engage with their national politicians and convince their taxpayers of the Moon Village's benefits. ESA should invest on the creation of a European new Space industry (similar to the one in the U.S.) and therefore simplify their processes in order to make it easier for the industry to invest and work with ESA with less bureaucracy. In order to succeed in this large-scale international collaboration, a political & legal framework needs to be established. It is recommended to push for an International Moon Village Treaty agreement at the U.N. and to start a conversation about the Moon Village at the UNCOPUOS, so the delegations and member states can start providing ESA with their political and legal inputs. The aim should be to present a sound concept already at the ESA ministerial 2016. Conclusion: Since a long-term human presence in the cis-lunar and lunar surface environment is envisaged, human factors become an even more crucial element in defining the success of the missions. Therefore, it is very important that not only a set of technical problems is solved to survive the harsh environment on the Moon. It is also necessary that psychological and physiological factors will be considered in the design of the systems, equipment and habitats. In that light, the Moon Habitat Design group noticed a missing link between the currently developed space technologies and the actual long-term usability by astronauts. It is therefore critical that ESA would collaborate more with urban planners, architects and industrial designers who provide the expertise in creating suitable environments and products, which are not only technically sound and functional, but also easy to use, comfortable and aesthetically pleasing. The Science and Technology group has in general analyzed the key challenges, technologies, objectives and issues related to the development of a manned colony on the moon, classifying them from an importance vs. Technology Readiness Level (TRL) point of view. The Engaging Stakeholders working group has identified the main stakeholders and groups that could play a role towards the Moon Village project. These stake-holders were classified on their influence towards the program, and their attitude towards it. One clear conclusion was that most of the stakeholders showed a positive view towards the Moon Village program, and that the most important step within a short term strategy should focus on the actions to be taken to engage stakeholders for th next ESA Ministerial to support the program. Finally, the group came up with some recommendations on which actions should be taken by the ESA DG to invite partners and to engage the most direct stakeholders: ESA delegations, media, national governments, citizens and taxpayers. References: [1] http://sci.esa.int/ilewg/ and https://ildwg.wordpress.com/ [2] Foing B. Moon explora-tion highlights and Moon Village introduction. [3] Young Lunar Explorers Report ESTEC Moon village sessions with community and young professionals. *Organisation: Bernard Foing, ESA/ESTEC & ILEWG, ESTEC Moon Village workshop WGs co-conveners: Peter Batenburg, Andrea Jaime, Abigail Calzada, Angeliki Kapoglou, Chris Welch, Susanne Pieterse, Daniel Esser, Audrey Berquand, Daniel Winter, Hanna Läkk, Dmitri Ivanov, S Paternostro, Matias Hazadi, Oscar Kamps

Half Moon Bay, Grays Harbor, Washington: Movable-Bed Physical Model Study

DTIC Science & Technology

2006-09-01

wave machine used in Half Moon Bay physical model.................................50 Figure 28. Wave analysis output from model wave measurements...Point Chehalis used to reduce strong longshore current................82 Figure 46. Analysis of irregular waves measured at model wave Gauge 4...required several reconstruction efforts between origi- nal construction and present day due to the harsh wave climate on the Washington coast. After

Necessary conditions for weighted mean convergence of Lagrange interpolation for exponential weights

NASA Astrophysics Data System (ADS)

Damelin, S. B.; Jung, H. S.; Kwon, K. H.

2001-07-01

Given a continuous real-valued function f which vanishes outside a fixed finite interval, we establish necessary conditions for weighted mean convergence of Lagrange interpolation for a general class of even weights w which are of exponential decay on the real line or at the endpoints of (-1,1).

Visualizing and Understanding the Components of Lagrange and Newton Interpolation

ERIC Educational Resources Information Center

Yang, Yajun; Gordon, Sheldon P.

2016-01-01

This article takes a close look at Lagrange and Newton interpolation by graphically examining the component functions of each of these formulas. Although interpolation methods are often considered simply to be computational procedures, we demonstrate how the components of the polynomial terms in these formulas provide insight into where these…

Improved methods for nightside time domain Lunar Electromagnetic Sounding

NASA Astrophysics Data System (ADS)

Fuqua-Haviland, H.; Poppe, A. R.; Fatemi, S.; Delory, G. T.; De Pater, I.

2017-12-01

Time Domain Electromagnetic (TDEM) Sounding isolates induced magnetic fields to remotely deduce material properties at depth. The first step of performing TDEM Sounding at the Moon is to fully characterize the dynamic plasma environment, and isolate geophysically induced currents from concurrently present plasma currents. The transfer function method requires a two-point measurement: an upstream reference measuring the pristine solar wind, and one downstream near the Moon. This method was last performed during Apollo assuming the induced fields on the nightside of the Moon expand as in an undisturbed vacuum within the wake cavity [1]. Here we present an approach to isolating induction and performing TDEM with any two point magnetometer measurement at or near the surface of the Moon. Our models include a plasma induction model capturing the kinetic plasma environment within the wake cavity around a conducting Moon, and a geophysical forward model capturing induction in a vacuum. The combination of these two models enable the analysis of magnetometer data within the wake cavity. Plasma hybrid models use the upstream plasma conditions and interplanetary magnetic field (IMF) to capture the wake current systems formed around the Moon. The plasma kinetic equations are solved for ion particles with electrons as a charge-neutralizing fluid. These models accurately capture the large scale lunar wake dynamics for a variety of solar wind conditions: ion density, temperature, solar wind velocity, and IMF orientation [2]. Given the 3D orientation variability coupled with the large range of conditions seen within the lunar plasma environment, we characterize the environment one case at a time. The global electromagnetic induction response of the Moon in a vacuum has been solved numerically for a variety of electrical conductivity models using the finite-element method implemented within the COMSOL software. This model solves for the geophysically induced response in vacuum to any driving transient event for any specified 3D conductivity profile. Our models fit the analytic solutions to a Root-Mean-Square Error of better than 1%. Solutions are non-unique, however, serve to better understand and constrain the global interior composition and 3D structure of the Moon. [1] Dyal & Parkin (1971) JGR; [2] Fatemi et al. (2013) GRL.

Orbit period modulation for relative motion using continuous low thrust in the two-body and restricted three-body problems

NASA Astrophysics Data System (ADS)

Arnot, C. S.; McInnes, C. R.; McKay, R. J.; Macdonald, M.; Biggs, J.

2018-02-01

This paper presents rich new families of relative orbits for spacecraft formation flight generated through the application of continuous thrust with only minimal intervention into the dynamics of the problem. Such simplicity facilitates implementation for small, low-cost spacecraft with only position state feedback, and yet permits interesting and novel relative orbits in both two- and three-body systems with potential future applications in space-based interferometry, hyperspectral sensing, and on-orbit inspection. Position feedback is used to modify the natural frequencies of the linearised relative dynamics through direct manipulation of the system eigenvalues, producing new families of stable relative orbits. Specifically, in the Hill-Clohessy-Wiltshire frame, simple adaptations of the linearised dynamics are used to produce a circular relative orbit, frequency-modulated out-of-plane motion, and a novel doubly periodic cylindrical relative trajectory for the purposes of on-orbit inspection. Within the circular restricted three-body problem, a similar minimal approach with position feedback is used to generate new families of stable, frequency-modulated relative orbits in the vicinity of a Lagrange point, culminating in the derivation of the gain requirements for synchronisation of the in-plane and out-of-plane frequencies to yield a singly periodic tilted elliptical relative orbit with potential use as a Lunar far-side communications relay. The Δ v requirements for the cylindrical relative orbit and singly periodic Lagrange point orbit are analysed, and it is shown that these requirements are modest and feasible for existing low-thrust propulsion technology.

Simulating the Liaison Navigation Concept in a Geo + Earth-Moon Halo Constellation

NASA Technical Reports Server (NTRS)

Fujimoto, K.; Leonard, J. M.; McGranaghan, R. M.; Parker, J. S.; Anderson, R. L.; Born, G. H.

2012-01-01

Linked Autonomous Interplanetary Satellite Orbit Navigation, or LiAISON, is a novel satellite navigation technique where relative radiometric measurements between two or more spacecraft in a constellation are processed to obtain the absolute state of all spacecraft. The method leverages the asymmetry of the gravity field that the constellation exists in. This paper takes a step forward in developing a high fidelity navigation simulation for the LiAISON concept in an Earth-Moon constellation. In particular, we aim to process two-way Doppler measurements between a satellite in GEO orbit and another in a halo orbit about the Earth-Moon L1 point.

The disease of the moon: the linguistic and pathological evolution of the English term "lunatic".

PubMed

Riva, M A; Tremolizzo, L; Spicci, M; Ferrarese, C; De Vito, G; Cesana, G C; Sironi, V A

2011-01-01

The public opinion and the scientific community incorrectly believe that the English term "lunatic" was originally related only to insanity, but it also referred to epileptic people. The aim of this article is to clarify the original meaning of the English word "lunatic" by analyzing the evolution of the relationship between psychiatric and neurological diseases and by pointing out the influence of the moon in the history of medicine, in popular traditions, and in English literature. The article also contains a detailed and accurate review of the modern scientific literature on the relationship between moon and epilepsy/psychiatric disorders.

Research and Construction Lunar Stereoscopic Visualization System Based on Chang'E Data

NASA Astrophysics Data System (ADS)

Gao, Xingye; Zeng, Xingguo; Zhang, Guihua; Zuo, Wei; Li, ChunLai

2017-04-01

With lunar exploration activities carried by Chang'E-1, Chang'E-2 and Chang'E-3 lunar probe, a large amount of lunar data has been obtained, including topographical and image data covering the whole moon, as well as the panoramic image data of the spot close to the landing point of Chang'E-3. In this paper, we constructed immersive virtual moon system based on acquired lunar exploration data by using advanced stereoscopic visualization technology, which will help scholars to carry out research on lunar topography, assist the further exploration of lunar science, and implement the facilitation of lunar science outreach to the public. In this paper, we focus on the building of lunar stereoscopic visualization system with the combination of software and hardware by using binocular stereoscopic display technology, real-time rendering algorithm for massive terrain data, and building virtual scene technology based on panorama, to achieve an immersive virtual tour of the whole moon and local moonscape of Chang'E-3 landing point.

Automated Estimation of the Orbital Parameters of Jupiter's Moons

NASA Astrophysics Data System (ADS)

Western, Emma; Ruch, Gerald T.

2016-01-01

Every semester the Physics Department at the University of St. Thomas has the Physics 104 class complete a Jupiter lab. This involves taking around twenty images of Jupiter and its moons with the telescope at the University of St. Thomas Observatory over the course of a few nights. The students then take each image and find the distance from each moon to Jupiter and plot the distances versus the elapsed time for the corresponding image. Students use the plot to fit four sinusoidal curves of the moons of Jupiter. I created a script that automates this process for the professor. It takes the list of images and creates a region file used by the students to measure the distance from the moons to Jupiter, a png image that is the graph of all the data points and the fitted curves of the four moons, and a csv file that contains the list of images, the date and time each image was taken, the elapsed time since the first image, and the distances to Jupiter for Io, Europa, Ganymede, and Callisto. This is important because it lets the professor spend more time working with the students and answering questions as opposed to spending time fitting the curves of the moons on the graph, which can be time consuming.

2:30 pm Photographer : JPL Range : 2.6 million km. ( 1.6 million miles ) Ganymede is Jupiter's

NASA Technical Reports Server (NTRS)

1979-01-01

2:30 pm Photographer : JPL Range : 2.6 million km. ( 1.6 million miles ) Ganymede is Jupiter's largest satellite ( or moon ) With a radius of about 2600 km., about 1.5 times that of our moon, Ganymede has a bulk density of about 2.0 g/cc, almost half that of our moon, and is probably composed of rock and ice. The large dark regions, in the northeast quadrant, and the white spots, resemble features found on the moon, mare and impact respectively. The long white filaments resemble rays associated with impacts on the lunar surface. The various colors, other than the several blue, green, & orange dots, which are markings on the camera used for pointing determinations and are not physical markings, probably represent differing surface materials.

Evolutionary branching under multi-dimensional evolutionary constraints.

PubMed

Ito, Hiroshi; Sasaki, Akira

2016-10-21

The fitness of an existing phenotype and of a potential mutant should generally depend on the frequencies of other existing phenotypes. Adaptive evolution driven by such frequency-dependent fitness functions can be analyzed effectively using adaptive dynamics theory, assuming rare mutation and asexual reproduction. When possible mutations are restricted to certain directions due to developmental, physiological, or physical constraints, the resulting adaptive evolution may be restricted to subspaces (constraint surfaces) with fewer dimensionalities than the original trait spaces. To analyze such dynamics along constraint surfaces efficiently, we develop a Lagrange multiplier method in the framework of adaptive dynamics theory. On constraint surfaces of arbitrary dimensionalities described with equality constraints, our method efficiently finds local evolutionarily stable strategies, convergence stable points, and evolutionary branching points. We also derive the conditions for the existence of evolutionary branching points on constraint surfaces when the shapes of the surfaces can be chosen freely. Copyright © 2016 Elsevier Ltd. All rights reserved.

Using Microsoft PowerPoint as an Astronomical Image Analysis Tool

NASA Astrophysics Data System (ADS)

Beck-Winchatz, Bernhard

2006-12-01

Engaging students in the analysis of authentic scientific data is an effective way to teach them about the scientific process and to develop their problem solving, teamwork and communication skills. In astronomy several image processing and analysis software tools have been developed for use in school environments. However, the practical implementation in the classroom is often difficult because the teachers may not have the comfort level with computers necessary to install and use these tools, they may not have adequate computer privileges and/or support, and they may not have the time to learn how to use specialized astronomy software. To address this problem, we have developed a set of activities in which students analyze astronomical images using basic tools provided in PowerPoint. These include measuring sizes, distances, and angles, and blinking images. In contrast to specialized software, PowerPoint is broadly available on school computers. Many teachers are already familiar with PowerPoint, and the skills developed while learning how to analyze astronomical images are highly transferable. We will discuss several practical examples of measurements, including the following: -Variations in the distances to the sun and moon from their angular sizes -Magnetic declination from images of shadows -Diameter of the moon from lunar eclipse images -Sizes of lunar craters -Orbital radii of the Jovian moons and mass of Jupiter -Supernova and comet searches -Expansion rate of the universe from images of distant galaxies

Does the Man in the Moon Ever Sleep? An Analysis of Student Answers about Simple Astronomical Events: A Case Study.

ERIC Educational Resources Information Center

Dove, Jane

2002-01-01

Analyzes the answers provided by (n=98) 12-year-old students to questions on an end-of-the-year science examination. Points out that although students are able to explain day and night, they have difficulties explaining why the moon always presents the same face to Earth. Addresses implications for teaching and learning. (Contains 17 references.)…

Road map points US to beyond the Moon

NASA Astrophysics Data System (ADS)

Banks, Michael

2008-12-01

The new US administration under President Barack Obama should focus on sending humans to Mars and plan a manned voyage to a near-Earth asteroid. That is the conclusion of a road map published last month by the Planetary Society - a US non-governmental, non-profit organization. The report also says that any future manned missions to the Moon, including a potential lunar base, should instead be funded and performed internationally.

The moon illusion: I. How high is the sky?

PubMed

Baird, J C; Wagner, M

1982-09-01

The most common explanations of the moon illusion assume that the moon is seen at a specific distance in the sky, which is perceived as a definite surface. A decrease in the apparent distance to the sky with increasing elevation presumably leads to a corresponding decrease in apparent size. In Experiment 1 observers (N = 24) gave magnitude estimates of the distance to the night sky at different elevations. The results did not support the flattened-dome hypothesis. In Experiment 2 observers (N = 20) gave magnitude estimates of the distance to the sky at points around a 360 degrees circle just above the horizon. The results were consistent with those of Experiment 1, and in addition, estimates were highly correlated with the physical distances of buildings at the horizon. In a third, control experiment, observers (N = 20) gave magnitude estimates of the distances of buildings at the horizon. A power function fit the relation between estimated and physical distance (exponent = 1.17) as well as the relation between estimates of the sky points above the buildings (Experiment 2) and estimates of building distances (exponent = .46). Taken together, the results disconfirm all theories that attribute the moon illusion to a "sky illusion" of the sort exemplified by the flattened-dome hypothesis.

A Person Fit Test for IRT Models for Polytomous Items

ERIC Educational Resources Information Center

Glas, C. A. W.; Dagohoy, Anna Villa T.

2007-01-01

A person fit test based on the Lagrange multiplier test is presented for three item response theory models for polytomous items: the generalized partial credit model, the sequential model, and the graded response model. The test can also be used in the framework of multidimensional ability parameters. It is shown that the Lagrange multiplier…

Lagrange multiplier for perishable inventory model considering warehouse capacity planning

NASA Astrophysics Data System (ADS)

Amran, Tiena Gustina; Fatima, Zenny

2017-06-01

This paper presented Lagrange Muktiplier approach for solving perishable raw material inventory planning considering warehouse capacity. A food company faced an issue of managing perishable raw materials and marinades which have limited shelf life. Another constraint to be considered was the capacity of the warehouse. Therefore, an inventory model considering shelf life and raw material warehouse capacity are needed in order to minimize the company's inventory cost. The inventory model implemented in this study was the adapted economic order quantity (EOQ) model which is optimized using Lagrange multiplier. The model and solution approach were applied to solve a case industry in a food manufacturer. The result showed that the total inventory cost decreased 2.42% after applying the proposed approach.

Comparison of Numerical Modeling Methods for Soil Vibration Cutting

NASA Astrophysics Data System (ADS)

Jiang, Jiandong; Zhang, Enguang

2018-01-01

In this paper, we studied the appropriate numerical simulation method for vibration soil cutting. Three numerical simulation methods, commonly used for uniform speed soil cutting, Lagrange, ALE and DEM, are analyzed. Three models of vibration soil cutting simulation model are established by using ls-dyna.The applicability of the three methods to this problem is analyzed in combination with the model mechanism and simulation results. Both the Lagrange method and the DEM method can show the force oscillation of the tool and the large deformation of the soil in the vibration cutting. Lagrange method shows better effect of soil debris breaking. Because of the poor stability of ALE method, it is not suitable to use soil vibration cutting problem.

Towards a Moon Village : Community Workshops Highlights

NASA Astrophysics Data System (ADS)

Foing, Bernard H.

2016-07-01

A series of Moon Village Workshops were organised at ESTEC and at ILEWG community events in 2015 and 2016. They gathered a multi-disciplinary group of professionals from all around the world to discuss their ideas about the concept of a Moon Village, the vision of ESA's Director General (DG) Jan Woerner of a permanent lunar base within the next decades [1]. Three working groups focused on 1) Moon Habitat Design; 2) science and technology potentials of the Moon Village, and 3) engaging stake-holders [2-3]. Their results and recommendations are presented in this abstract. The Moon Habitat Design group identified that the lunar base design is strongly driven by the lunar environment, which is characterized by high radiation, meteoroids, abrasive dust particles, low gravity and vacuum. The base location is recommended to be near the poles to provide optimized illumination conditions for power generation, permanent communication to Earth, moderate temperature gradients at the surface and interesting subjects to scientific investigations. The abundance of nearby available resources, especially ice at the dark bottoms of craters, can be exploited in terms of In-Situ Resources Utilization (ISRU). The identified infrastructural requirements include a navigation, data- & commlink network, storage facilities and sustainable use of resources. This involves a high degree of recycling, closed-loop life support and use of 3D-printing technology, which are all technologies with great potential for terrestrial spin-off applications. For the site planning of the Moon Village, proven ideas from urban planning on Earth should be taken into account. A couple of principles, which could improve the quality of a long-term living milieu on the Moon, are creating spacious environments, visibility between interior and exterior spaces, areas with flora, such as gardens and greenhouses, establishing a sustainable community and creating social places for astronauts to interact and relax. The proposed establishment of the lunar base can be divided into 4 steps. First the primary base infrastructure is laid out through robotic missions, assisted by human tele-operations from Earth, from the lunar orbit, or via a human-tended gateway station in one of the Earth-Moon Lagrange points (EML-1/2). During the second phase, the first manned habitation module will be deployed. This module contains a bare minimum of functionality to support a small crew for a couple of months. During the third phase, additional modules with more dedicated functions will be sent to the Moon, in order to enhance functionality and to provide astronauts with more space and comfort for long-term missions. In the final phase of the lunar village, a new set of modules will be sent to the base in order to accommodate new arriving crew members. To ensure crew safety, the landing site for supply vessels shall be located in safe distance to the base. Extensive utilization of autonomous or tele-operated robots further minimizes the risk for the crew. From the very beginning, quickly accessible emergency escape vehicles, as well as a heavily shielded 'safe haven' module to protect the crew from solar flares, shall be available. Sustainable moon village development would require explorers to fully utilize and process in-situ resources, in order to manufacture necessary equipment and create new infrastructure. Mining activities would be performed by autonomous robotic systems and managed by colonists from the command center. Building upon the heritage of commercial mining activities on Earth the production would be divided into six stages: geological exploration and mapping, mine preparation, extraction of raw resources, processing of raw resources, separation of minerals, storage and utilization. Additional manufacturing techniques, such as forging, would also need to be explored so as not to limit the production capabilities. To facilitate the progress of the Moon Village initiative it is necessary to attract private industry investments. Potential sources range from technology testing in the moon environment and private R&D funding from science and academia fields, to space tourism, and more ambitious endeavors such as building a prototype launcher site as a ground segment for debris de-orbiting and satellite recycling activities. The Science and Technology team has identified key technologies and possible major scientific disciplines for a Moon Village and ranked them by importance and by Technology Readiness Level (TRL). In terms of basic technologies and objectives, rover exploration, life support systems, navigation and surveying technologies resulted to have the highest importance and readiness. Technologies for the development of the habitats (materials, modules connections, power supply, alternative energy technologies and energy storage) ended up on having high importance with medium-low technology readiness. Technologies intended to help the astronauts or improve techniques had low-medium importance together with low-medium TRL (e.g. space lift to transfer resources, bio cybernetic augmentation "Exoskeleton", jumping rover, telescope). After brainstorming for required technologies, the focus was shifted to what kinds of science can be expected to be performed, once a functional and usable habitat would be available. The group has categorized studies of planetary formation and the Solar System as a highly important scientific discipline with a medium-high TRL. Scientific areas with high-medium importance, but low technological readiness, were found to be ISRU, psychological effects, adaptations of life to low gravity and plant cultivation. The physiological effects of low-gravity on the body were considered of medium importance and readiness. The Engaging Stakeholders working group started by identifying the main stakeholders and groups that play a role or that could play a role towards the Moon Village project. These stakeholders were classified on their influence towards the program and their attitude towards it. Complex system innovations like the Moon Village initiative often encounter stiff resistance from intended beneficiaries and stakeholders, because they disrupt existing behaviors, organizational structures and business models. However, if this large-scale change is rather approached as two simultaneous and parallel challenges - the design of the artifact in question and the design of the intervention that brings it to life - the chances that it will take hold will increase. Finally, the group recommended actions to be taken by the ESA DG to engage the most direct stakeholders: The general public should be addressed on an emotional level, human centered design thinking and social movement design should be used to engage the civic society. When engaging with the Moon Village stakeholders, the emotional resonance of Moon Village's value proposition should be taken into account as much as its scientific and technical requirements. This involves (social) media, art and humanities and, for the long term, also investments on education. In this way, a social excitement similar as for the Apollo program might be triggered, which can be used by the member states to engage with their national politicians and convince their taxpayers of the Moon Village's benefits. ESA should invest on the creation of a European new Space industry (similar to the one in the U.S.) and therefore simplify their processes in order to make it easier for the industry to invest and work with ESA with less bureaucracy. In order to succeed in this large-scale international collaboration, a political & legal framework needs to be established. It is recommended to push for an International Moon Village Treaty agreement at the U.N. and to start a conversation about the Moon Village at the UNCOPUOS, so the delegations and member states can start providing ESA with their political and legal inputs. The aim should be to present a sound concept already at the ESA ministerial 2016. Conclusion: Since a long-term human presence in the cis-lunar and lunar surface environment is envisaged, human factors become an even more crucial element in defining the success of the missions. Therefore, it is very important that not only a set of technical problems is solved to survive the harsh environment on the Moon. It is also necessary that psychological and physiological factors will be considered in the design of the systems, equipment and habitats. In that light, the Moon Habitat Design group noticed a missing link between the currently developed space technologies and the actual long-term usability by astronauts. It is therefore critical that ESA would collaborate more with urban planners, architects and industrial designers who provide the expertise in creating suitable environments and products, which are not only technically sound and functional, but also easy to use, comfortable and aesthetically pleasing. The Science and Technology group has in general analyzed the key challenges, technologies, objectives and issues related to the development of a manned colony on the moon, classifying them from an importance vs. Technology Readiness Level (TRL) point of view. The Engaging Stakeholders working group has identified the main stakeholders and groups that could play a role towards the Moon Village project. These stake-holders were classified on their influence towards the program, and their attitude towards it. One clear conclusion was that most of the stakeholders showed a positive view towards the Moon Village program, and that the most important step within a short term strategy should focus on the actions to be taken to engage stakeholders for the next ESA Ministerial to support the program. Finally, the group came up with some recommendations on which actions should be taken by the ESA DG to invite partners and to engage the most direct stakeholders: ESA delegations, media, national governments, citizens and taxpayers. References: [1] http://sci.esa.int/ilewg/ and https://ildwg.wordpress.com/ [2] Foing B. Moon exploration highlights and Moon Village introduction. [3] Young Lunar Explorers Report ESTEC Moon village sessions with community and young professionals.

Deep Space Transportation System Using the Sun-Earth L2 Point

NASA Technical Reports Server (NTRS)

Matsumoto, Michihiro

2007-01-01

Recently, various kinds of planetary explorations have become more feasible, taking the advantage of low thrust propulsion means such as ion engines that have come into practical use. The field of space activity has now been expanded even to the rim of the outer solar system. In this context, the Japan Aerospace Exploration Agency (JAXA) has started investigating a Deep Space Port built at the L2 Lagrange point in the Sun-Earth system. For the purpose of making the deep space port practically useful, there is a need to establish a method to making spaceship depart and return from/to the port. This paper first discusses the escape maneuvers originating from the L2 point under the restricted three-body problem. Impulsive maneuvers from the L2 point are extensively studied here, and using the results, optimal low-thrust escape strategies are synthesized. Furthermore, this paper proposes the optimal escape and acceleration maneuvers schemes using Electric Delta-V Earth Gravity Assist (EDVEGA) technique.

The Moon as Possible Calibration Reference for Microwave Radiometers

NASA Astrophysics Data System (ADS)

Burgdorf, Martin; Buehler, Stefan; Hans, Imke; Lang, Theresa; Michel, Simon

2016-04-01

Instruments on satellites for Earth observation on polar orbits usually employ a two-point calibration technique, in which deep space and an on-board calibration target provide two reference flux levels. As the direction of the deep space view is in general close to the celestial equator, the Moon moves sometimes through the field of view and introduces an unwelcome additional signal. One can take advantage of this intrusion, however, by using the Moon as a third flux standard, and this has actually been done for checking the lifetime stability of sensors operating at visible wavelengths. We discuss the advantages and problems of extending this concept to microwaves, concentrating on the frequency of appearances of the Moon in the deep space view, the factors limiting the accuracy of both measurements and models of the Moon's brightness, as well as benefits from complementing the naturally occurring appearances of the Moon with dedicated spacecraft maneuvers. Such pre-planned rotations of the instrument would allow to observe the Moon at a well-defined phase angle and to put it at the exact center of the field of view. This way they would eliminate the need for a model of the Moon's brightness temperature when checking instrumental stability. Finally we investigate the question, whether foreground emission from objects other than the Moon can contaminate the measurements of the Cosmic Microwave Background, which provides the low reference flux in the deep space view. We show that even the brightest discreet sources do not increase significantly the signal from a single scan.

Active and Passive Sensing from Geosynchronous and Libration Orbits

NASA Technical Reports Server (NTRS)

Schoeberl, Mark; Raymond, Carol; Hildebrand, Peter

2003-01-01

The development of the LEO (EOS) missions has led the way to new technologies and new science discoveries. However, LEO measurements alone cannot cost effectively produce high time resolution measurements needed to move the science to the next level. Both GEO and the Lagrange points, L1 and L2, provide vantage points that will allow higher time resolution measurements. GEO is currently being exploited by weather satellites, but the sensors currently operating at GEO do not provide the spatial or spectral resolution needed for atmospheric trace gas, ocean or land surface measurements. It is also may be possible to place active sensors in geostationary orbit. It seems clear, that the next era in earth observation and discovery will be opened by sensor systems operating beyond near earth orbit.

Mapping the cosmos

NASA Astrophysics Data System (ADS)

Clery, Daniel

2009-04-01

For the last seven years, NASA's Wilkinson Microwave Anisotropy Probe (WMAP) has kept a lonely vigil in an area in space some 1.5 million kilometres further out from the Sun beyond the Earth. Known as Lagrange point L2, it is where a space probe can usefully hover, little disturbed by stray signals from home and without having to use much fuel to keep it in position. But WMAP will soon have company: two groundbreaking missions from the European Space Agency (ESA), due to be launched on the same Ariane-5 rocket later this month, will take up their positions next to NASA's craft.

On the dynamics of chain systems. [applications in manipulator and human body models

NASA Technical Reports Server (NTRS)

Huston, R. L.; Passerello, C. E.

1974-01-01

A computer-oriented method for obtaining dynamical equations of motion for chain systems is presented. A chain system is defined as an arbitrarily assembled set of rigid bodies such that adjoining bodies have at least one common point and such that closed loops are not formed. The equations of motion are developed through the use of Lagrange's form of d'Alembert's principle. The method and procedure is illustrated with an elementary study of a tripod space manipulator. The method is designed for application with systems such as human body models, chains and cables, and dynamic finite-segment models.

Unified formalism for higher order non-autonomous dynamical systems

NASA Astrophysics Data System (ADS)

Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso

2012-03-01

This work is devoted to giving a geometric framework for describing higher order non-autonomous mechanical systems. The starting point is to extend the Lagrangian-Hamiltonian unified formalism of Skinner and Rusk for these kinds of systems, generalizing previous developments for higher order autonomous mechanical systems and first-order non-autonomous mechanical systems. Then, we use this unified formulation to derive the standard Lagrangian and Hamiltonian formalisms, including the Legendre-Ostrogradsky map and the Euler-Lagrange and the Hamilton equations, both for regular and singular systems. As applications of our model, two examples of regular and singular physical systems are studied.

Explicitly computing geodetic coordinates from Cartesian coordinates

NASA Astrophysics Data System (ADS)

Zeng, Huaien

2013-04-01

This paper presents a new form of quartic equation based on Lagrange's extremum law and a Groebner basis under the constraint that the geodetic height is the shortest distance between a given point and the reference ellipsoid. A very explicit and concise formulae of the quartic equation by Ferrari's line is found, which avoids the need of a good starting guess for iterative methods. A new explicit algorithm is then proposed to compute geodetic coordinates from Cartesian coordinates. The convergence region of the algorithm is investigated and the corresponding correct solution is given. Lastly, the algorithm is validated with numerical experiments.

Split-step eigenvector-following technique for exploring enthalpy landscapes at absolute zero.

PubMed

Mauro, John C; Loucks, Roger J; Balakrishnan, Jitendra

2006-03-16

The mapping of enthalpy landscapes is complicated by the coupling of particle position and volume coordinates. To address this issue, we have developed a new split-step eigenvector-following technique for locating minima and transition points in an enthalpy landscape at absolute zero. Each iteration is split into two steps in order to independently vary system volume and relative atomic coordinates. A separate Lagrange multiplier is used for each eigendirection in order to provide maximum flexibility in determining step sizes. This technique will be useful for mapping the enthalpy landscapes of bulk systems such as supercooled liquids and glasses.

Space Art "Titan"

NASA Image and Video Library

2006-09-13

Artist Daniel Zeller used the breathtaking imagery from the Cassini spacecraft as a departure point to interpret the intricate surface of Saturn’s moon Titan in this peice titled "Titan". Cassini entered Saturn's orbit in July of 2004 after a seven-year voyage. It then began a four-year mission that includes more than 70 orbits around the ringed planet and its moons. Ink on Paper, 17x21. 2006. Copyrighted: For more information contact Curator, NASA Art Program.

Mars Odyssey Observes Phobos

NASA Image and Video Library

2018-02-22

Colors in this image of the Martian moon Phobos indicate a range of surface temperatures detected by observing the moon on February 15, 2018, with the Thermal Emission Imaging System (THEMIS) camera on NASA's Mars Odyssey orbiter. The left edge of the small moon is in darkness, and the right edge in sunlight. Phobos has an oblong shape with average diameter of about 14 miles (22 kilometers). Temperature information was derived from thermal-infrared imaging such as the grayscale image shown smaller at lower left with the moon in the same orientation. The color-coding merges information from THEMIS observations made in 10 thermal-infrared wavelength bands. This was the second observation of Phobos by Mars Odyssey; the first was on September 29, 2017. Researchers have been using THEMIS to examine Mars since early 2002, but the maneuver turning the orbiter around to point the camera at Phobos was developed only recently. https://photojournal.jpl.nasa.gov/catalog/PIA22249

Lunar Rotation, Orientation and Science

NASA Astrophysics Data System (ADS)

Williams, J. G.; Ratcliff, J. T.; Boggs, D. H.

2004-12-01

The Moon is the most familiar example of the many satellites that exhibit synchronous rotation. For the Moon there is Lunar Laser Ranging measurements of tides and three-dimensional rotation variations plus supporting theoretical understanding of both effects. Compared to uniform rotation and precession the lunar rotational variations are up to 1 km, while tidal variations are about 0.1 m. Analysis of the lunar variations in pole direction and rotation about the pole gives moment of inertia differences, third-degree gravity harmonics, tidal Love number k2, tidal dissipation Q vs. frequency, dissipation at the fluid-core/solid-mantle boundary, and emerging evidence for an oblate boundary. The last two indicate a fluid core, but a solid inner core is not ruled out. Four retroreflectors provide very accurate positions on the Moon. The experience with the Moon is a starting point for exploring the tides, rotation and orientation of the other synchronous bodies of the solar system.

Estimates of the moon's geometry using lunar orbiter imagery and Apollo laser altimeter data

NASA Technical Reports Server (NTRS)

Jones, R. L.

1973-01-01

Selenographic coordinates for about 6000 lunar points identified on the Lunar Orbiter photographs are tabulated and have been combined with those lunar radii derived from the Apollo 15 laser altimeter data. These coordinates were used to derive that triaxial ellipsoid which best fits the moon's irregular surface. Fits were obtaind for different constraints on both the axial orientations and the displacement of the center of the ellipsoid. The semiaxes for the unconstrained ellipsoid were a = 1737.6 km, b = 1735.6 km, and c = 1735.0 km which correspond to a mean radius of about 1736.1 km. These axes were found to be nearly parallel to the moon's principal axes of inertia, and the origin was displaced about 2.0 km from the moon's center of gravity in a direction away from the earth and to the south of the lunar equator.

Applications of laser ranging and VLBI observations for selenodetic control

NASA Technical Reports Server (NTRS)

Fajemirokun, F. A.

1971-01-01

The observation equations necessary to utilize lunar laser ranging and very long baseline interferometry measurements were developed for the establishment of a primary control network on the moon. The network consists of coordinates of moon points in the selenodetic Cartesian coordinate system, which is fixed to the lunar body, oriented along the three principal axes of inertia of the moon, and centered at the lunar center of mass. The observation equations derived are based on a general model in which the unknown parameters included: the selenodetic Cartesian coordinates, the geocentric coordinates of earth stations, parameters of the orientation of the selenodetic coordinate system with respect to a fixed celestial system, the parameters of the orientation of the average terrestrial coordinate system with respect to a fixed celestial coordinate system, and the geocentric coordinates of the center of mass of the moon, given by a lunar ephemeris.

Observation of the cosmic-ray shadow of the Moon with IceCube

NASA Astrophysics Data System (ADS)

Aartsen, M. G.; Abbasi, R.; Abdou, Y.; Ackermann, M.; Adams, J.; Aguilar, J. A.; Ahlers, M.; Altmann, D.; Auffenberg, J.; Bai, X.; Baker, M.; Barwick, S. W.; Baum, V.; Bay, R.; Beatty, J. J.; Bechet, S.; Becker Tjus, J.; Becker, K.-H.; Bell, M.; Benabderrahmane, M. L.; BenZvi, S.; Berdermann, J.; Berghaus, P.; Berley, D.; Bernardini, E.; Bernhard, A.; Bertrand, D.; Besson, D. Z.; Binder, G.; Bindig, D.; Bissok, M.; Blaufuss, E.; Blumenthal, J.; Boersma, D. J.; Bohaichuk, S.; Bohm, C.; Bose, D.; Böser, S.; Botner, O.; Brayeur, L.; Bretz, H.-P.; Brown, A. M.; Bruijn, R.; Brunner, J.; Carson, M.; Casey, J.; Casier, M.; Chirkin, D.; Christov, A.; Christy, B.; Clark, K.; Clevermann, F.; Coenders, S.; Cohen, S.; Cowen, D. F.; Cruz Silva, A. H.; Danninger, M.; Daughhetee, J.; Davis, J. C.; De Clercq, C.; De Ridder, S.; Desiati, P.; de With, M.; DeYoung, T.; Díaz-Vélez, J. C.; Dunkman, M.; Eagan, R.; Eberhardt, B.; Eisch, J.; Ellsworth, R. W.; Euler, S.; Evenson, P. A.; Fadiran, O.; Fazely, A. R.; Fedynitch, A.; Feintzeig, J.; Feusels, T.; Filimonov, K.; Finley, C.; Fischer-Wasels, T.; Flis, S.; Franckowiak, A.; Franke, R.; Frantzen, K.; Fuchs, T.; Gaisser, T. K.; Gallagher, J.; Gerhardt, L.; Gladstone, L.; Glüsenkamp, T.; Goldschmidt, A.; Golup, G.; Gonzalez, J. G.; Goodman, J. A.; Góra, D.; Grandmont, D. T.; Grant, D.; Groß, A.; Ha, C.; Haj Ismail, A.; Hallen, P.; Hallgren, A.; Halzen, F.; Hanson, K.; Heereman, D.; Heinen, D.; Helbing, K.; Hellauer, R.; Hickford, S.; Hill, G. C.; Hoffman, K. D.; Hoffmann, R.; Homeier, A.; Hoshina, K.; Huelsnitz, W.; Hulth, P. O.; Hultqvist, K.; Hussain, S.; Ishihara, A.; Jacobi, E.; Jacobsen, J.; Jagielski, K.; Japaridze, G. S.; Jero, K.; Jlelati, O.; Kaminsky, B.; Kappes, A.; Karg, T.; Karle, A.; Kelley, J. L.; Kiryluk, J.; Kislat, F.; Kläs, J.; Klein, S. R.; Köhne, J.-H.; Kohnen, G.; Kolanoski, H.; Köpke, L.; Kopper, C.; Kopper, S.; Koskinen, D. J.; Kowalski, M.; Krasberg, M.; Krings, K.; Kroll, G.; Kunnen, J.; Kurahashi, N.; Kuwabara, T.; Labare, M.; Landsman, H.; Larson, M. J.; Lesiak-Bzdak, M.; Leuermann, M.; Leute, J.; Lünemann, J.; Madsen, J.; Maruyama, R.; Mase, K.; Matis, H. S.; McNally, F.; Meagher, K.; Merck, M.; Mészáros, P.; Meures, T.; Miarecki, S.; Middell, E.; Milke, N.; Miller, J.; Mohrmann, L.; Montaruli, T.; Morse, R.; Nahnhauer, R.; Naumann, U.; Niederhausen, H.; Nowicki, S. C.; Nygren, D. R.; Obertacke, A.; Odrowski, S.; Olivas, A.; Olivo, M.; O'Murchadha, A.; Paul, L.; Pepper, J. A.; Pérez de los Heros, C.; Pfendner, C.; Pieloth, D.; Pinat, E.; Pirk, N.; Posselt, J.; Price, P. B.; Przybylski, G. T.; Rädel, L.; Rameez, M.; Rawlins, K.; Redl, P.; Reimann, R.; Resconi, E.; Rhode, W.; Ribordy, M.; Richman, M.; Riedel, B.; Rodrigues, J. P.; Rott, C.; Ruhe, T.; Ruzybayev, B.; Ryckbosch, D.; Saba, S. M.; Salameh, T.; Sander, H.-G.; Santander, M.; Sarkar, S.; Schatto, K.; Scheel, M.; Scheriau, F.; Schmidt, T.; Schmitz, M.; Schoenen, S.; Schöneberg, S.; Schönwald, A.; Schukraft, A.; Schulte, L.; Schulz, O.; Seckel, D.; Sestayo, Y.; Seunarine, S.; Sheremata, C.; Smith, M. W. E.; Soldin, D.; Spiczak, G. M.; Spiering, C.; Stamatikos, M.; Stanev, T.; Stasik, A.; Stezelberger, T.; Stokstad, R. G.; Stößl, A.; Strahler, E. A.; Ström, R.; Sullivan, G. W.; Taavola, H.; Taboada, I.; Tamburro, A.; Tepe, A.; Ter-Antonyan, S.; Tešić, G.; Tilav, S.; Toale, P. A.; Toscano, S.; Usner, M.; van der Drift, D.; van Eijndhoven, N.; Van Overloop, A.; van Santen, J.; Vehring, M.; Voge, M.; Vraeghe, M.; Walck, C.; Waldenmaier, T.; Wallraff, M.; Wasserman, R.; Weaver, Ch.; Wellons, M.; Wendt, C.; Westerhoff, S.; Whitehorn, N.; Wiebe, K.; Wiebusch, C. H.; Williams, D. R.; Wissing, H.; Wolf, M.; Wood, T. R.; Woschnagg, K.; Xu, C.; Xu, D. L.; Xu, X. W.; Yanez, J. P.; Yodh, G.; Yoshida, S.; Zarzhitsky, P.; Ziemann, J.; Zierke, S.; Zoll, M.; IceCube Collaboration

2014-05-01

We report on the observation of a significant deficit of cosmic rays from the direction of the Moon with the IceCube detector. The study of this "Moon shadow" is used to characterize the angular resolution and absolute pointing capabilities of the detector. The detection is based on data taken in two periods before the completion of the detector: between April 2008 and May 2009, when IceCube operated in a partial configuration with 40 detector strings deployed in the South Pole ice, and between May 2009 and May 2010 when the detector operated with 59 strings. Using two independent analysis methods, the Moon shadow has been observed to high significance (>6σ) in both detector configurations. The observed location of the shadow center is within 0.2° of its expected position when geomagnetic deflection effects are taken into account. This measurement validates the directional reconstruction capabilities of IceCube.

The Tethered Moon

NASA Technical Reports Server (NTRS)

Zahnle, K.; Lupu, R.; Dobrovolskis, A.

2014-01-01

Cosmic collisions between terrestrial planets resemble somewhat the life cycle of the phoenix: worlds collide, are consumed in flame, and after the debris has cleared, shiny new worlds emerge aglow with possibilities. And glow they do, for they are molten. How brightly they glow, and for how long, is determined by their atmospheres and their moons. A reasonable initial condition on Earth after the Moon-forming impact is that it begins as a hot global magma ocean. We therefore begin our study with the mantle as a liquid ocean with a surface temperature on the order of 3000-4000 K at a time some 100-1000 years after the impact, by which point we can hope that early transients have settled down.

Pairwise-interaction extended point-particle model for particle-laden flows

NASA Astrophysics Data System (ADS)

Akiki, G.; Moore, W. C.; Balachandar, S.

2017-12-01

In this work we consider the pairwise interaction extended point-particle (PIEP) model for Euler-Lagrange simulations of particle-laden flows. By accounting for the precise location of neighbors the PIEP model goes beyond local particle volume fraction, and distinguishes the influence of upstream, downstream and laterally located neighbors. The two main ingredients of the PIEP model are (i) the undisturbed flow at any particle is evaluated as a superposition of the macroscale flow and a microscale flow that is approximated as a pairwise superposition of perturbation fields induced by each of the neighboring particles, and (ii) the forces and torque on the particle are then calculated from the undisturbed flow using the Faxén form of the force relation. The computational efficiency of the standard Euler-Lagrange approach is retained, since the microscale perturbation fields induced by a neighbor are pre-computed and stored as PIEP maps. Here we extend the PIEP force model of Akiki et al. [3] with a corresponding torque model to systematically include the effect of perturbation fields induced by the neighbors in evaluating the net torque. Also, we use DNS results from a uniform flow over two stationary spheres to further improve the PIEP force and torque models. We then test the PIEP model in three different sedimentation problems and compare the results against corresponding DNS to assess the accuracy of the PIEP model and improvement over the standard point-particle approach. In the case of two sedimenting spheres in a quiescent ambient the PIEP model is shown to capture the drafting-kissing-tumbling process. In cases of 5 and 80 sedimenting spheres a good agreement is obtained between the PIEP simulation and the DNS. For all three simulations, the DEM-PIEP was able to recreate, to a good extent, the results from the DNS, while requiring only a negligible fraction of the numerical resources required by the fully-resolved DNS.

Dynamical computation of constrained flexible systems using a modal Udwadia-Kalaba formulation: Application to musical instruments.

PubMed

Antunes, J; Debut, V

2017-02-01

Most musical instruments consist of dynamical subsystems connected at a number of constraining points through which energy flows. For physical sound synthesis, one important difficulty deals with enforcing these coupling constraints. While standard techniques include the use of Lagrange multipliers or penalty methods, in this paper, a different approach is explored, the Udwadia-Kalaba (U-K) formulation, which is rooted on analytical dynamics but avoids the use of Lagrange multipliers. This general and elegant formulation has been nearly exclusively used for conceptual systems of discrete masses or articulated rigid bodies, namely, in robotics. However its natural extension to deal with continuous flexible systems is surprisingly absent from the literature. Here, such a modeling strategy is developed and the potential of combining the U-K equation for constrained systems with the modal description is shown, in particular, to simulate musical instruments. Objectives are twofold: (1) Develop the U-K equation for constrained flexible systems with subsystems modelled through unconstrained modes; and (2) apply this framework to compute string/body coupled dynamics. This example complements previous work [Debut, Antunes, Marques, and Carvalho, Appl. Acoust. 108, 3-18 (2016)] on guitar modeling using penalty methods. Simulations show that the proposed technique provides similar results with a significant improvement in computational efficiency.

Synoptic ozone, cloud reflectivity, and erythemal irradiance from sunrise to sunset for the whole earth as viewed by the DSCOVR spacecraft from the earth-sun Lagrange 1 orbit

NASA Astrophysics Data System (ADS)

Herman, Jay; Huang, Liang; McPeters, Richard; Ziemke, Jerry; Cede, Alexander; Blank, Karin

2018-01-01

EPIC (Earth Polychromatic Imaging Camera) on board the DSCOVR (Deep Space Climate Observatory) spacecraft is the first earth science instrument located near the earth-sun gravitational plus centrifugal force balance point, Lagrange 1. EPIC measures earth-reflected radiances in 10 wavelength channels ranging from 317.5 to 779.5 nm. Of these channels, four are in the UV range 317.5, 325, 340, and 388 nm, which are used to retrieve O3, 388 nm scene reflectivity (LER: Lambert equivalent reflectivity), SO2, and aerosol properties. These new synoptic quantities are retrieved for the entire sunlit globe from sunrise to sunset multiple times per day as the earth rotates in EPIC's field of view. Retrieved ozone amounts agree with ground-based measurements and satellite data to within 3 %. The ozone amounts and LER are combined to derive the erythemal irradiance for the earth's entire sunlit surface at a nadir resolution of 18 × 18 km2 using a computationally efficient approximation to a radiative transfer calculation of irradiance. The results show very high summertime values of the UV index (UVI) in the Andes and Himalayas (greater than 18), and high values of UVI near the Equator at equinox.

Application of shifted Jacobi pseudospectral method for solving (in)finite-horizon min-max optimal control problems with uncertainty

NASA Astrophysics Data System (ADS)

Nikooeinejad, Z.; Delavarkhalafi, A.; Heydari, M.

2018-03-01

The difficulty of solving the min-max optimal control problems (M-MOCPs) with uncertainty using generalised Euler-Lagrange equations is caused by the combination of split boundary conditions, nonlinear differential equations and the manner in which the final time is treated. In this investigation, the shifted Jacobi pseudospectral method (SJPM) as a numerical technique for solving two-point boundary value problems (TPBVPs) in M-MOCPs for several boundary states is proposed. At first, a novel framework of approximate solutions which satisfied the split boundary conditions automatically for various boundary states is presented. Then, by applying the generalised Euler-Lagrange equations and expanding the required approximate solutions as elements of shifted Jacobi polynomials, finding a solution of TPBVPs in nonlinear M-MOCPs with uncertainty is reduced to the solution of a system of algebraic equations. Moreover, the Jacobi polynomials are particularly useful for boundary value problems in unbounded domain, which allow us to solve infinite- as well as finite and free final time problems by domain truncation method. Some numerical examples are given to demonstrate the accuracy and efficiency of the proposed method. A comparative study between the proposed method and other existing methods shows that the SJPM is simple and accurate.

General invertible transformation and physical degrees of freedom

NASA Astrophysics Data System (ADS)

Takahashi, Kazufumi; Motohashi, Hayato; Suyama, Teruaki; Kobayashi, Tsutomu

2017-04-01

An invertible field transformation is such that the old field variables correspond one-to-one to the new variables. As such, one may think that two systems that are related by an invertible transformation are physically equivalent. However, if the transformation depends on field derivatives, the equivalence between the two systems is nontrivial due to the appearance of higher derivative terms in the equations of motion. To address this problem, we prove the following theorem on the relation between an invertible transformation and Euler-Lagrange equations: If the field transformation is invertible, then any solution of the original set of Euler-Lagrange equations is mapped to a solution of the new set of Euler-Lagrange equations, and vice versa. We also present applications of the theorem to scalar-tensor theories.

Color-coded topography and shaded relief map of the lunar near side and far side hemispheres

USGS Publications Warehouse

,

2003-01-01

This publication is a set of three sheets of topographic maps that presents color-coded topographic data digitally merged with shaded relief data. Adopted figure: The figure for the Moon, used for the computation of the map projection, is a sphere with a radius of 1737.4 km. Because the Moon has no surface water, and hence no sea level, the datum (the 0 km contour) for elevations is defined as the radius of 1737.4 km. Coordinates are based on the mean Earth/polar axis (M.E.) coordinates system, the z axis is the axis of the Moon's rotation, and the x axis is the mean Earth direction. The center of mass is the origin of the coordinate system. The equator lies in the x-y plane and the prime meridian lies in the x-z plane with east longitude values being positive. Projection: The projection is Lambert Azimuthal Equal Area Projection. The scale factor at the central latitude and central longitude point is 1:10,000,000. For the near side hemisphere the central latitude and central longitude point is at 0° and 0°. For the far side hemisphere the central latitude and central longitude point is at 0° and 180°.

Laser observations of the moon: Normal points for 1973

NASA Technical Reports Server (NTRS)

Mulholland, J. D.; Shelus, P. J.; Silverburg, E. C.

1975-01-01

McDonald Observatory lunar laser ranging observations for 1973 are presented in the form of compressed normal points and amendments for the 1969-1972 data set are given. Observations of the reflector mounted on the Soviet roving vehicle Lunakhod 2 have also been included.

Laser observations of the moon - Normal points for 1973

NASA Technical Reports Server (NTRS)

Mulholland, J. D.; Shelus, P. J.; Silverberg, E. C.

1975-01-01

McDonald Observatory lunar laser-ranging observations for 1973 are presented in the form of compressed normal points, and amendments for the 1969-1972 data set are given. Observations of the reflector mounted on the Soviet roving vehicle Lunakhod 2 have also been included.

Earth to Moon Transfer: Direct vs Via Libration Points (L1, L2)

NASA Technical Reports Server (NTRS)

Condon, Gerald L.; Wilson, Samuel W.

2004-01-01

For some three decades, the Apollo-style mission has served as a proven baseline technique for transporting flight crews to the Moon and back with expendable hardware. This approach provides an optimal design for expeditionary missions, emphasizing operational flexibility in terms of safely returning the crew in the event of a hardware failure. However, its application is limited essentially to low-latitude lunar sites, and it leaves much to be desired as a model for exploratory and evolutionary programs that employ reusable space-based hardware. This study compares the performance requirements for a lunar orbit rendezvous mission type with one using the cislunar libration point (L1) as a stopover and staging point for access to arbitrary sites on the lunar surface. For selected constraints and mission objectives, it contrasts the relative uniformity of performance cost when the L1 staging point is used with the wide variation of cost for the Apollo-style lunar orbit rendezvous.

Pointwise convergence of derivatives of Lagrange interpolation polynomials for exponential weights

NASA Astrophysics Data System (ADS)

Damelin, S. B.; Jung, H. S.

2005-01-01

For a general class of exponential weights on the line and on (-1,1), we study pointwise convergence of the derivatives of Lagrange interpolation. Our weights include even weights of smooth polynomial decay near +/-[infinity] (Freud weights), even weights of faster than smooth polynomial decay near +/-[infinity] (Erdos weights) and even weights which vanish strongly near +/-1, for example Pollaczek type weights.

Immersive Virtual Moon Scene System Based on Panoramic Camera Data of Chang'E-3

NASA Astrophysics Data System (ADS)

Gao, X.; Liu, J.; Mu, L.; Yan, W.; Zeng, X.; Zhang, X.; Li, C.

2014-12-01

The system "Immersive Virtual Moon Scene" is used to show the virtual environment of Moon surface in immersive environment. Utilizing stereo 360-degree imagery from panoramic camera of Yutu rover, the system enables the operator to visualize the terrain and the celestial background from the rover's point of view in 3D. To avoid image distortion, stereo 360-degree panorama stitched by 112 images is projected onto inside surface of sphere according to panorama orientation coordinates and camera parameters to build the virtual scene. Stars can be seen from the Moon at any time. So we render the sun, planets and stars according to time and rover's location based on Hipparcos catalogue as the background on the sphere. Immersing in the stereo virtual environment created by this imaged-based rendering technique, the operator can zoom, pan to interact with the virtual Moon scene and mark interesting objects. Hardware of the immersive virtual Moon system is made up of four high lumen projectors and a huge curve screen which is 31 meters long and 5.5 meters high. This system which take all panoramic camera data available and use it to create an immersive environment, enable operator to interact with the environment and mark interesting objects contributed heavily to establishment of science mission goals in Chang'E-3 mission. After Chang'E-3 mission, the lab with this system will be open to public. Besides this application, Moon terrain stereo animations based on Chang'E-1 and Chang'E-2 data will be showed to public on the huge screen in the lab. Based on the data of lunar exploration，we will made more immersive virtual moon scenes and animations to help the public understand more about the Moon in the future.

Identification of craters on Moon using Crater Density Parameter

NASA Astrophysics Data System (ADS)

Vandana, Vandana

2016-07-01

Lunar craters are the most noticeable features on the face of the moon. They take up 40.96% of the lunar surface and, their accumulated area is approximately three times as much as the lunar surface area. There are many myths about the moon. Some says moon is made of cheese. The moon and the sun chase each other across the sky etc. but scientifically the moon are closest and are only natural satellite of earth. The orbit plane of the moon is tilted by 5° and orbit period around the earth is 27-3 days. There are two eclipse i.e. lunar eclipse and solar eclipse which always comes in pair. Moon surface has 3 parts i.e. highland, Maria, and crater. For crater diagnostic crater density parameter is one of the means for measuring distance can be easily identity the density between two craters. Crater size frequency distribution (CSFD) is being computed for lunar surface using TMC and MiniSAR image data and hence, also the age for the selected test sites of mars is also determined. The GIS-based program uses the density and orientation of individual craters within LCCs (as vector points) to identify potential source craters through a series of cluster identification and ejection modeling analyses. JMars software is also recommended and operated only the time when connected with server but work can be done in Arc GIS with the help of Arc Objects and Model Builder. The study plays a vital role to determine the lunar surface based on crater (shape, size and density) and exploring affected craters on the basis of height, weight and velocity. Keywords: Moon; Crater; MiniSAR.

NASA Technology Area 07: Human Exploration Destination Systems Roadmap

NASA Technical Reports Server (NTRS)

Kennedy, Kriss J.; Alexander, Leslie; Landis, Rob; Linne, Diane; Mclemore, Carole; Santiago-Maldonado, Edgardo; Brown, David L.

2011-01-01

This paper gives an overview of the National Aeronautics and Space Administration (NASA) Office of Chief Technologist (OCT) led Space Technology Roadmap definition efforts. This paper will given an executive summary of the technology area 07 (TA07) Human Exploration Destination Systems (HEDS). These are draft roadmaps being reviewed and updated by the National Research Council. Deep-space human exploration missions will require many game changing technologies to enable safe missions, become more independent, and enable intelligent autonomous operations and take advantage of the local resources to become self-sufficient thereby meeting the goal of sustained human presence in space. Taking advantage of in-situ resources enhances and enables revolutionary robotic and human missions beyond the traditional mission architectures and launch vehicle capabilities. Mobility systems will include in-space flying, surface roving, and Extra-vehicular Activity/Extravehicular Robotics (EVA/EVR) mobility. These push missions will take advantage of sustainability and supportability technologies that will allow mission independence to conduct human mission operations either on or near the Earth, in deep space, in the vicinity of Mars, or on the Martian surface while opening up commercialization opportunities in low Earth orbit (LEO) for research, industrial development, academia, and entertainment space industries. The Human Exploration Destination Systems (HEDS) Technology Area (TA) 7 Team has been chartered by the Office of the Chief Technologist (OCT) to strategically roadmap technology investments that will enable sustained human exploration and support NASA s missions and goals for at least the next 25 years. HEDS technologies will enable a sustained human presence for exploring destinations such as remote sites on Earth and beyond including, but not limited to, LaGrange points, low Earth orbit (LEO), high Earth orbit (HEO), geosynchronous orbit (GEO), the Moon, near-Earth objects (NEOs), which > 95% are asteroidal bodies, Phobos, Deimos, Mars, and beyond. The HEDS technology roadmap will strategically guide NASA and other U.S. Government agency technology investments that will result in capabilities enabling human exploration missions to diverse destinations generating high returns on investments.

Optimal ballistically captured Earth-Moon transfers

NASA Astrophysics Data System (ADS)

Ricord Griesemer, Paul; Ocampo, Cesar; Cooley, D. S.

2012-07-01

The optimality of a low-energy Earth-Moon transfer terminating in ballistic capture is examined for the first time using primer vector theory. An optimal control problem is formed with the following free variables: the location, time, and magnitude of the transfer insertion burn, and the transfer time. A constraint is placed on the initial state of the spacecraft to bind it to a given initial orbit around a first body, and on the final state of the spacecraft to limit its Keplerian energy with respect to a second body. Optimal transfers in the system are shown to meet certain conditions placed on the primer vector and its time derivative. A two point boundary value problem containing these necessary conditions is created for use in targeting optimal transfers. The two point boundary value problem is then applied to the ballistic lunar capture problem, and an optimal trajectory is shown. Additionally, the problem is then modified to fix the time of transfer, allowing for optimal multi-impulse transfers. The tradeoff between transfer time and fuel cost is shown for Earth-Moon ballistic lunar capture transfers.

Feasibility of cooling the Earth with a cloud of small spacecraft near the inner Lagrange point (L1).

PubMed

Angel, Roger

2006-11-14

If it were to become apparent that dangerous changes in global climate were inevitable, despite greenhouse gas controls, active methods to cool the Earth on an emergency basis might be desirable. The concept considered here is to block 1.8% of the solar flux with a space sunshade orbited near the inner Lagrange point (L1), in-line between the Earth and sun. Following the work of J. Early [Early, JT (1989) J Br Interplanet Soc 42:567-569], transparent material would be used to deflect the sunlight, rather than to absorb it, to minimize the shift in balance out from L1 caused by radiation pressure. Three advances aimed at practical implementation are presented. First is an optical design for a very thin refractive screen with low reflectivity, leading to a total sunshade mass of approximately 20 million tons. Second is a concept aimed at reducing transportation cost to 50 dollars/kg by using electromagnetic acceleration to escape Earth's gravity, followed by ion propulsion. Third is an implementation of the sunshade as a cloud of many spacecraft, autonomously stabilized by modulating solar radiation pressure. These meter-sized "flyers" would be assembled completely before launch, avoiding any need for construction or unfolding in space. They would weigh a gram each, be launched in stacks of 800,000, and remain for a projected lifetime of 50 years within a 100,000-km-long cloud. The concept builds on existing technologies. It seems feasible that it could be developed and deployed in approximately 25 years at a cost of a few trillion dollars, <0.5% of world gross domestic product (GDP) over that time.

Feasibility of cooling the Earth with a cloud of small spacecraft near the inner Lagrange point (L1)

PubMed Central

Angel, Roger

2006-01-01

If it were to become apparent that dangerous changes in global climate were inevitable, despite greenhouse gas controls, active methods to cool the Earth on an emergency basis might be desirable. The concept considered here is to block 1.8% of the solar flux with a space sunshade orbited near the inner Lagrange point (L1), in-line between the Earth and sun. Following the work of J. Early [Early, JT (1989) J Br Interplanet Soc 42:567–569], transparent material would be used to deflect the sunlight, rather than to absorb it, to minimize the shift in balance out from L1 caused by radiation pressure. Three advances aimed at practical implementation are presented. First is an optical design for a very thin refractive screen with low reflectivity, leading to a total sunshade mass of ≈20 million tons. Second is a concept aimed at reducing transportation cost to $50/kg by using electromagnetic acceleration to escape Earth's gravity, followed by ion propulsion. Third is an implementation of the sunshade as a cloud of many spacecraft, autonomously stabilized by modulating solar radiation pressure. These meter-sized “flyers” would be assembled completely before launch, avoiding any need for construction or unfolding in space. They would weigh a gram each, be launched in stacks of 800,000, and remain for a projected lifetime of 50 years within a 100,000-km-long cloud. The concept builds on existing technologies. It seems feasible that it could be developed and deployed in ≈25 years at a cost of a few trillion dollars, <0.5% of world gross domestic product (GDP) over that time. PMID:17085589

Galileo infrared imaging spectrometry measurements at the Moon

NASA Technical Reports Server (NTRS)

Mccord, Thomas B.; Soderblom, Larry A.; Carlson, Robert W.; Fanale, Fraser P.; Lopes-Gautier, Rosaly; Ocampo, Adriano; Forsythe, Jennifer; Campbell, Bruce; Granahan, James C.; Smythe, W. D.

1994-01-01

Imaging spectrometer observations were made of the surface of the Moon during the December 1990 flyby of the Earth-Moon system by the Galileo spacecraft. This article documents this data set and presents analyses of some of the data. The near infrared mapping spectrometer (NIMS) investigation obtained 17 separate mosaics of the Moon in 408 spectral channels between about 0.7 and 5.2 micrometers. The instrument was originally designed to operate in orbit about Jupiter and therefore saturates at many spectral channels for most measurement situations at 1 AU. However, sufficient measurements were made of the Moon to verify the proper operation of the instrument and to demonstrate its capabilities. Analysis of these data show that the NIMS worked as expected and produced measurements consistent with previous ground-based telescopic studies. These are the first imaging spectrometer measurements of this type from space for the Moon, and they illustrate several major points concerning this type of observation and about the NIMS capabilities specifically. Of major importance are the difference between framing and scanning instruments and the effects of the spacecraft and the scan platform on the performance of such and experiment. The science return of subsequent NIMS and other investigation measurements will be significantly enhanced by the experience and results gained.

Comparative Studies for the Sodium and Potassium Atmospheres of the Moon and Mercury

NASA Technical Reports Server (NTRS)

Smyth, William H.

1999-01-01

A summary discussion of recent sodium and potassium observations for the atmospheres of the Moon and Mercury is presented with primary emphasis on new full-disk images that have become available for sodium. For the sodium atmosphere, image observations for both the Moon and Mercury are fitted with model calculations (1) that have the same source speed distribution, one recently measured for electron-stimulated desorption and thought to apply equally well to photon-stimulated desorption, (2) that have similar average surface sodium fluxes, about 2.8 x 10(exp 5) to 8.9 x 10(exp 5) atoms cm(exp -2)s(exp -1) for the Moon and approximately 3.5 x 10(exp 5) to 1.4 x 10(exp 6) atoms cm(exp -2)s(exp -1) for Mercury, but (3) that have very different distributions for the source surface area. For the Moon, a sunlit hemispherical surface source of between approximately 5.3 x 10(exp 22) to 1.2 x 10(exp 23) atoms/s is required with a spatial dependence at least as sharp as the square of the cosine of the solar zenith angle. For Mercury, a time dependent source that varies from 1.5 x 10(exp 22) to 5.8 x l0(exp 22) atoms/s is required which is confined to a small surface area located at, but asymmetrically distributed about, the subsolar point. The nature of the Mercury source suggest that the planetary magnetopause near the subsolar point acts as a time varying and partially protective shield through which charged particles may pass to interact with and liberate gas from the planetary surface. Suggested directions for future research activities are discussed.

The origin of the moon and the single-impact hypothesis. I

NASA Technical Reports Server (NTRS)

Benz, W.; Slattery, W. L.; Cameron, A. G. W.

1986-01-01

One of the newer ideas regarding the origin of the moon is concerned with a single-impact hypothesis. It is pointed out that this theory has the advantage of overcoming most of the difficulties with the classical theories. The angular momentum of the earth-moon system can easily be obtained by varying the initial conditions of the impact. A series of three-dimensional numerical simulations of the collision between the earth and an object of about 1/10 its mass is presented. Different impact velocities, impact parameters, and initial internal energies are considered. Attention is given to assumptions, the equation of state, numerical techniques utilizing the momentum equation and the energy conservation equation, tests, and initial conditions and units.

Extended hamiltonian formalism and Lorentz-violating lagrangians

NASA Astrophysics Data System (ADS)

Colladay, Don

2017-09-01

A new perspective on the classical mechanical formulation of particle trajectories in Lorentz-violating theories is presented. Using the extended hamiltonian formalism, a Legendre Transformation between the associated covariant lagrangian and hamiltonian varieties is constructed. This approach enables calculation of trajectories using Hamilton's equations in momentum space and the Euler-Lagrange equations in velocity space away from certain singular points that arise in the theory. Singular points are naturally de-singularized by requiring the trajectories to be smooth functions of both velocity and momentum variables. In addition, it is possible to identify specific sheets of the dispersion relations that correspond to specific solutions for the lagrangian. Examples corresponding to bipartite Finsler functions are computed in detail. A direct connection between the lagrangians and the field-theoretic solutions to the Dirac equation is also established for a special case.

Transition from the mechanics of material points to the mechanics of structured particles

NASA Astrophysics Data System (ADS)

Somsikov, V. M.

2016-01-01

In this paper, necessity of creation of mechanics of structured particles is discussed. The way to create this mechanics within the laws of classical mechanics with the use of energy equation is shown. The occurrence of breaking of time symmetry within the mechanics of structured particles is shown, as well as the introduction of concept of entropy in the framework of classical mechanics. The way to create the mechanics of non-equilibrium systems in the thermodynamic approach is shown. It is also shown that the use of hypothesis of holonomic constraints while deriving the canonical Lagrange equation made it impossible to describe irreversible dynamics. The difference between the mechanics of structured particles and the mechanics of material points is discussed. It is also shown that the matter is infinitely divisible according to the laws of classical mechanics.

Fractal basins of attraction in the restricted four-body problem when the primaries are triaxial rigid bodies

NASA Astrophysics Data System (ADS)

Suraj, Md Sanam; Asique, Md Chand; Prasad, Umakant; Hassan, M. R.; Shalini, Kumari

2017-11-01

The planar equilateral restricted four-body problem, formulated on the basis of Lagrange's triangular solutions is used to determine the existence and locations of libration points and the Newton-Raphson basins of convergence associated with these libration points. We have supposed that all the three primaries situated on the vertices of an equilateral triangle are triaxial rigid bodies. This paper also deals with the effect of these triaxiality parameters on the regions of motion where the test particle is free to move. Further, the regions on the configuration plane filled by the basins of attraction are determined by using the multivariate version of the Newton-Raphson iterative system. The numerical study reveals that the triaxiality of the primaries is one of the most influential parameters in the four-body problem.

Lunar Solar Origins Exploration (LunaSOX)

NASA Technical Reports Server (NTRS)

Cooper, John F.; King, Joseph H.; Papitashvili, Natasha; Lipatov, Alexander S.; Sittler, Edward C.; Hartle, Richard E.

2011-01-01

The Moon offers a unique vantage point from which to investigate the Sun and its interaction via the solar wind magnetic fields, plasma, and energetic particles with the geospace system including the Moon itself. The lunar surface and exosphere provide in part a record of solar coronal plasma material input and resultant space weathering over billions of years. The structure and dynamics of solar wind interactions with the Moon provide an accessible near-Earth laboratory environment for study of general solar wind interactions with the vast multitude of airless asteroidal bodies of the inner solar system. Spacecraft in lunar orbit have the often simultaneous opportunity, except when in the Earth's magnetosphere, to make in-situ compositional measurements of the solar wind plasma and to carry out remote observations from the Moon of the solar corona, potentially enabled by lunar limb occultation of the solar disk. The LunaSOX project at NASA Goddard Space Flight Center is addressing these heliophysical science objectives from and of the Moon with support from NASA's Lunar Advanced Science and Exploration Research (LASER) program: (1) specify history of solar wind parameters at and sunward of the Moon through enhanced access (http://lunasox.gsfc.nasa.gov/) to legacy and operational mission data products from the Apollo era to the present, (2) model field and plasma interactions with the lunar surface, exosphere, and wake, as constrained by the available data, through hybrid kinetic code simulations, and (3) advance mission concepts for heliophysics from and of the Moon.

Seneca And The Moon: The Cultural Importance Of Our Satellite

NASA Astrophysics Data System (ADS)

Berno, Francesca Romana

Scientists answered the famous Leopardian questions [``Tell me, silent Moon, what are you doing in the sky, silent Moon?''] since ancient times. Among them, Seneca (4 B.C.-65 A.C.) answered: the presence of the Moon in the sky makes us good (by making the corn grow, etc.). Just like the whole Universe, it is a part of the world that is the best of possible ones. And so, the movements of the Moon are regulated as a perfect machine. Therefore, the eclipses are not predictions of disasters - despite a superstition that is still alive nowadays. Moreover, the Moon is perfect, like all planets, and so it provides a wonderful, charming sight. But we look at it only when something strange happens, so Seneca says we are quite wrong. He suggests to study the Moon every day, when it is performing its duty in order to help us feeling good. It is useless watching it when there is something wrong about it. These events do not change our way of life. From this point of view, the Asian shepherd of Leopardi's poem would agree with Seneca: The contemplation of the sky is a sublime way to become relaxed and quiet. But no scientist would answer his question, because it concerns the aim of this planet, not the thing itself. In this case, also in 21st century, we need Seneca's philosophy, or faith in God, or, like Leopardi, illusion.

Project Cassini: a Saturn Orbiter/titan Probe Mission Proposal

NASA Astrophysics Data System (ADS)

Gautier, D.; Ip, W. H.

1984-12-01

Titan is the only moon in the solar system with a substantial atmosphere. The organic chemistry of its N2-CH4 atmosphere may resemble that of the earth's primitive atmosphere before life arose. The investigation of the synthesis of prebiotic molecules in Titan's atmosphere and the atmospheric and surface environments of this planet-sized moon will be the focal point of the Cassini Project proposed to the European Space Agency for an international Saturn Orbiter/Titan Probe mission.

Nature's optics and our understanding of light

NASA Astrophysics Data System (ADS)

Berry, M. V.

2015-01-01

Optical phenomena visible to everyone have been central to the development of, and abundantly illustrate, important concepts in science and mathematics. The phenomena considered from this viewpoint are rainbows, sparkling reflections on water, mirages, green flashes, earthlight on the moon, glories, daylight, crystals and the squint moon. And the concepts involved include refraction, caustics (focal singularities of ray optics), wave interference, numerical experiments, mathematical asymptotics, dispersion, complex angular momentum (Regge poles), polarisation singularities, Hamilton's conical intersections of eigenvalues ('Dirac points'), geometric phases and visual illusions.

Sandia Higher Order Elements (SHOE) v 0.5 alpha

DOE Office of Scientific and Technical Information (OSTI.GOV)

2013-09-24

SHOE is research code for characterizing and visualizing higher-order finite elements; it contains a framework for defining classes of interpolation techniques and element shapes; methods for interpolating triangular, quadrilateral, tetrahedral, and hexahedral cells using Lagrange and Legendre polynomial bases of arbitrary order; methods to decompose each element into domains of constant gradient flow (using a polynomial solver to identify critical points); and an isocontouring technique that uses this decomposition to guarantee topological correctness. Please note that this is an alpha release of research software and that some time has passed since it was actively developed; build- and run-time issues likelymore » exist.« less

Acoustic response of a rectangular levitator with orifices

NASA Technical Reports Server (NTRS)

El-Raheb, Michael; Wagner, Paul

1990-01-01

The acoustic response of a rectangular cavity to speaker-generated excitation through waveguides terminating at orifices in the cavity walls is analyzed. To find the effects of orifices, acoustic pressure is expressed by eigenfunctions satisfying Neumann boundary conditions as well as by those satisfying Dirichlet ones. Some of the excess unknowns can be eliminated by point constraints set over the boundary, by appeal to Lagrange undetermined multipliers. The resulting transfer matrix must be further reduced by partial condensation to the order of a matrix describing unmixed boundary conditions. If the cavity is subjected to an axial temperature dependence, the transfer matrix is determined numerically.

The Impact of Discontinuity Front Orientation on the Accuracy of L1 Space Weather Forecasting

NASA Astrophysics Data System (ADS)

Szabo, A.

2013-12-01

Current space weather forecasting from the Sun-Earth first Lagrange (L1) point assumes that all observed solar wind discontinuity fronts (interplanetary shocks, ICME boundaries) are perpendicular to the Sun-Earth line and are propagating radially out from eh Sun. In reality, these weather fronts can have significantly tilted orientation. Combined ACE, Wind and Soho observations allow the quantification of this effect. With the launch of the DSCOVR spacecraft in early 2015, dual real-time solar wind measurements will become available (at least at some time). Algorithms and their impact exploiting this unique scenario will be discussed.

The James Webb Space Telescope

NASA Technical Reports Server (NTRS)

Mather, John C.

2003-01-01

The James Webb Space Telescope (JWST) will extend the discoveries of the Hubble Space Telescope by deploying a large cooled infrared telescope at the Sun-Earth Lagrange point L2. With a 6 m aperture and three instruments covering the wavelength range from 0.6 to 28 pm, it will provide sensitivities orders of magnitude better than any other facilities. It is intended to observe the light from the first galaxies and the first supernovae, the assembly of galaxies, and the formation and evolution of stars and planetary systems. In this talk I will review the scientific objectives, the hardware concepts and technology, and the predicted system performance.

The James Webb Space Telscope

NASA Technical Reports Server (NTRS)

Mather, John C.

2003-01-01

The James Webb Space Telescope (JWST) will extend the discoveries of the Hubble Space Telescope by deploying a large cooled infrared telescope at the Sun-Earth Lagrange point L2. With a 6 m aperture and three instruments covering the wavelength range from 0.6 to 28 microns, it will provide sensitivities orders of magnitude better than any other facilities. It is intended to observe the light from the first galaxies and the first supernovae, the assembly of galaxies, and the formation and evolution of stars and planetary systems. In this talk I will review the scientific objectives, the hardware concepts and technology, and the predicted system performance.

Utilization of multi-body trajectories in the Sun-Earth-Moon system

NASA Technical Reports Server (NTRS)

Farquhar, R. W.

1980-01-01

An overview of three uncommon trajectory concepts for space missions in the Sun-Earth-Moon System is presented. One concept uses a special class of libration-point orbits called 'halo orbits.' It is shown that members of this orbit family are advantageous for monitoring the solar wind input to the Earth's magnetosphere, and could also be used to establish a continuous communications link between the Earth and the far side of the Moon. The second concept employs pretzel-like trajectories to explore the Earth's geomagnetic tail. These trajectories are formed by using the Moon to carry out a prescribed sequence of gravity-assist maneuvers. Finally, there is the 'boomerang' trajectory technique for multiple-encounter missions to comets and asteroids. In this plan, Earth-swingby maneuvers are used to retarget the original spacecraft trajectory. The boomerang method could be used to produce a triple-encounter sequence which includes flybys of comets Halley and Tempel-2 as well as the asteroid Geographos.

PID position regulation in one-degree-of-freedom Euler-Lagrange systems actuated by a PMSM

NASA Astrophysics Data System (ADS)

Verastegui-Galván, J.; Hernández-Guzmán, V. M.; Orrante-Sakanassi, J.

2018-02-01

This paper is concerned with position regulation in one-degree-of-freedom Euler-Lagrange Systems. We consider that the mechanical subsystem is actuated by a permanent magnet synchronous motor (PMSM). Our proposal consists of a Proportional-Integral-Derivative (PID) controller for the mechanical subsystem and a slight variation of field oriented control for the PMSM. We take into account the motor electric dynamics during the stability analysis. We present, for the first time, a global asymptotic stability proof for such a control scheme without requiring the mechanical subsystem to naturally possess viscous friction. Finally, as a corollary of our main result we prove global asymptotic stability for output feedback PID regulation of one-degree-of-freedom Euler-Lagrange systems when generated torque is considered as the system input, i.e. when the electric dynamics of PMSM's is not taken into account.

Application of parallel distributed Lagrange multiplier technique to simulate coupled Fluid-Granular flows in pipes with varying Cross-Sectional area

DOE PAGES

Kanarska, Yuliya; Walton, Otis

2015-11-30

Fluid-granular flows are common phenomena in nature and industry. Here, an efficient computational technique based on the distributed Lagrange multiplier method is utilized to simulate complex fluid-granular flows. Each particle is explicitly resolved on an Eulerian grid as a separate domain, using solid volume fractions. The fluid equations are solved through the entire computational domain, however, Lagrange multiplier constrains are applied inside the particle domain such that the fluid within any volume associated with a solid particle moves as an incompressible rigid body. The particle–particle interactions are implemented using explicit force-displacement interactions for frictional inelastic particles similar to the DEMmore » method with some modifications using the volume of an overlapping region as an input to the contact forces. Here, a parallel implementation of the method is based on the SAMRAI (Structured Adaptive Mesh Refinement Application Infrastructure) library.« less

Modeling of Mixing Behavior in a Combined Blowing Steelmaking Converter with a Filter-Based Euler-Lagrange Model

NASA Astrophysics Data System (ADS)

Li, Mingming; Li, Lin; Li, Qiang; Zou, Zongshu

2018-05-01

A filter-based Euler-Lagrange multiphase flow model is used to study the mixing behavior in a combined blowing steelmaking converter. The Euler-based volume of fluid approach is employed to simulate the top blowing, while the Lagrange-based discrete phase model that embeds the local volume change of rising bubbles for the bottom blowing. A filter-based turbulence method based on the local meshing resolution is proposed aiming to improve the modeling of turbulent eddy viscosities. The model validity is verified through comparison with physical experiments in terms of mixing curves and mixing times. The effects of the bottom gas flow rate on bath flow and mixing behavior are investigated and the inherent reasons for the mixing result are clarified in terms of the characteristics of bottom-blowing plumes, the interaction between plumes and top-blowing jets, and the change of bath flow structure.

The roles of humans and robots as field geologists on the Moon

NASA Technical Reports Server (NTRS)

Spudis, Paul D.; Taylor, G. Jeffrey

1992-01-01

The geologic exploration of the Moon will be one of the primary scientific functions of any lunar base program. Geologic reconnaissance, the broad-scale characterization of processes and regions, is an ongoing effort that has already started and will continue after base establishment. Such reconnaissance is best done by remote sensing from lunar orbit and simple, automated, sample return missions of the Soviet Luna class. Field study, in contrast, requires intensive work capabilities and the guiding influence of human intelligence. We suggest that the most effective way to accomplish the goals of geologic field study on the Moon is through the use of teleoperated robots, under the direct control of a human geologists who remains at the lunar base, or possibly on Earth. These robots would have a global traverse range, could possess sensory abilities optimized for geologic field work, and would accomplish surface exploration goals without the safety and life support concerns attendance with the use of human geologists on the Moon. By developing the capability to explore any point on the Moon immediately after base establishment, the use of such teleoperated, robotic field geologists makes the single-site lunar base into a 'global' base from the viewpoint of geologic exploration.

Inferences About the Early Moon From Gravity and Topography

NASA Technical Reports Server (NTRS)

Smith, D. E.; Zuber, M. T.

1998-01-01

Recent spacecraft missions to the Moon have significantly improved our knowledge of the lunar gravity and topography fields, and have raised some new and old questions about the early lunar history. It has frequently been assumed that the shape of the Moon today reflects an earlier equilibrium state and that the Moon has retained some internal strength. Recent analysis indicating a superisostatic state of some lunar basins lends support to this hypothesis. On its simplest level, the present shape of the Moon is slightly flattened by 2.2 +/- 0.2 km while its gravity field, represented by an equipotential surface, is flattened only about 0.5 km. The hydrostatic component to the flattening arising from the Moon's present day rotation contributes only 7 m. This difference between the topographic shape of the MOon and the shape of its gravitational equipotential has frequently been explained as the "memory" of an earlier moon that was rotating faster and had a correspondingly larger hydrostatic flattening. To obtain this amount of hydrostatic flattening from rotation alone, and accounting for the contribution of the present-day gravity field, the Moon's rotation rate would need to be about 15x greater than at present, leading ot a period of < 2 days. Maintaining its synchronous rotation with Earth would require a radius for the Moon's orbit of approximately 9 Earth Radii. Unfortunately, our confidence in the observed lunar flattening is not as great as we would like. The uncertainty of .02 km may not properly reflect the limitations of the Clementine dataset, which did not sample poleward of latitudes 81 N and 79 S. Also, the large variation of topography +/- 8 km seen on the MOon dwarfs our estimate fo the flattening. Further the lunar south pole is on the edge of, or possibly inside the massive deep, South Pole-Aitken Basin. Thus, polar radii could be underestimated. This would yield a smaller flattening, which would imply a greater lunar rotation period and orbital radius. However, Basin compensation states and analyses of support and relaxation of topography at long wavelengths point to a lunar shape that has retained a flattening from an earlier faster rotation period.

Some Historical Resources for Teaching about Curved Mirrors.

ERIC Educational Resources Information Center

Mihas, Pavlos

2002-01-01

Presents resources from Alhazens' investigations on curved mirrors that investigate diffuse reflection from the moon's surface, composite mirrors, and the problem of possible points of reflection. (Author/YDS)

Gravity fields of the solar system

NASA Technical Reports Server (NTRS)

Zendell, A.; Brown, R. D.; Vincent, S.

1975-01-01

The most frequently used formulations of the gravitational field are discussed and a standard set of models for the gravity fields of the earth, moon, sun, and other massive bodies in the solar system are defined. The formulas are presented in standard forms, some with instructions for conversion. A point-source or inverse-square model, which represents the external potential of a spherically symmetrical mass distribution by a mathematical point mass without physical dimensions, is considered. An oblate spheroid model is presented, accompanied by an introduction to zonal harmonics. This spheroid model is generalized and forms the basis for a number of the spherical harmonic models which were developed for the earth and moon. The triaxial ellipsoid model is also presented. These models and their application to space missions are discussed.

Lunar libration point flight dynamics study

NASA Technical Reports Server (NTRS)

1969-01-01

Two satellite concepts, Halo and Hummingbird, for a lunar libration point satellite to be used as a tracking and communications link with the far side of the moon were evaluated. Study areas included flight dynamics, communications, attitude control, propulsion, and system integration. Both concepts were proved feasible, but Halo was shown to be the better concept.

The cislunar low-thrust trajectories via the libration point

NASA Astrophysics Data System (ADS)

Qu, Qingyu; Xu, Ming; Peng, Kun

2017-05-01

The low-thrust propulsion will be one of the most important propulsion in the future due to its large specific impulse. Different from traditional low-thrust trajectories (LTTs) yielded by some optimization algorithms, the gradient-based design methodology is investigated for LTTs in this paper with the help of invariant manifolds of LL1 point and Halo orbit near the LL1 point. Their deformations under solar gravitational perturbation are also presented to design LTTs in the restricted four-body model. The perturbed manifolds of LL1 point and its Halo orbit serve as the free-flight phase to reduce the fuel consumptions as much as possible. An open-loop control law is proposed, which is used to guide the spacecraft escaping from Earth or captured by Moon. By using a two-dimensional search strategy, the ON/OFF time of the low-thrust engine in the Earth-escaping and Moon-captured phases can be obtained. The numerical implementations show that the LTTs achieved in this paper are consistent with the one adopted by the SMART-1 mission.

Stable orbits for lunar landing assistance

NASA Astrophysics Data System (ADS)

Condoleo, Ennio; Cinelli, Marco; Ortore, Emiliano; Circi, Christian

2017-10-01

To improve lunar landing performances in terms of mission costs, trajectory determination and visibility the use of a single probe located over an assistance orbit around the Moon has been taken into consideration. To this end, the properties of two quasi-circular orbits characterised by a stable behaviour of semi-major axis, eccentricity and inclination have been investigated. The analysis has demonstrated the possibility of using an assistance probe, located over one of these orbits, as a relay satellite between lander and Earth, even in the case of landings on the far side of the Moon. A comparison about the accuracy in retrieving the lander's state with respect to the use of a probe located in the Lagrangian point L2 of the Earth-Moon system has also been carried out.

A Sustainable Architecture for Lunar Resource Prospecting from an EML-based Exploration Platform

NASA Astrophysics Data System (ADS)

Klaus, K.; Post, K.; Lawrence, S. J.

2012-12-01

Introduction - We present a point of departure architecture for prospecting for Lunar Resources from an Exploration Platform at the Earth - Moon Lagrange points. Included in our study are launch vehicle, cis-lunar transportation architecture, habitat requirements and utilization, lander/rover concepts and sample return. Different transfer design techniques can be explored by mission designers, testing various propulsive systems, maneuvers, rendezvous, and other in-space and surface operations. Understanding the availability of high and low energy trajectory transfer options opens up the possibility of exploring the human and logistics support mission design space and deriving solutions never before contemplated. For sample return missions from the lunar surface, low-energy transfers could be utilized between EML platform and the surface as well as return of samples to EML-based spacecraft. Human Habitation at the Exploration Platform - Telerobotic and telepresence capabilities are considered by the agency to be "grand challenges" for space technology. While human visits to the lunar surface provide optimal opportunities for field geologic exploration, on-orbit telerobotics may provide attractive early opportunities for geologic exploration, resource prospecting, and other precursor activities in advance of human exploration campaigns and ISRU processing. The Exploration Platform provides a perfect port for a small lander which could be refueled and used for multiple missions including sample return. The EVA and robotic capabilities of the EML Exploration Platform allow the lander to be serviced both internally and externally, based on operational requirements. The placement of the platform at an EML point allows the lander to access any site on the lunar surface, thus providing the global lunar surface access that is commonly understood to be required in order to enable a robust lunar exploration program. Designing the sample return lander for low-energy trajectories would reduce the overall mass and potentially increase the sample return mass. The Initial Lunar Mission -Building upon Apollo sample investigations, the recent results of the LRO/LCROSS, international missions such as Chandrayaan-1, and legacy missions including Lunar Prospector, and Clementine, among the most important science and exploration goals is surface prospecting for lunar resources and to provide ground truth for orbital observations. Being able to constrain resource production potential will allow us to estimate the prospect for reducing the size of payloads launched from Earth required for Solar System exploration. Flight opportunities for something like the NASA RESOLVE instrument suite to areas of high science and exploration interest could be used to refine and improve future Exploration architectures, reducing the outlays required for cis-lunar operations. Summary - EML points are excellent for placement of a semi-permanent human-tended Exploration Platform both in the near term, while providing important infrastructure and deep-space experience that will be built upon to gradually increase long-term operational capabilities.

Lunar Laser Ranging trial at Koganei SLR station

NASA Astrophysics Data System (ADS)

Noda, Hirotomo; Kunimori, Hiroo; Araki, Hiroshi

Introduction: The Lunar Laser Ranging (LLR) is a technique to measure the distance between laser stations on the Earth and retroreflectors on the Moon, by detecting the time of flight of high-powered laser emitted from the ground station. Since the Earth-Moon distance contains information of lunar orbit, lunar solid tides, and lunar orientation and rotation, observation data of LLR have contributed to the lunar science, especially for the estimation of the inner structure of the Moon through orientation, rotation and tide. There are five refroreflectors on the Moon, Apollo 11, 14, 15 (U. S. A.), Lunokhod 1 and 2 (french-made, carried by former U. S. S. R.). The Apollo 15 has largest aperture among them, and almost 75 % of the total LLR data are from Apollo 15 site. System Description: Since there is no Japanese station which can range the Moon so far, a precursor ranging experiment by using the Satellite Laser Ranging (SLR) facility in the NICT Koganei campus in Tokyo is ongoing. The SLR station has a 1.5 m Cassegrain telescope with Coude focus. Normally it is equipped with a laser with 20mJ, 20Hz repetition rate, and 35 picoseconds pulse width for satellite ranging. In addition to it, a wide-pulse width laser (3 nanoseconds, which corresponds to 45 cm in 2-way range) with energy of about 350 mJ per shot, repetition rate of 10Hz, wavelength of 532 nm is introduced to detect photons from the lunar retroreflectors for demonstration. As the pulse width is broad, the high accuracy ranging is not expected, therefore it is solely used for the confirmation of the optical link budget between the ground station and retroreflectors on the Moon. As the photon detector, we use a SPAD (Single Photon Avalanche Diode) and also an MCP (Micro Channel Plate) photo multiplier whose quantum efficiency is twice as much as that of the SPAD in use. For the pointing, a CCD imager is also available in the same detector box. They can be switched by reflecting mirrors. To suppress the background noise, a bandpass filter (0.3 nm FWHM, 50 % transparency) and spatial filter (pinhole) with diameter of 400 microns are installed and checked. For better link budget, the contamination of optical elements of the telescope and on the optical bench was checked. The alignment of the laser emission path with respect to the laser receiving path and laser beam divergence has been adjusted to maximize the efficiency of the laser emission. Pointing: Because the retroreflectors are small and they are not visible from ground telescopes, we point the telescope to known small-sized craters ( 10 km in diameter) whose positions are known in selenographic coordinate and thus in topocentric coordinate at the observation site. Then the offset angles in azimuth and elevation direction from the predicted pointing direction are determined so that the center of the crater comes to the center of the CCD images which are coalligned with the SPAD and the MCP. This procedure confirms the pointing of the telescope.

Titanium Isotopes Provide Clues to Lunar Origin

NASA Astrophysics Data System (ADS)

Taylor, G. J.

2012-05-01

The idea that the Moon formed as the result of the giant impact of a Mars-sized impactor with the still-growing Earth explains two central facts about the Earth-Moon system: its total angular momentum (Earth's spin and the Moon's orbital motion), and the sizes of the metallic cores of the Earth (large) and Moon (tiny). This gives cosmochemists some confidence in the hypothesis, but they would greatly appreciate additional compositional tests. One undisputed point is the identical abundance of the three oxygen isotopes in Earth and Moon. Junjun Zhang and colleagues at the University of Chicago (USA) and the University of Bern (Switzerland) have added another isotopic system to the cosmochemical testing tool kit, titanium isotopes. They find that the ratio of titanium-50 to titanium-47 is identical in Earth and Moon to within four parts per million. In contrast, other solar system materials, such as carbonaceous chondrites, vary by considerably more than this-- up to 150 times as much. The identical oxygen and titanium isotopic compositions in Earth and Moon are surprising in light of what we think we know about planet formation and formation of the Moon after a giant impact. The variations in oxygen and titanium isotopes among meteorite types suggest that it is unlikely that the Moon-forming giant impactor would have had the same isotopic composition as the Earth. Simulations show that the Moon ends up constructed mostly (40-75%) from the impactor materials. Thus, the Moon ought to have different isotopic composition than does Earth. The isotopes might have exchanged in the complicated, messy proto-lunar disk (as has been suggested for oxygen isotopes), making them the same. However, Zhang and colleagues suggest that this exchange is unlikely for a refractory element like titanium. Could the impact simulations be greatly overestimating the contributions from the impactor? Was the mixing of building-block materials throughout the inner solar system much less than thought so that the impactor and early Earth actually had the same isotopic compositions? Zhang and coauthors also draw attention to the possibility that the impactor could have been rich in ice, so that the Moon formed mostly from Earth's rocky materials. Questions abound as our understanding of planet formation evolves. Whatever the cause of the titanium-isotope homogeneity in the Earth-Moon system, the new data from titanium isotopes herald new directions for understanding the complicated processes involved in forming the Moon by a giant impact.

Solar Array Disturbances to Spacecraft Pointing During the Lunar Reconnaissance Orbiter (LRO) Mission

NASA Technical Reports Server (NTRS)

Calhoun, Philip

2010-01-01

The Lunar Reconnaissance Orbiter (LRO), the first spacecraft to support NASA s return to the Moon, launched on June 18, 2009 from the Cape Canaveral Air Force Station aboard an Atlas V launch vehicle. It was initially inserted into a direct trans-lunar trajectory to the Moon. After a five day transit to the Moon, LRO was inserted into the Lunar orbit and successfully lowered to a low altitude elliptical polar orbit for spacecraft commissioning. Successful commissioning was completed in October 2009 when LRO was placed in its near circular mission orbit with an approximate altitude of 50km. LRO will spend at least one year orbiting the Moon, collecting lunar environment science and mapping data, utilizing a suite of seven instruments to enable future human exploration. The objective is to provide key science data necessary to facilitate human return to the Moon as well as identification of opportunities for future science missions. LRO's instrument suite will provide the high resolution imaging data with sub-meter accuracy, highly accurate lunar cartographic maps, mineralogy mapping, amongst other science data of interest. LRO employs a 3-axis stabilized attitude control system (ACS) whose primary control mode, the "Observing Mode", provides Lunar nadir, off-nadir, and inertial fine pointing for the science data collection and instrument calibration. This controller combines the capability of fine pointing with on-demand large angle full-sky attitude reorientation. It provides simplicity of spacecraft operation as well as additional flexibility for science data collection. A conventional suite of ACS components is employed in the Observing Mode to meet the pointing and control objectives. Actuation is provided by a set of four reaction wheels developed in-house at NASA Goddard Space Flight Center (GSFC). Attitude feedback is provided by a six state Kalman filter which utilizes two SELEX Galileo Star Trackers for attitude updates, and a single Honeywell Miniature Inertial Measurement Unit (MIMU) to provide body rates for attitude propagation. Rate is computed by differentiating accumulated angle provided by the MIMU. The Observing Mode controller is required to maintain fine pointing while a large fully-articulated solar array (SA) maintains its panel normal to the solar incidence. This paper describes the disturbances to the attitude control resulting from the SA articulation. Observing Mode performance in the presence of this disturbance was assessed while the spacecraft was in an initial elliptical low altitude orbit during the commissioning phase, which started about two weeks after launch and lasted for 90 days. LRO demonstrated excellent pointing performance during Observing Mode nadir and inertial attitude target operations during this phase. Transient LRO attitude errors observed during commissioning resulted primarily from three sources, Diviner instrument calibrations, RW zero crossings, and SA articulation. Even during times of considerable disturbance from SA articulation, the attitude errors were maintained below the statistical attitude error requirement level of 15 arc-sec (3 sigma).

A Novel Multi-Receiver Signcryption Scheme with Complete Anonymity.

PubMed

Pang, Liaojun; Yan, Xuxia; Zhao, Huiyang; Hu, Yufei; Li, Huixian

2016-01-01

Anonymity, which is more and more important to multi-receiver schemes, has been taken into consideration by many researchers recently. To protect the receiver anonymity, in 2010, the first multi-receiver scheme based on the Lagrange interpolating polynomial was proposed. To ensure the sender's anonymity, the concept of the ring signature was proposed in 2005, but afterwards, this scheme was proven to has some weakness and at the same time, a completely anonymous multi-receiver signcryption scheme is proposed. In this completely anonymous scheme, the sender anonymity is achieved by improving the ring signature, and the receiver anonymity is achieved by also using the Lagrange interpolating polynomial. Unfortunately, the Lagrange interpolation method was proven a failure to protect the anonymity of receivers, because each authorized receiver could judge whether anyone else is authorized or not. Therefore, the completely anonymous multi-receiver signcryption mentioned above can only protect the sender anonymity. In this paper, we propose a new completely anonymous multi-receiver signcryption scheme with a new polynomial technology used to replace the Lagrange interpolating polynomial, which can mix the identity information of receivers to save it as a ciphertext element and prevent the authorized receivers from verifying others. With the receiver anonymity, the proposed scheme also owns the anonymity of the sender at the same time. Meanwhile, the decryption fairness and public verification are also provided.

Recent Origin of Titan's Orbital Eccentricity

NASA Astrophysics Data System (ADS)

Cuk, Matija

2014-05-01

Saturn's regular satellite system contains several dynamical mysteries, including the high tidal heating of Enceladus and undamped eccentricity of Titan. Lainey et al.(2012) proposed that the tidal evolution of the system is much faster than previously thought, which would explain heating of Enceladus and implies that some of the current satellites are less than 1 Gyr old. Cuk et al.(2014) pointed out that this fast tidal evolution could also explain the Titan-Hyperion resonance. If the inner, mid-sized Saturnian moons were re-accreted within the last Gyr, then the same event could have generated the observed eccentricity of Titan. Titan-Hyperion resonance puts strong constraints on this event, as many scenarios lead to the loss of Hyperion (usually through collision with Titan). Here I report on the ongoing study of the history of the Saturnian system, using symplectic integrators SIMPL (for stable configurations) and COMPLEX (for situations when the moons' orbits crossed). I find that the past system of icy satellites could have naturally evolved into instability, by having Dione and Rhea-like moons enter the mutual 4:3 resonance. This resonance is chaotic due to overlap with the solar evection resonance (i.e. the moons' precession rates in the mean-motion resonance overlap with Saturn's mean motion). The outcome of such resonance is a collision between the mid-sized moons, likely followed by re-accretion, with Titan being largely unaffected. I also find that close encounters between a mid-sized moon and Titan could with significant probability both excite Titan and preserve its resonance with Hyperion (cf. Hamilton 2013). I will present possible scenarios in which the previous system had an additional moon exterior to Rhea. This additional moon would have been destabilized by resonances with the inner moons and eventually absorbed by Titan, which acquired its eccentricity in the process. This research is supported by NASA's Outer Planet Research Program.

Tidal Friction in the Earth-Moon System and Laplace Planes: Darwin Redux

NASA Technical Reports Server (NTRS)

Rubincam, David P.

2015-01-01

The dynamical evolution of the Earth-Moon system due to tidal friction is treated here. George H. Darwin used Laplace planes (also called proper planes) in his study of tidal evolution. The Laplace plane approach is adapted here to the formalisms of W.M. Kaula and P. Goldreich. Like Darwin, the approach assumes a three-body problem: Earth, Moon, and Sun, where the Moon and Sun are point-masses. The tidal potential is written in terms of the Laplace plane angles. The resulting secular equations of motion can be easily integrated numerically assuming the Moon is in a circular orbit about the Earth and the Earth is in a circular orbit about the Sun. For Earth-Moon distances greater than 10 Earth radii, the Earth's approximate tidal response can be characterized with a single parameter, which is a ratio: a Love number times the sine of a lag angle divided by another such product. For low parameter values it can be shown that Darwin's low-viscosity molten Earth, M. Ross's and G. Schubert's model of an Earth near melting, and Goldreich's equal tidal lag angles must all give similar histories. For higher parameter values, as perhaps has been the case at times with the ocean tides, the Earth's obliquity may have decreased slightly instead of increased once the Moon's orbit evolved further than 50 Earth radii from the Earth, with possible implications for climate. This is contrast to the other tidal friction models mentioned, which have the obliquity always increasing with time. As for the Moon, its orbit is presently tilted to its Laplace plane by 5.2deg. The equations do not allow the Moon to evolve out of its Laplace plane by tidal friction alone, so that if it was originally in its Laplace plane, the tilt arose with the addition of other mechanisms, such as resonance passages.

Servicing and Deployment of National Resources in Sun-Earth Libration Point Orbits

NASA Technical Reports Server (NTRS)

Folta, David C.; Beckman, Mark; Mar, Greg C.; Mesarch, Michael; Cooley, Steven; Leete, Steven J.

2002-01-01

Spacecraft travel between the Sun-Earth system, the Earth-Moon system, and beyond has received extensive attention recently. The existence of a connection between unstable regions enables mission designers to envision scenarios of multiple spacecraft traveling cheaply from system to system, rendezvousing, servicing, and refueling along the way. This paper presents examples of transfers between the Sun-Earth and Earth-Moon systems using a true ephemeris and perturbation model. It shows the (Delta)V costs associated with these transfers, including the costs to reach the staging region from the Earth. It explores both impulsive and low thrust transfer trajectories. Additionally, analysis that looks specifically at the use of nuclear power in libration point orbits and the issues associated with them such as inadvertent Earth return is addressed. Statistical analysis of Earth returns and the design of biased orbits to prevent any possible return are discussed. Lastly, the idea of rendezvous between spacecraft in libration point orbits using impulsive maneuvers is addressed.

Uncertainty propagation in the calibration equations for NTC thermistors

NASA Astrophysics Data System (ADS)

Liu, Guang; Guo, Liang; Liu, Chunlong; Wu, Qingwen

2018-06-01

The uncertainty propagation problem is quite important for temperature measurements, since we rely so much on the sensors and calibration equations. Although uncertainty propagation for platinum resistance or radiation thermometers is well known, there have been few publications concerning negative temperature coefficient (NTC) thermistors. Insight into the propagation characteristics of uncertainty that develop when equations are determined using the Lagrange interpolation or least-squares fitting method is presented here with respect to several of the most common equations used in NTC thermistor calibration. Within this work, analytical expressions of the propagated uncertainties for both fitting methods are derived for the uncertainties in the measured temperature and resistance at each calibration point. High-precision calibration of an NTC thermistor in a precision water bath was performed by means of the comparison method. Results show that, for both fitting methods, the propagated uncertainty is flat in the interpolation region but rises rapidly beyond the calibration range. Also, for temperatures interpolated between calibration points, the propagated uncertainty is generally no greater than that associated with the calibration points. For least-squares fitting, the propagated uncertainty is significantly reduced by increasing the number of calibration points and can be well kept below the uncertainty of the calibration points.

A new lunar absolute control point: established by images from the landing camera on Chang'e-3

NASA Astrophysics Data System (ADS)

Wang, Fen-Fei; Liu, Jian-Jun; Li, Chun-Lai; Ren, Xin; Mu, Ling-Li; Yan, Wei; Wang, Wen-Rui; Xiao, Jing-Tao; Tan, Xu; Zhang, Xiao-Xia; Zou, Xiao-Duan; Gao, Xing-Ye

2014-12-01

The establishment of a lunar control network is one of the core tasks in selenodesy, in which defining an absolute control point on the Moon is the most important step. However, up to now, the number of absolute control points has been very sparse. These absolute control points have mainly been lunar laser ranging retroreflectors, whose geographical location can be observed by observations on Earth and also identified in high resolution lunar satellite images. The Chang'e-3 (CE-3) probe successfully landed on the Moon, and its geographical location has been monitored by an observing station on Earth. Since its positional accuracy is expected to reach the meter level, the CE-3 landing site can become a new high precision absolute control point. We use a sequence of images taken from the landing camera, as well as satellite images taken by CE-1 and CE-2, to identify the location of the CE-3 lander. With its geographical location known, the CE-3 landing site can be established as a new absolute control point, which will effectively expand the current area of the lunar absolute control network by 22%, and can greatly facilitate future research in the field of lunar surveying and mapping, as well as selenodesy.

A Direct Method for Fuel Optimal Maneuvers of Distributed Spacecraft in Multiple Flight Regimes

NASA Technical Reports Server (NTRS)

Hughes, Steven P.; Cooley, D. S.; Guzman, Jose J.

2005-01-01

We present a method to solve the impulsive minimum fuel maneuver problem for a distributed set of spacecraft. We develop the method assuming a non-linear dynamics model and parameterize the problem to allow the method to be applicable to multiple flight regimes including low-Earth orbits, highly-elliptic orbits (HEO), Lagrange point orbits, and interplanetary trajectories. Furthermore, the approach is not limited by the inter-spacecraft separation distances and is applicable to both small formations as well as large constellations. Semianalytical derivatives are derived for the changes in the total AV with respect to changes in the independent variables. We also apply a set of constraints to ensure that the fuel expenditure is equalized over the spacecraft in formation. We conclude with several examples and present optimal maneuver sequences for both a HE0 and libration point formation.

Pairwise Interaction Extended Point-Particle (PIEP) model for multiphase jets and sedimenting particles

NASA Astrophysics Data System (ADS)

Liu, Kai; Balachandar, S.

2017-11-01

We perform a series of Euler-Lagrange direct numerical simulations (DNS) for multiphase jets and sedimenting particles. The forces the flow exerts on the particles in these two-way coupled simulations are computed using the Basset-Bousinesq-Oseen (BBO) equations. These forces do not explicitly account for particle-particle interactions, even though such pairwise interactions induced by the perturbations from neighboring particles may be important especially when the particle volume fraction is high. Such effects have been largely unaddressed in the literature. Here, we implement the Pairwise Interaction Extended Point-Particle (PIEP) model to simulate the effect of neighboring particle pairs. A simple collision model is also applied to avoid unphysical overlapping of solid spherical particles. The simulation results indicate that the PIEP model provides a more elaborative and complicated movement of the dispersed phase (droplets and particles). Office of Naval Research (ONR) Multidisciplinary University Research Initiative (MURI) project N00014-16-1-2617.

Concept Assessment of a Fission Fragment Rocket Engine (FFRE) Propelled Spacecraft

NASA Technical Reports Server (NTRS)

Werka, Robert; Clark, Rod; Sheldon, Rob; Percy, Tom

2012-01-01

The March, 2012 issue of Aerospace America stated that ?the near-to-medium prospects for applying advanced propulsion to create a new era of space exploration are not very good. In the current world, we operate to the Moon by climbing aboard a Carnival Cruise Lines vessel (Saturn 5), sail from the harbor (liftoff) shedding whole decks of the ship (staging) along the way and, having reached the return leg of the journey, sink the ship (burnout) and return home in a lifeboat (Apollo capsule). Clearly this is an illogical way to travel, but forced on Explorers by today's propulsion technology. However, the article neglected to consider the one propulsion technology, using today's physical principles that offer continuous, substantial thrust at a theoretical specific impulse of 1,000,000 sec. This engine unequivocally can create a new era of space exploration that changes the way spacecraft operate. Today's space Explorers could travel in Cruise Liner fashion using the technology not considered by Aerospace America, the novel Dusty Plasma Fission Fragment Rocket Engine (FFRE). This NIAC study addresses the FFRE as well as its impact on Exploration Spacecraft design and operation. It uses common physics of the relativistic speed of fission fragments to produce thrust. It radiatively cools the fissioning dusty core and magnetically controls the fragments direction to practically implement previously patented, but unworkable designs. The spacecraft hosting this engine is no more complex nor more massive than the International Space Station (ISS) and would employ the successful ISS technology for assembly and check-out. The elements can be lifted in "chunks" by a Heavy Lift Launcher. This Exploration Spacecraft would require the resupply of small amounts of nuclear fuel for each journey and would be an in-space asset for decades just as any Cruise Liner on Earth. This study has synthesized versions of the FFRE, integrated one concept onto a host spacecraft designed for manned travel to Jupiter's moon, Callisto, and assessed that round trip journey. This engine, although unoptimized, produced 10 pounds force of thrust at a delivered specific impulse of 527,000 seconds for the entire 15-year mission while providing enormous amounts of electrical power to the spacecraft. A payload of 60 metric tons, included in the 300 metric ton vehicle, was carried to Callisto and back; the propellant tanks holding the 4 metric tons of fuel were not jettisoned in the process. The study concluded that the engine and spacecraft are within today's technology, could be built, tested, launched on several SLS (Space Launch System) (or similar) launchers, integrated, checked out, moved to an in-space base such as at a Lagrange point and operated for decades.

KSC-99pp0859

NASA Image and Video Library

1999-07-16

KENNEDY SPACE CENTER, FLA. -- Former Apollo astronaut Gene Cernan makes a point during a presentation at the Apollo 11 anniversary banquet honoring the Apollo team, the people who made the entire lunar landing program possible. The banquet was held in the Apollo/Saturn V Center, part of the KSC Visitor Complex. This is the 30th anniversary of the Apollo 11 launch and moon landing, July 16 and July 20, 1969. Cernan appeared with other former astronauts Neil Armstrong, the first man to walk on the moon; Edwin "Buzz" Aldrin; Walt Cunningham; and others

NASA Provides Coast-to-Coast Coverage of Aug. 21 Solar Eclipse (Moon's Shadow Seen From Gulfstream III Aircraft, Off Oregon Coast)

NASA Image and Video Library

2017-08-21

On Monday, Aug. 21 NASA provided coast-to-coast coverage of the solar eclipse across America- featuring views of the phenomenon from unique vantage points, including from the ground, from aircraft, and from spacecraft including the ISS, during live broadcast seen on NASA Television and the agency’s website. Footage of the moon's shadow moving across the planet is captured from NASA's Gulfstream III aircraft as it flew in the skies off the coast of Oregon during the Aug. 21 solar eclipse

Earth to Moon Transfers - Direct vs Via Libration Points (L1, L2)

NASA Technical Reports Server (NTRS)

Condon, Gerald L.; Wilson, Sam

2002-01-01

Recommend Direct Remote Ocean Area impact disposal for caseswithout hazardous (e.g., radioactive) material on LTV kickstage Controlled Earth contact. Relatively small disposal AV. Avoids close encounter with Moon. Trajectories can be very sensitive to initial conditions (at disposalmaneuver).V to correct for errors is small. Recommend Heliocentric Orbit disposal for cases with hazardousmaterial on LTV kickstage. No Earth or Lunar disposal issues (e.g.. impact location, debris footprint,litter). Relatively low disposal AV cost. Further study required to determine possibility of re-contact with Earth.

Evolution of the Janus-Epimetheus coorbital resonance due to torques from Saturn's rings

NASA Technical Reports Server (NTRS)

Lissauer, J. J.; Goldreich, P.; Tremaine, S.

1985-01-01

The effects of the gravitational interactions between Saturn's rings and the coorbital satellites, Janus and Epimetheus, on the 1:1 horseshoe resonance between these moons is examined. It is shown that the 7:6 resonance of these moons, which presumably maintains the sharp outer edge of the A ring, leads to a rapid tightening of the coorbital lock. The results lead to the prediction that the orbital configuration might evolve from the current horseshoe-type lock to one of tadpole orbits around a single Lagrangian point in about 20 myr.

The Relation Among the Likelihood Ratio-, Wald-, and Lagrange Multiplier Tests and Their Applicability to Small Samples,

DTIC Science & Technology

1982-04-01

S. (1979), "Conflict Among Criteria for Testing Hypothesis: Extension and Comments," Econometrica, 47, 203-207 Breusch , T. S. and Pagan , A. R. (1980...Savin, N. E. (1977), "Conflict Among Criteria for Testing Hypothesis in the Multivariate Linear Regression Model," Econometrica, 45, 1263-1278 Breusch , T...VNCLASSIFIED RAND//-6756NL U l~ I- THE RELATION AMONG THE LIKELIHOOD RATIO-, WALD-, AND LAGRANGE MULTIPLIER TESTS AND THEIR APPLICABILITY TO SMALL SAMPLES

Subscale Fast Cookoff Testing and Modeling for the Hazard Assessment of Large Rocket Motors

DTIC Science & Technology

2001-03-01

41 LIST OF TABLES Table 1 Heats of Vaporization Parameter for Two-liner Phase Transformation - Complete Liner Sublimation and/or Combined Liner...One-dimensional 2-D Two-dimensional ALE3D Arbitrary-Lagrange-Eulerian (3-D) Computer Code ALEGRA 3-D Arbitrary-Lagrange-Eulerian Computer Code for...case-liner bond areas and in the grain inner bore to explore the pre-ignition and ignition phases , as well as burning evolution in rocket motor fast

50 CFR 660.112 - Trawl fishery-prohibitions.

Code of Federal Regulations, 2010 CFR

2010-10-01

... reports of groundfish landings, containing all data, and in the exact manner, required by the regulation.../Biogenic Area, Farallon Islands/Fanny Shoal, Half Moon Bay, Monterey Bay/Canyon, Point Sur Deep, Big Sur...

Pan Progress

NASA Image and Video Library

2007-01-18

Pan is seen in this color view as it sweeps through the Encke Gap with its attendant ringlets. As the lemon-shaped little moon orbits Saturn, it always keeps its long axis pointed along a line toward the planet

Human Exploration on the Moon, Mars and NEOs: PEX.2/ICEUM12B

NASA Astrophysics Data System (ADS)

Foing, Bernard H.

2016-07-01

The session COSPAR-16-PEX.2: "Human Exploration on the Moon, Mars and NEOs", co-sponsored by Commissions B, F will include solicited and contributed talks and poster/interactive presentations. It will also be part of the 12th International Conference on Exploration and Utilisation of the Moon ICEUM12B from the ILEWG ICEUM series started in 1994. It will address various themes and COSPAR communities: - Sciences (of, on, from) the Moon enabled by humans - Research from cislunar and libration points - From robotic villages to international lunar bases - Research from Mars & NEOs outposts - Humans to Phobos/Deimos, Mars and NEOS - Challenges and preparatory technologies, field research operations - Human and robotic partnerships and precursor missions - Resource utilisation, life support and sustainable exploration - Stakeholders for human exploration One half-day session will be dedicated to a workshop format and meetings/reports of task groups: Science, Technology, Agencies, Robotic village, Human bases, Society & Commerce, Outreach, Young Explorers. COSPAR has provided through Commissions, Panels and Working Groups (such as ILEWG, IMEWG) an international forum for supporting and promoting the robotic and human exploration of the Moon, Mars and NEOS. Proposed sponsors : ILEWG, ISECG, IKI, ESA, NASA, DLR, CNES, ASI, UKSA, JAXA, ISRO, SRON, CNSA, SSERVI, IAF, IAA, Lockheed Martin, Google Lunar X prize, UNOOSA

On Choosing a Rational Flight Trajectory to the Moon

NASA Astrophysics Data System (ADS)

Gordienko, E. S.; Khudorozhkov, P. A.

2017-12-01

The algorithm for choosing a trajectory of spacecraft flight to the Moon is discussed. The characteristic velocity values needed for correcting the flight trajectory and a braking maneuver are estimated using the Monte Carlo method. The profile of insertion and flight to a near-circular polar orbit with an altitude of 100 km of an artificial lunar satellite (ALS) is given. The case of two corrections applied during the flight and braking phases is considered. The flight to an ALS orbit is modeled in the geocentric geoequatorial nonrotating coordinate system with the influence of perturbations from the Earth, the Sun, and the Moon factored in. The characteristic correction costs corresponding to corrections performed at different time points are examined. Insertion phase errors, the errors of performing the needed corrections, and the errors of determining the flight trajectory parameters are taken into account.

Uranus' largest moon Oberon

NASA Technical Reports Server (NTRS)

1986-01-01

Uranus' outermost and largest moon, Oberon, is seen in this Voyager 2 image, obtained Jan. 22, 1986, from a distance of 2.77 million kilometers (1.72 million miles). The clear-filter image, shuttered by Voyager's narrow-angle camera, shows that Oberon displays several distinct highly reflective (high-albedo) patches with low-albedo centers. Some of the bright patches are suggestive of radial patterns that could represent impact craters excavated from an icy surface. On average, Oberon reflects about 20 percent of the incident sunlight. The moon is about 1,600 km (1,000 mi) in diameter; resolution of this image is 51 km (32 mi). It was taken two days before Voyager's closest approach to Oberon, at which point the spacecraft will be about 471,000 km (293,000 mi) away. The Voyager project is managed for NASA by the Jet Propulsion Laboratory.

Relationship between seismic status of Earth and relative position of bodies in sun-earth-moon system

NASA Astrophysics Data System (ADS)

Kulanin, N. V.

1985-03-01

The time spectrum of variations in seismicity is quite broad. There are seismic seasons, as well as multiannual variations. The range of characteristic times of variation from days to about one year is studied. Seismic activity as a function of the position of the moon relative to the Earth and the direction toward the Sun is studied. The moments of strong earthquakes, over 5.8 on the Richter scale, between 1968 and June 1980 are plotted in time coordinates relating them to the relative positions of the three bodies in the sun-earth-moon system. Methods of mathematical statistics are applied to the points produced, indicating at least 99% probability that the distribution was not random. a periodicity of the earth's seismic state of 413 days is observed.

Lunar-based Earth observation geometrical characteristics research

NASA Astrophysics Data System (ADS)

Ren, Yuanzhen; Liu, Guang; Ye, Hanlin; Guo, Huadong; Ding, Yixing; Chen, Zhaoning

2016-07-01

As is known to all, there are various platforms for carrying sensors to observe Earth, such as automobiles, aircrafts and satellites. Nowadays, we focus on a new platform, Moon, because of its longevity, stability and vast space. These advantages make it to be the next potential platform for observing Earth, enabling us to get the consistent and global measurements. In order to get a better understanding of lunar-based Earth observation, we discuss its geometrical characteristics. At present, there are no sensors on the Moon for observing Earth and we are not able to obtain a series of real experiment data. As a result, theoretical modeling and numerical calculation are used in this paper. At first, we construct an approximate geometrical model of lunar-based Earth observation, which assumes that Earth and Moon are spheres. Next, we calculate the position of Sun, Earth and Moon based on the JPL ephemeris. With the help of positions data and geometrical model, it is possible for us to decide the location of terminator and substellar points. However, in order to determine their precise position in the conventional terrestrial coordinate system, reference frames transformations are introduced as well. Besides, taking advantages of the relative positions of Sun, Earth and Moon, we get the total coverage of lunar-based Earth optical observation. Furthermore, we calculate a more precise coverage, considering placing sensors on different positions of Moon, which is influenced by its attitude parameters. In addition, different ephemeris data are compared in our research and little difference is found.

Supermoon

NASA Image and Video Library

2017-12-08

Share YOUR Supermoon images with NASA in our Flickr Group: www.flickr.com/groups/supermoon2013/ Up there in the sky – it's not a bird or a plane; it's a "Supermoon." Bigger and brighter then normal full moons, the supermoon on June 22/23 will be the closest and largest full moon for all of 2013. The moon will be some 29,000 miles closer to Earth than the farthest point in its orbit, but not to worry the moon will still be more than 221,000 miles away from our blue planet. --- This is an animation of the moon that was created using data from NASA's LRO satellite. Details: Time: Sunday, June 23, 2013, 15:00 UT (11:00 AM EDT) Phase: 99.9% Diameter:2007.5 arcseconds Distance:357015 km (28.02 Earth diameters) J2000 Right Ascension, Declination18h 17m 42s, -19° 31' 35" Subsolar Longitude, Latitude-1.905°, -1.129° Sub-Earth Longitude, Latitude0.093°, -5.002° Position Angle:359.213° Credit: NASA/Goddard/LRO More images and animarions of the moon can be found here: 1.usa.gov/14bPRjT NASA image use policy. NASA Goddard Space Flight Center enables NASA’s mission through four scientific endeavors: Earth Science, Heliophysics, Solar System Exploration, and Astrophysics. Goddard plays a leading role in NASA’s accomplishments by contributing compelling scientific knowledge to advance the Agency’s mission. Follow us on Twitter Like us on Facebook Find us on Instagram

An Exposition on the Nonlinear Kinematics of Shells, Including Transverse Shearing Deformations

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.

2013-01-01

An in-depth exposition on the nonlinear deformations of shells with "small" initial geometric imperfections, is presented without the use of tensors. First, the mathematical descriptions of an undeformed-shell reference surface, and its deformed image, are given in general nonorthogonal coordinates. The two-dimensional Green-Lagrange strains of the reference surface derived and simplified for the case of "small" strains. Linearized reference-surface strains, rotations, curvatures, and torsions are then derived and used to obtain the "small" Green-Lagrange strains in terms of linear deformation measures. Next, the geometry of the deformed shell is described mathematically and the "small" three-dimensional Green-Lagrange strains are given. The deformations of the shell and its reference surface are related by introducing a kinematic hypothesis that includes transverse shearing deformations and contains the classical Love-Kirchhoff kinematic hypothesis as a proper, explicit subset. Lastly, summaries of the essential equations are given for general nonorthogonal and orthogonal coordinates, and the basis for further simplification of the equations is discussed.

Augmented Lagrange Hopfield network for solving economic dispatch problem in competitive environment

NASA Astrophysics Data System (ADS)

Vo, Dieu Ngoc; Ongsakul, Weerakorn; Nguyen, Khai Phuc

2012-11-01

This paper proposes an augmented Lagrange Hopfield network (ALHN) for solving economic dispatch (ED) problem in the competitive environment. The proposed ALHN is a continuous Hopfield network with its energy function based on augmented Lagrange function for efficiently dealing with constrained optimization problems. The ALHN method can overcome the drawbacks of the conventional Hopfield network such as local optimum, long computational time, and linear constraints. The proposed method is used for solving the ED problem with two revenue models of revenue based on payment for power delivered and payment for reserve allocated. The proposed ALHN has been tested on two systems of 3 units and 10 units for the two considered revenue models. The obtained results from the proposed methods are compared to those from differential evolution (DE) and particle swarm optimization (PSO) methods. The result comparison has indicated that the proposed method is very efficient for solving the problem. Therefore, the proposed ALHN could be a favorable tool for ED problem in the competitive environment.

Holonomicity analysis of electromechanical systems

NASA Astrophysics Data System (ADS)

Wcislik, Miroslaw; Suchenia, Karol

2017-12-01

Electromechanical systems are described using state variables that contain electrical and mechanical components. The equations of motion, both electrical and mechanical, describe the relationships between these components. These equations are obtained using Lagrange functions. On the basis of the function and Lagrange - d'Alembert equation the methodology of obtaining equations for electromechanical systems was presented, together with a discussion of the nonholonomicity of these systems. The electromechanical system in the form of a single-phase reluctance motor was used to verify the presented method. Mechanical system was built as a system, which can oscillate as the element of physical pendulum. On the base of the pendulum oscillation, parameters of the electromechanical system were defined. The identification of the motor electric parameters as a function of the rotation angle was carried out. In this paper the characteristics and motion equations parameters of the motor are presented. The parameters of the motion equations obtained from the experiment and from the second order Lagrange equations are compared.

Size effects in non-linear heat conduction with flux-limited behaviors

NASA Astrophysics Data System (ADS)

Li, Shu-Nan; Cao, Bing-Yang

2017-11-01

Size effects are discussed for several non-linear heat conduction models with flux-limited behaviors, including the phonon hydrodynamic, Lagrange multiplier, hierarchy moment, nonlinear phonon hydrodynamic, tempered diffusion, thermon gas and generalized nonlinear models. For the phonon hydrodynamic, Lagrange multiplier and tempered diffusion models, heat flux will not exist in problems with sufficiently small scale. The existence of heat flux needs the sizes of heat conduction larger than their corresponding critical sizes, which are determined by the physical properties and boundary temperatures. The critical sizes can be regarded as the theoretical limits of the applicable ranges for these non-linear heat conduction models with flux-limited behaviors. For sufficiently small scale heat conduction, the phonon hydrodynamic and Lagrange multiplier models can also predict the theoretical possibility of violating the second law and multiplicity. Comparisons are also made between these non-Fourier models and non-linear Fourier heat conduction in the type of fast diffusion, which can also predict flux-limited behaviors.

A macroscopic plasma Lagrangian and its application to wave interactions and resonances

NASA Technical Reports Server (NTRS)

Peng, Y. K. M.

1974-01-01

The derivation of a macroscopic plasma Lagrangian is considered, along with its application to the description of nonlinear three-wave interaction in a homogeneous plasma and linear resonance oscillations in a inhomogeneous plasma. One approach to obtain the Lagrangian is via the inverse problem of the calculus of variations for arbitrary first and second order quasilinear partial differential systems. Necessary and sufficient conditions for the given equations to be Euler-Lagrange equations of a Lagrangian are obtained. These conditions are then used to determine the transformations that convert some classes of non-Euler-Lagrange equations to Euler-Lagrange equation form. The Lagrangians for a linear resistive transmission line and a linear warm collisional plasma are derived as examples. Using energy considerations, the correct macroscopic plasma Lagrangian is shown to differ from the velocity-integrated low Lagrangian by a macroscopic potential energy that equals twice the particle thermal kinetic energy plus the energy lost by heat conduction.

NASA's SDO Shows Moon Transiting the Sun

NASA Image and Video Library

2017-12-08

On Nov. 22, 2014 from 5:29 to 6:04 p.m. EST., the moon partially obscured the view of the sun from NASA's Solar Dynamics Observatory. This phenomenon, which is called a lunar transit, could only be seen from SDO's point of view. In 2014, SDO captured four such transits -- including its longest ever recorded, which occurred on Jan. 30, and lasted two and a half hours. SDO imagery during a lunar transit always shows a crisp horizon on the moon -- a reflection of the fact that the moon has no atmosphere around it to distort the light from the sun. The horizon is so clear in these images that mountains and valleys in the terrain can be seen. Credit: NASA/SDO NASA image use policy. NASA Goddard Space Flight Center enables NASA’s mission through four scientific endeavors: Earth Science, Heliophysics, Solar System Exploration, and Astrophysics. Goddard plays a leading role in NASA’s accomplishments by contributing compelling scientific knowledge to advance the Agency’s mission. Follow us on Twitter Like us on Facebook Find us on Instagram

High-Resolution Mars Camera Test Image of Moon (Infrared)

NASA Technical Reports Server (NTRS)

2005-01-01

This crescent view of Earth's Moon in infrared wavelengths comes from a camera test by NASA's Mars Reconnaissance Orbiter spacecraft on its way to Mars. The mission's High Resolution Imaging Science Experiment camera took the image on Sept. 8, 2005, while at a distance of about 10 million kilometers (6 million miles) from the Moon. The dark feature on the right is Mare Crisium. From that distance, the Moon would appear as a star-like point of light to the unaided eye. The test verified the camera's focusing capability and provided an opportunity for calibration. The spacecraft's Context Camera and Optical Navigation Camera also performed as expected during the test.

The Mars Reconnaissance Orbiter, launched on Aug. 12, 2005, is on course to reach Mars on March 10, 2006. After gradually adjusting the shape of its orbit for half a year, it will begin its primary science phase in November 2006. From the mission's planned science orbit about 300 kilometers (186 miles) above the surface of Mars, the high resolution camera will be able to discern features as small as one meter or yard across.

Smart-1 Moon Impact Operations

NASA Technical Reports Server (NTRS)

Ayala, Andres; Rigger, Ralf

2007-01-01

This paper describes the operations to control the Moon impact of the 3-axis stabilized spacecraft SMART-1 in September 2006. SMART-1 was launched on 27/09/2003. It was the first ESA mission to use an Electric Propulsion (EP) engine as the main motor to spiral out of the Earth gravity field and reach a scientific moon orbit [1]. During September 2005 the last EP maneuvers were performed using the remaining Xenon, in order to compensate for the 3rd body perturbations of the Sun and Earth. These operations extended the mission for an additional year. Afterwards the EP performance became unpredictable and low, so that no meaningful operation for the moon impact could be done. To move the predicted impact point on the 16/8/2006 into visibility from Earth an alternative Delta-V strategy was designed. Due to their alignment, the attitude thrusters could not be used directly to generate the Delta-V, so this strategy was based on controlled angular momentum biasing. Firing along the velocity vector around apolune, the remaining Hydrazine left from the attitude control budget was used, to shift the impact to the required coordinates.

An Overview of the Formation and Attitude Control System for the Terrestrial Planet Finder Formation Flying Interferometer

NASA Technical Reports Server (NTRS)

Scharf, Daniel P.; Hadaegh, Fred Y.; Rahman, Zahidul H.; Shields, Joel F.; Singh, Gurkipal; Wette, Matthew R.

2004-01-01

The Terrestrial Planet Finder formation flying Interferometer (TPF-I) will be a five-spacecraft, precision formation operating near the second Sun-Earth Lagrange point. As part of technology development for TPF-I, a formation and attitude control system (FACS) is being developed that achieves the precision and functionality needed for the TPF-I formation and that will be demonstrated in a distributed, real-time simulation environment. In this paper we present an overview of FACS and discuss in detail its formation estimation, guidance and control architectures and algorithms. Since FACS is currently being integrated into a high-fidelity simulation environment, component simulations demonstrating algorithm performance are presented.

An Overview of the Formation and Attitude Control System for the Terrestrial Planet Finder Formation Flying Interferometer

NASA Technical Reports Server (NTRS)

Scharf, Daniel P.; Hadaegh, Fred Y.; Rahman, Zahidul H.; Shields, Joel F.; Singh, Gurkipal

2004-01-01

The Terrestrial Planet Finder formation flying Interferometer (TPF-I) will be a five-spacecraft, precision formation operating near a Sun-Earth Lagrange point. As part of technology development for TPF-I, a formation and attitude control system (FACS) is being developed that achieves the precision and functionality associated with the TPF-I formation. This FACS will be demonstrated in a distributed, real-time simulation environment. In this paper we present an overview of the FACS and discuss in detail its constituent formation estimation, guidance and control architectures and algorithms. Since the FACS is currently being integrated into a high-fidelity simulation environment, component simulations demonstrating algorithm performance are presented.

Besieged by Trojans: Material Exchange between Tethys and its Coorbital Moons

NASA Astrophysics Data System (ADS)

Nayak, Michael; Rhoden, Alyssa R.; Asphaug, Erik

2016-10-01

Two small Trojan moons are coorbital with the Saturnian moon Tethys: Calypso (20-km diameter) resides in the trailing L5 Lagrangian point of Tethys' orbit around Saturn, while Telesto (25-km diameter) occupies the leading L4 Lagrangian point. Due to their fixed location with respect to Tethys, consistent material transfer to Tethys occurs whenever there is a primary impact on either of the Trojan moons. Here we investigate this material exchange, and its implications for the cratering history of Tethys. Multiple craters in excess of 1-km in diameter are seen on both Trojan moons [1]. We model the evolution of ejecta escaping from the largest five and seven craters on Calypso and Telesto respectively. The Maxwell Z-model [2] is used, with an implicit gravity-regime cratering assumption, to approximate outbound ejecta velocity distributions. The smallest craters considered on Calypso and Telesto are 1.35 and 1.9 km in diameter respectively; these impacts would have generated a significant amount of sesquinary ejecta [3] in orbits coorbital to that of Tethys. We model the evolution of these sesquinary ejecta in the Saturnian gravity system across 100 years and track their impact locations [e.g. 4]. Our results show that a large fraction of sesquinary ejecta created by primary impacts to either Trojan is likely to impact Tethys; the coorbital nature of the source bodies results in a significant fraction of this ejecta being incident at low impact velocities and low (oblique) impact angles. We present results of ongoing work to convolve these results with observed crater populations and morphologies on Tethys. The persistence of sesquinary impactors inbound to Tethys suggests that such impacts are a relatively frequent process. Additional sources of impactor material, such as from material excavated by primary impacts to Tethys and later reaccreted, will also be discussed. [1] Thomas et al., 2013, Icarus [2] Melosh, 1989, Oxford Univ. Press [3] Zahnle et al., 2008, Icarus [4] Nayak and Asphaug, 2016, Nature Communications.

Spacecraft transfer trajectory design exploiting resonant orbits in multi-body environments

NASA Astrophysics Data System (ADS)

Vaquero Escribano, Tatiana Mar

Historically, resonant orbits have been employed in mission design for multiple planetary flyby trajectories and, more recently, as a source of long-term orbital stability. For instance, in support of a mission concept in NASA's Outer Planets Program, the Jupiter Europa Orbiter spacecraft is designed to encounter two different resonances with Europa during the 'endgame' phase, leading to Europa orbit insertion on the final pass. In 2011, the Interstellar Boundary Explorer spacecraft was inserted into a stable out-of-plane lunar-resonant orbit, the first of this type for a spacecraft in a long-term Earth orbit. However, resonant orbits have not yet been significantly explored as transfer mechanisms between non-resonant orbits in multi-body systems. This research effort focuses on incorporating resonant orbits into the design process to potentially enable the construction of more efficient or even novel transfer scenarios. Thus, the goals in this investigation are twofold: i) to expand the orbit architecture in multi-body environments by cataloging families of resonant orbits, and ii) to assess the role of such families in the design of transfer trajectories with specific patterns and itineraries. The benefits and advantages of employing resonant orbits in the design process are demonstrated through a variety of astrodynamics applications in several multi-body systems. In the Earth-Moon system, locally optimal transfer trajectories from low Earth orbit to selected libration point orbits are designed by leveraging conic arcs and invariant manifolds associated with resonant orbits. Resonant manifolds in the Earth-Moon system offer trajectories that tour the entire space within reasonable time intervals, facilitating the design of libration point orbit tours as well as Earth-Moon cyclers. In the Saturnian system, natural transitions between resonant and libration point orbits are sought and the problem of accessing Hyperion from orbits that are resonant with Titan is also examined. To add versatility to the proposed design method, a system translation technique enables the straightforward transition of solutions from the Earth-Moon system to any Sun-planet or planet-moon three-body system. The circular restricted three-body problem serves as a basis to quickly generate solutions that meet specific requirements, but candidate transfer trajectories are then transitioned to an ephemeris model for validation.

Lunar flyby transfers between libration point orbits

NASA Astrophysics Data System (ADS)

Qi, Yi; Xu, Shijie; Qi, Rui

2017-06-01

Lunar flyby or lunar gravity assist is a classical technique to change the energy and trajectory of space vehicle in space mission. In this paper, lunar flyby transfers between Sun-Earth/Moon libration point orbits with different energies are investigated in the Sun-Earth-Moon restricted four-body problem. Distinguished by behaviours before and after lunar flyby, classification of lunar flyby orbits is defined and studied. Research indicates that junction point of special regions of four types of lunar flyby orbits denotes the perilune of lunar flyby transfer between libration point orbits. Based on those special perilunes, retrograde and prograde lunar flyby transfers are discussed in detail, respectively. The mean energy level transition distribution is proposed and applied to analyse the influence of phase angle and eccentricity on lunar flyby transfers. The phase space is divided into normal and chaotic intervals based on the topology pattern of transfers. A continuation strategy of lunar flyby transfer in the bicircular model is presented. Numerical examples show that compared with the single-impulse transfers based on patched invariant manifolds, lunar flyby transfers are more energy efficient. Finally, lunar flyby transfers are further extended to the realistic models.

Scientific objectives and selection of targets for the SMART-1 Infrared Spectrometer (SIR)

USGS Publications Warehouse

Basilevsky, A.T.; Keller, H.U.; Nathues, A.; Mall, U.; Hiesinger, H.; Rosiek, M.

2004-01-01

The European SMART-1 mission to the Moon, primarily a testbed for innovative technologies, was launched in September 2003 and will reach the Moon in 2005. On board are several scientific instruments, including the point-spectrometer SMART-1 Infrared Spectrometer (SIR). Taking into account the capabilities of the SMART-1 mission and the SIR instrument in particular, as well as the open questions in lunar science, a selection of targets for SIR observations has been compiled. SIR can address at least five topics: (1) Surface/regolith processes; (2) Lunar volcanism; (3) Lunar crust structure; (4) Search for spectral signatures of ices at the lunar poles; and (5) Ground truth and study of geometric effects on the spectral shape. For each topic we will discuss specific observation modes, necessary to achieve our scientific goals. The majority of SIR targets will be observed in the nadir-tracking mode. More than 100 targets, which require off-nadir pointing and off-nadir tracking, are planned. It is expected that results of SIR observations will significantly increase our understanding of the Moon. Since the exact arrival date and the orbital parameters of the SMART-1 spacecraft are not known yet, a more detailed planning of the scientific observations will follow in the near future. ?? 2004 Elsevier Ltd. All rights reserved.

Observation of the shadowing of cosmic rays by the Moon using a deep underground detector

NASA Astrophysics Data System (ADS)

Ambrosio, M.; Antolini, R.; Aramo, C.; Auriemma, G.; Baldini, A.; Barbarino, G. C.; Barish, B. C.; Battistoni, G.; Bellotti, R.; Bemporad, C.; Bernardini, P.; Bilokon, H.; Bisi, V.; Bloise, C.; Bower, C.; Bussino, S.; Cafagna, F.; Calicchio, M.; Campana, D.; Carboni, M.; Castellano, M.; Cecchini, S.; Cei, F.; Chiarella, V.; Choudhary, B. C.; Coutu, S.; de Benedictis, L.; de Cataldo, G.; Dekhissi, H.; de Marzo, C.; de Mitri, I.; Derkaoui, J.; de Vincenzi, M.; di Credico, A.; Erriquez, O.; Favuzzi, C.; Forti, C.; Fusco, P.; Giacomelli, G.; Giannini, G.; Giglietto, N.; Giorgini, M.; Grassi, M.; Gray, L.; Grillo, A.; Guarino, F.; Guarnaccia, P.; Gustavino, C.; Habig, A.; Hanson, K.; Heinz, R.; Huang, Y.; Iarocci, E.; Katsavounidis, E.; Kearns, E.; Kim, H.; Kyriazopoulou, S.; Lamanna, E.; Lane, C.; Levin, D. S.; Lipari, P.; Longley, N. P.; Longo, M. J.; Maaroufi, F.; Mancarella, G.; Mandrioli, G.; Manzoor, S.; Neri, A. Margiotta; Marini, A.; Martello, D.; Marzari-Chiesa, A.; Mazziotta, M. N.; Mazzotta, C.; Michael, D. G.; Mikheyev, S.; Miller, L.; Monacelli, P.; Montaruli, T.; Monteno, M.; Mufson, S.; Musser, J.; Nicoló, D.; Orth, C.; Osteria, G.; Ouchrif, M.; Palamara, O.; Patera, V.; Patrizii, L.; Pazzi, R.; Peck, C. W.; Petrera, S.; Pistilli, P.; Popa, V.; Pugliese, V.; Rainò, A.; Reynoldson, J.; Ronga, F.; Rubizzo, U.; Satriano, C.; Satta, L.; Scapparone, E.; Scholberg, K.; Sciubba, A.; Serra-Lugaresi, P.; Severi, M.; Sioli, M.; Sitta, M.; Spinelli, P.; Spinetti, M.; Spurio, M.; Steinberg, R.; Stone, J. L.; Sulak, L. R.; Surdo, A.; Tarlè, G.; Togo, V.; Ugolotti, D.; Vakili, M.; Walter, C. W.; Webb, R.

1999-01-01

Using data collected by the MACRO experiment during the years 1989-1996, we show evidence for the shadow of the Moon in the underground cosmic ray flux with a significance of 3.6σ. This detection of the shadowing effect is the first by an underground detector. A maximum-likelihood analysis is used to determine that the angular resolution of the apparatus is 0.9°+/-0.3°. These results demonstrate MACRO's capabilities as a muon telescope by confirming its absolute pointing ability and quantifying its angular resolution.

[Dogs, man-wolves and full moon].

PubMed

Goddemeier, Christof

2002-06-01

According to a study of the British Medical Journal in England the incidence of dog bites increases at the time of a full moon. The following article first passes the myths dealing with the werewolf. By changing from delinquent to patient during the Enlightenment the werewolf gets important to the history of medicine and psychiatry. From the anthropological point of view the so-called Lycorexia may be understood as an unconscious effort to undo evolution by transformation into beast. By the figure of the "Huckup" in recent variants concerning the werewolf subject a psychological turn of the legend is expressed.

History of the mass of Mercury

NASA Technical Reports Server (NTRS)

Lyttleton, R. A.

1980-01-01

This paper discusses the calculation of the masses of planets, as a means to construct reliable tables for their positions. Emphasis is placed on the four inner planets and the moon, with additional consideration given to the history of the masses of Jupiter and Saturn. A smooth curve can be drawn with the logarithm of the masses of the earth, Venus, Mars, and the moon, but the point for Mercury lies substantially off the curve. An investigation of the material content, surface examination, and planet radius for the planets leads to a reexamination of the history of the value for the mass of Mercury.

Proceedings of the Annual Symposium on Frequency Control (33rd) Held in Atlantic City, New Jersey on 30 May-1 June 1979

DTIC Science & Technology

1979-01-01

from the Bernoullis was Daniel Bernoulli’s n’est pas la meme dans tous les sens", Exercices addition of the acceleration term to the beam e- de Math...frequencies). improved during 1811-1816 by Germain and Lagrange and, finally, the correct derivation was produced 1852 G. Lame, "Leqons sur la ...de la re- tropic membranes and plates (low frequencies) sistance des solides et des solides d’egale by Euler, Jacques Bernoulli, Germin, Lagrange

A novel iterative scheme and its application to differential equations.

PubMed

Khan, Yasir; Naeem, F; Šmarda, Zdeněk

2014-01-01

The purpose of this paper is to employ an alternative approach to reconstruct the standard variational iteration algorithm II proposed by He, including Lagrange multiplier, and to give a simpler formulation of Adomian decomposition and modified Adomian decomposition method in terms of newly proposed variational iteration method-II (VIM). Through careful investigation of the earlier variational iteration algorithm and Adomian decomposition method, we find unnecessary calculations for Lagrange multiplier and also repeated calculations involved in each iteration, respectively. Several examples are given to verify the reliability and efficiency of the method.

Euler-Lagrange formulas for pseudo-Kähler manifolds

NASA Astrophysics Data System (ADS)

Park, JeongHyeong

2016-01-01

Let c be a characteristic form of degree k which is defined on a Kähler manifold of real dimension m > 2 k. Taking the inner product with the Kähler form Ωk gives a scalar invariant which can be considered as a generalized Lovelock functional. The associated Euler-Lagrange equations are a generalized Einstein-Gauss-Bonnet gravity theory; this theory restricts to the canonical formalism if c =c2 is the second Chern form. We extend previous work studying these equations from the Kähler to the pseudo-Kähler setting.

An inverse problem strategy based on forward model evaluations: Gradient-based optimization without adjoint solves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aguilo Valentin, Miguel Alejandro

2016-07-01

This study presents a new nonlinear programming formulation for the solution of inverse problems. First, a general inverse problem formulation based on the compliance error functional is presented. The proposed error functional enables the computation of the Lagrange multipliers, and thus the first order derivative information, at the expense of just one model evaluation. Therefore, the calculation of the Lagrange multipliers does not require the solution of the computationally intensive adjoint problem. This leads to significant speedups for large-scale, gradient-based inverse problems.

Gene Expression Data to Mouse Atlas Registration Using a Nonlinear Elasticity Smoother and Landmark Points Constraints

PubMed Central

Lin, Tungyou; Guyader, Carole Le; Dinov, Ivo; Thompson, Paul; Toga, Arthur; Vese, Luminita

2013-01-01

This paper proposes a numerical algorithm for image registration using energy minimization and nonlinear elasticity regularization. Application to the registration of gene expression data to a neuroanatomical mouse atlas in two dimensions is shown. We apply a nonlinear elasticity regularization to allow larger and smoother deformations, and further enforce optimality constraints on the landmark points distance for better feature matching. To overcome the difficulty of minimizing the nonlinear elasticity functional due to the nonlinearity in the derivatives of the displacement vector field, we introduce a matrix variable to approximate the Jacobian matrix and solve for the simplified Euler-Lagrange equations. By comparison with image registration using linear regularization, experimental results show that the proposed nonlinear elasticity model also needs fewer numerical corrections such as regridding steps for binary image registration, it renders better ground truth, and produces larger mutual information; most importantly, the landmark points distance and L2 dissimilarity measure between the gene expression data and corresponding mouse atlas are smaller compared with the registration model with biharmonic regularization. PMID:24273381

Relative Critical Points

NASA Astrophysics Data System (ADS)

Lewis, Debra

2013-05-01

Relative equilibria of Lagrangian and Hamiltonian systems with symmetry are critical points of appropriate scalar functions parametrized by the Lie algebra (or its dual) of the symmetry group. Setting aside the structures - symplectic, Poisson, or variational - generating dynamical systems from such functions highlights the common features of their construction and analysis, and supports the construction of analogous functions in non-Hamiltonian settings. If the symmetry group is nonabelian, the functions are invariant only with respect to the isotropy subgroup of the given parameter value. Replacing the parametrized family of functions with a single function on the product manifold and extending the action using the (co)adjoint action on the algebra or its dual yields a fully invariant function. An invariant map can be used to reverse the usual perspective: rather than selecting a parametrized family of functions and finding their critical points, conditions under which functions will be critical on specific orbits, typically distinguished by isotropy class, can be derived. This strategy is illustrated using several well-known mechanical systems - the Lagrange top, the double spherical pendulum, the free rigid body, and the Riemann ellipsoids - and generalizations of these systems.

Statistical Study of Turbulence: Spectral Functions and Correlation Coefficients

NASA Technical Reports Server (NTRS)

Frenkiel, Francois N.

1958-01-01

In reading the publications on turbulence of different authors, one often runs the risk of confusing the various correlation coefficients and turbulence spectra. We have made a point of defining, by appropriate concepts, the differences which exist between these functions. Besides, we introduce in the symbols a few new characteristics of turbulence. In the first chapter, we study some relations between the correlation coefficients and the different turbulence spectra. Certain relations are given by means of demonstrations which could be called intuitive rather than mathematical. In this way we demonstrate that the correlation coefficients between the simultaneous turbulent velocities at two points are identical, whether studied in Lagrange's or in Euler's systems. We then consider new spectra of turbulence, obtained by study of the simultaneous velocities along a straight line of given direction. We determine some relations between these spectra and the correlation coefficients. Examining the relation between the spectrum of the turbulence measured at a fixed point and the longitudinal-correlation curve given by G. I. Taylor, we find that this equation is exact only when the coefficient is very small.

Task-space separation principle: a force-field approach to motion planning for redundant manipulators.

PubMed

Tommasino, Paolo; Campolo, Domenico

2017-02-03

In this work, we address human-like motor planning in redundant manipulators. Specifically, we want to capture postural synergies such as Donders' law, experimentally observed in humans during kinematically redundant tasks, and infer a minimal set of parameters to implement similar postural synergies in a kinematic model. For the model itself, although the focus of this paper is to solve redundancy by implementing postural strategies derived from experimental data, we also want to ensure that such postural control strategies do not interfere with other possible forms of motion control (in the task-space), i.e. solving the posture/movement problem. The redundancy problem is framed as a constrained optimization problem, traditionally solved via the method of Lagrange multipliers. The posture/movement problem can be tackled via the separation principle which, derived from experimental evidence, posits that the brain processes static torques (i.e. posture-dependent, such as gravitational torques) separately from dynamic torques (i.e. velocity-dependent). The separation principle has traditionally been applied at a joint torque level. Our main contribution is to apply the separation principle to Lagrange multipliers, which act as task-space force fields, leading to a task-space separation principle. In this way, we can separate postural control (implementing Donders' law) from various types of tasks-space movement planners. As an example, the proposed framework is applied to the (redundant) task of pointing with the human wrist. Nonlinear inverse optimization (NIO) is used to fit the model parameters and to capture motor strategies displayed by six human subjects during pointing tasks. The novelty of our NIO approach is that (i) the fitted motor strategy, rather than raw data, is used to filter and down-sample human behaviours; (ii) our framework is used to efficiently simulate model behaviour iteratively, until it converges towards the experimental human strategies.

Habitation Concepts and Tools for Asteroid Missions and Commercial Applications

NASA Technical Reports Server (NTRS)

Smitherman, David

2010-01-01

In 2009 studies were initiated in response to the Augustine Commission s review of the Human Spaceflight Program to examine the feasibility of additional options for space exploration beyond the lunar missions planned in the Constellation Program. One approach called a Flexible Path option included possible human missions to near-Earth asteroids. This paper presents an overview of possible asteroid missions with emphasis on the habitation options and vehicle configurations conceived for the crew excursion vehicles. One launch vehicle concept investigated for the Flexible Path option was to use a dual launch architecture that could serve a wide variety of exploration goals. The dual launch concept used two medium sized heavy lift launch vehicles for lunar missions as opposed to the single Saturn V architecture used for the Apollo Program, or the one-and-a-half vehicle Ares I / Ares V architecture proposed for the Constellation Program. This dual launch approach was studied as a Flexible Path option for lunar missions and for possible excursions to other destinations like geosynchronous earth orbiting satellites, Lagrange points, and as presented in this paper, asteroid rendezvous. New habitation and exploration systems for the crew are presented that permit crew sizes from 2 to 4, and mission durations from 100 to 360 days. Vehicle configurations are presented that include habitation systems and tools derived from International Space Station (ISS) experience and new extra-vehicular activity tools for asteroid exploration, Figure 1. Findings from these studies and as presented in this paper indicate that missions to near-Earth asteroids appear feasible in the near future using the dual launch architecture, the technologies under development from the Constellation Program, and systems derived from the current ISS Program. In addition, the capabilities derived from this approach that are particularly beneficial to the commercial sector include human access to geosynchronous orbit and the Lagrange points with new tools for satellite servicing and in-space assembly.

Calibration View of Earth and the Moon by Mars Color Imager

NASA Technical Reports Server (NTRS)

2005-01-01

Three days after the Mars Reconnaissance Orbiter's Aug. 12, 2005, launch, the spacecraft was pointed toward Earth and the Mars Color Imager camera was powered up to acquire a suite of images of Earth and the Moon. When it gets to Mars, the Mars Color Imager's main objective will be to obtain daily global color and ultraviolet images of the planet to observe martian meteorology by documenting the occurrence of dust storms, clouds, and ozone. This camera will also observe how the martian surface changes over time, including changes in frost patterns and surface brightness caused by dust storms and dust devils.

The purpose of acquiring an image of Earth and the Moon just three days after launch was to help the Mars Color Imager science team obtain a measure, in space, of the instrument's sensitivity, as well as to check that no contamination occurred on the camera during launch. Prior to launch, the team determined that, three days out from Earth, the planet would only be about 4.77 pixels across, and the Moon would be less than one pixel in size, as seen from the Mars Color Imager's wide-angle perspective. If the team waited any longer than three days to test the camera's performance in space, Earth would be too small to obtain meaningful results.

The Earth and Moon images were acquired by turning Mars Reconnaissance Orbiter toward Earth, then slewing the spacecraft so that the Earth and Moon would pass before each of the five color and two ultraviolet filters of the Mars Color Imager. The distance to the Moon was about 1,440,000 kilometers (about 895,000 miles); the range to Earth was about 1,170,000 kilometers (about 727,000 miles).

This view combines a sequence of frames showing the passage of Earth and the Moon across the field of view of a single color band of the Mars Color Imager. As the spacecraft slewed to view the two objects, they passed through the camera's field of view. Earth has been saturated white in this image so that both Earth and the Moon can be seen in the same frame. The Sun was coming from the left, so Earth and the Moon are seen in a quarter phase. Earth is on the left. The Moon appears briefly on the right. The Moon fades in and out; the Moon is only one pixel in size, and its fading is an artifact of the size and configuration of the light-sensitive pixels of the camera's charge-coupled device (CCD) detector.

Stationkeeping of Lissajous Trajectories in the Earth-Moon System with Applications to ARTEMIS

NASA Technical Reports Server (NTRS)

Folta, D. C.; Pavlak, T. A.; Howell, K. C.; Woodard, M. A.; Woodfork, D. W.

2010-01-01

In the last few decades, several missions have successfully exploited trajectories near the.Sun-Earth L1 and L2 libration points. Recently, the collinear libration points in the Earth-Moon system have emerged as locations with immediate application. Most libration point orbits, in any system, are inherently unstable. and must be controlled. To this end, several stationkeeping strategies are considered for application to ARTEMIS. Two approaches are examined to investigate the stationkeeping problem in this regime and the specific options. available for ARTEMIS given the mission and vehicle constraints. (I) A baseline orbit-targeting approach controls the vehicle to remain near a nominal trajectory; a related global optimum search method searches all possible maneuver angles to determine an optimal angle and magnitude; and (2) an orbit continuation method, with various formulations determines maneuver locations and minimizes costs. Initial results indicate that consistent stationkeeping costs can be achieved with both approaches and the costs are reasonable. These methods are then applied to Lissajous trajectories representing a baseline ARTEMIS libration orbit trajectory.

New Worlds Observer Formation Control Design Based on the Dynamics of Relative Motion

NASA Technical Reports Server (NTRS)

Luquette, Richard J.

2008-01-01

The New Worlds Observer (NWO) mission is designed for the direct detection and characterization of extrasolar planets. The NWO mission concept employs a two spacecraft leader-follower formation on a trajectory around the Earth/Moon-Sun L(sub 2) Libration Point. The leader spacecraft is baselined as a 4 meter optical telescope. The follower, Starshade spacecraft, is designed to suppress light from a central body star permitting direct detection of a surrounding exoplanetary system. The current design requires a nominal leader-follower separation range of 72 Megameters. NWO poses many challenges including formation control. NWO cycles between three principal control modes during the nominal mission timeline: science (fine pointing), realignment and transition. This paper examines formation control strategies in the context of dynamics of relative motion for two spacecraft operating in the vicinity of the Earth/Moon-Sun L(sub 2)libration point. The paper presents an overview of the equations of relative motion followed by a discussion of each of the control modes. Discussion and analysis characterize control strategies for each of the mission control modes, including requirements, implementation challenges and project fuel budgets.

From Galileo's telescope to the Galileo spacecraft: our changing views of the Jupiter system

NASA Astrophysics Data System (ADS)

Lopes, R. M.

2008-12-01

In four centuries, we have gone from the discovery of the four large moons of Jupiter - Io, Europa, Ganymede, and Callisto - to important discoveries about these four very different worlds. Galileo's telescopic discovery was a major turning point in the understanding of science. His observations of the moons' motion around Jupiter challenged the notion of an Earth-centric Universe. A few months later, Galileo discovered the phases of Venus, which had been predicted by the heliocentric model of the Solar System. Galileo also observed the rings of Saturn (which he mistook for planets) and sunspots, and was the first person to report mountains and craters on the Moon, whose existence he deduced from the patterns of light and shadow on the Moon's surface, concluding that the surface was topographically rough. Centuries later, the Galileo spacecraft's discoveries challenged our understanding of outer planet satellites. Results included the discovery of an icy ocean underneath Europa's surface, the possibility of life on Europa, the widespread volcanism on Io, and the detection of a magnetic field around Ganymede. All four of these satellites revealed how the major geologic processes - volcanism, tectonism, impact cratering and erosion - operate in these different bodies, from the total lack of impact craters on Io to the heavily cratered, ancient surface of Callisto. The Galileo spacecraft's journey also took it to Venus and the Moon, making important scientific observations about these bodies. The spacecraft discovered the first moon orbiting around an asteroid which, had Galileo the man observed, would have been another major blow for the geocentric model of our Solar System.

SUPERMOON is here and we want to see YOUR photos of it!

NASA Image and Video Library

2017-12-08

Share YOUR Supermoon images with NASA in our Flickr Group: www.flickr.com/groups/supermoon2013/ Up there in the sky – it's not a bird or a plane; it's a "Supermoon." Bigger and brighter then normal full moons, the supermoon on June 22/23 will be the closest and largest full moon for all of 2013. The moon will be some 29,000 miles closer to Earth than the farthest point in its orbit, but not to worry the moon will still be more than 221,000 miles away from our blue planet. --- This is an animation of the moon that was created using data from NASA's LRO satellite. Details: Time: Sunday, June 23, 2013, 15:00 UT (11:00 AM EDT) Phase: 99.9% Diameter:2007.5 arcseconds Distance:357015 km (28.02 Earth diameters) J2000 Right Ascension, Declination18h 17m 42s, -19° 31' 35" Subsolar Longitude, Latitude-1.905°, -1.129° Sub-Earth Longitude, Latitude0.093°, -5.002° Position Angle:359.213° Credit: NASA/Goddard/LRO More images and animarions of the moon can be found here: 1.usa.gov/14bPRjT NASA image use policy. NASA Goddard Space Flight Center enables NASA’s mission through four scientific endeavors: Earth Science, Heliophysics, Solar System Exploration, and Astrophysics. Goddard plays a leading role in NASA’s accomplishments by contributing compelling scientific knowledge to advance the Agency’s mission. Follow us on Twitter Like us on Facebook Find us on Instagram

Energy variational analysis of ions in water and channels: Field theory for primitive models of complex ionic fluids

PubMed Central

Eisenberg, Bob; Hyon, YunKyong; Liu, Chun

2010-01-01

Ionic solutions are mixtures of interacting anions and cations. They hardly resemble dilute gases of uncharged noninteracting point particles described in elementary textbooks. Biological and electrochemical solutions have many components that interact strongly as they flow in concentrated environments near electrodes, ion channels, or active sites of enzymes. Interactions in concentrated environments help determine the characteristic properties of electrodes, enzymes, and ion channels. Flows are driven by a combination of electrical and chemical potentials that depend on the charges, concentrations, and sizes of all ions, not just the same type of ion. We use a variational method EnVarA (energy variational analysis) that combines Hamilton’s least action and Rayleigh’s dissipation principles to create a variational field theory that includes flow, friction, and complex structure with physical boundary conditions. EnVarA optimizes both the action integral functional of classical mechanics and the dissipation functional. These functionals can include entropy and dissipation as well as potential energy. The stationary point of the action is determined with respect to the trajectory of particles. The stationary point of the dissipation is determined with respect to rate functions (such as velocity). Both variations are written in one Eulerian (laboratory) framework. In variational analysis, an “extra layer” of mathematics is used to derive partial differential equations. Energies and dissipations of different components are combined in EnVarA and Euler–Lagrange equations are then derived. These partial differential equations are the unique consequence of the contributions of individual components. The form and parameters of the partial differential equations are determined by algebra without additional physical content or assumptions. The partial differential equations of mixtures automatically combine physical properties of individual (unmixed) components. If a new component is added to the energy or dissipation, the Euler–Lagrange equations change form and interaction terms appear without additional adjustable parameters. EnVarA has previously been used to compute properties of liquid crystals, polymer fluids, and electrorheological fluids containing solid balls and charged oil droplets that fission and fuse. Here we apply EnVarA to the primitive model of electrolytes in which ions are spheres in a frictional dielectric. The resulting Euler–Lagrange equations include electrostatics and diffusion and friction. They are a time dependent generalization of the Poisson–Nernst–Planck equations of semiconductors, electrochemistry, and molecular biophysics. They include the finite diameter of ions. The EnVarA treatment is applied to ions next to a charged wall, where layering is observed. Applied to an ion channel, EnVarA calculates a quick transient pile-up of electric charge, transient and steady flow through the channel, stationary “binding” in the channel, and the eventual accumulation of salts in “unstirred layers” near channels. EnVarA treats electrolytes in a unified way as complex rather than simple fluids. Ad hoc descriptions of interactions and flow have been used in many areas of science to deal with the nonideal properties of electrolytes. It seems likely that the variational treatment can simplify, unify, and perhaps derive and improve those descriptions. PMID:20849161

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heller, René; Zuluaga, Jorge I., E-mail: rheller@physics.mcmaster.ca, E-mail: jzuluaga@fisica.udea.edu.co

With most planets and planetary candidates detected in the stellar habitable zone (HZ) being super-Earths and gas giants rather than Earth-like planets, we naturally wonder if their moons could be habitable. The first detection of such an exomoon has now become feasible, and due to observational biases it will be at least twice as massive as Mars. However, formation models predict that moons can hardly be as massive as Earth. Hence, a giant planet's magnetosphere could be the only possibility for such a moon to be shielded from cosmic and stellar high-energy radiation. Yet, the planetary radiation belt could alsomore » have detrimental effects on exomoon habitability. Here we synthesize models for the evolution of the magnetic environment of giant planets with thresholds from the runaway greenhouse (RG) effect to assess the habitability of exomoons. For modest eccentricities, we find that satellites around Neptune-sized planets in the center of the HZ around K dwarf stars will either be in an RG state and not be habitable, or they will be in wide orbits where they will not be affected by the planetary magnetosphere. Saturn-like planets have stronger fields, and Jupiter-like planets could coat close-in habitable moons soon after formation. Moons at distances between about 5 and 20 planetary radii from a giant planet can be habitable from an illumination and tidal heating point of view, but still the planetary magnetosphere would critically influence their habitability.« less

The micron- to kilometer-scale Moon: linking samples to orbital observations, Apollo to LRO

NASA Astrophysics Data System (ADS)

Crites, S.; Lucey, P. G.; Taylor, J.; Martel, L.; Sun, L.; Honniball, C.; Lemelin, M.

2017-12-01

The Apollo missions have shaped the field of lunar science and our understanding of the Moon, from global-scale revelations like the magma ocean hypothesis, to providing ground truth for compositional remote sensing and absolute ages to anchor cratering chronologies. While lunar meteorite samples can provide a global- to regional-level view of the Moon, samples returned from known locations are needed to directly link orbital-scale observations with laboratory measurements-a link that can be brought to full fruition with today's extremely high spatial resolution observations from Lunar Reconnaissance Orbiter and other recent missions. Korotev et al. (2005) described a scenario of the Moon without Apollo to speculate about our understanding of the Moon if our data were confined to lunar meteorites and remote sensing. I will review some of the major points discussed by Korotev et al. (2005), and focus on some of the ways in which spectroscopic remote sensing in particular has benefited from the Apollo samples. For example, could the causes and effects of lunar-style space weathering have been unraveled without the Apollo samples? What would be the limitations on remote sensing compositional measurements that rely on Apollo samples for calibration and validation? And what new opportunities to bring together orbital and sample analyses now exist, in light of today's high spatial and spectral resolution remote sensing datasets?

L1 libration point manned space habitat

NASA Technical Reports Server (NTRS)

Luttges, Marvin; Johnson, Steve; Banks, Gary; Johnson, Richard; Meyer, Christian; Pepin, Scott; Macelroy, Robert

1989-01-01

Second generation stations or Manned Space Habitats (MSHs) are discussed for an Earth-Moon libration point and in lunar orbit. The conceptual design of such a station is outlined. Systems and subsystems described reflect anticipation of moderate technology growth. The evolution of the L1 environments is discussed, several selected subsystems are outlined, and how the L1 MSH will complete some of its activities is described.

Project 5S: A Safe Stepping Stone into the Solar System

NASA Technical Reports Server (NTRS)

Brophy, John; Culick, Fred; Dimotakis, Paul; Friedman, Louis

2012-01-01

The human exploration program, at least in NASA, has been directed to move beyond the Moon and travel on a flexible path into the solar system. Reaching a Near-Earth Asteroid (NEA) is a major human space flight goal but such missions have tight times and life-support requirements that require huge steps from current capabilities. An objective between the Moon and a NEA is needed. Example interim objectives are the Lagrangian points in either the Sun-Earth or Earth-Moon (EM) system. The nearest of these points beyond the Moon is E-M L2. The Lagrangian points are empty (as far as we know). As objectives for human flight,it has been argued that they suffer from a lack of public interest and of meaningful objectives for astronaut operations. To provide a physical target, a robotic spacecraft could retrieve a small NEA and bring it to a Lagrangian or other nearer-Earth point to be accessed and utilized for human-mission objectives. This paper reports on the results of a recently completed study of an asteroid retrieval mission sponsored by the Keck Institute for Space Studies (KISS) at the California Institute of Technology. The study included an evaluation of potential targets, mission objectives, mission and system design, and potential capture mechanisms. The study concluded that, while challenging, there are no fundamental show stoppers and that such a mission would be possible with technology expected to be available in this decade. The final destination selected (for safety and mission operations) was high lunar orbit. Two options for target selection are considered: (i) retrieving a small (7 meter) NEA with a mass of order 500,000 kg, and (ii) taking a similar size boulder of a large known carbonaceous NEA. Several areas of technology and program requirements were identified, but the most important conclusion was that this approach enables meeting a goal of humans going to a NEA by the mid-2020s. The advantages and benefits for human exploration are considerable as are the advances that would be made in space-resource utilization and science for further exploration and development of the solar system. The combination of the robotic mission to move the asteroid and the human mission to go to its new destination and conduct astronaut operations there would provide a boost and purpose to human space flight.

Natural motion around the Martian moon Phobos: the dynamical substitutes of the Libration Point Orbits in an elliptic three-body problem with gravity harmonics

NASA Astrophysics Data System (ADS)

Zamaro, M.; Biggs, J. D.

2015-07-01

The Martian moon Phobos is becoming an appealing destination for future scientific missions. The orbital dynamics around this planetary satellite is particularly complex due to the unique combination of both small mass-ratio and length-scale of the Mars-Phobos couple: the resulting sphere of influence of the moon is very close to its surface, therefore both the classical two-body problem and circular restricted three-body problem (CR3BP) do not provide an accurate approximation to describe the spacecraft's dynamics in the vicinity of Phobos. The aim of this paper is to extend the model of the CR3BP to consider the orbital eccentricity and the highly-inhomogeneous gravity field of Phobos, by incorporating the gravity harmonics series expansion into an elliptic R3BP, named ER3BP-GH. Following this, the dynamical substitutes of the Libration Point Orbits (LPOs) are computed in this more realistic model of the relative dynamics around Phobos, combining methodologies from dynamical systems theory and numerical continuation techniques. Results obtained show that the structure of the periodic and quasi-periodic LPOs differs substantially from the classical case without harmonics. Several potential applications of these natural orbits are presented to enable unique low-cost operations in the proximity of Phobos, such as close-range observation, communication, and passive radiation shielding for human spaceflight. Furthermore, their invariant manifolds are demonstrated to provide high-performance natural landing and take-off pathways to and from Phobos' surface, and transfers from and to Martian orbits. These orbits could be exploited in upcoming and future space missions targeting the exploration of this Martian moon.

The Apache Point Observatory Lunar Laser-ranging Operation: Instrument Description and First Detections

DOE Office of Scientific and Technical Information (OSTI.GOV)

Murphy, TW; Adelberger, Eric G.; Battat, J.

2008-01-01

A next-generation lunar laser ranging apparatus using the 3.5 m telescope at the Apache Point Observatory in southern New Mexico has begun science operation. APOLLO (the Apache Point Observatory Lunar Laser-ranging Operation) has achieved one-millimeter range precision to the moon which should lead to aproximately one-orderof-magnitude improvements in the precision of several tests of fundamental properties of gravity. We briefly motivate the scientific goals, and then give a detailed discussion of the APOLLO instrumentation.

Compressible cavitation with stochastic field method

NASA Astrophysics Data System (ADS)

Class, Andreas; Dumond, Julien

2012-11-01

Non-linear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally the simulation of pdf transport requires Monte-Carlo codes based on Lagrange particles or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic field method solving pdf transport based on Euler fields has been proposed which eliminates the necessity to mix Euler and Lagrange techniques or prescribed pdf assumptions. In the present work, part of the PhD Design and analysis of a Passive Outflow Reducer relying on cavitation, a first application of the stochastic field method to multi-phase flow and in particular to cavitating flow is presented. The application considered is a nozzle subjected to high velocity flow so that sheet cavitation is observed near the nozzle surface in the divergent section. It is demonstrated that the stochastic field formulation captures the wide range of pdf shapes present at different locations. The method is compatible with finite-volume codes where all existing physical models available for Lagrange techniques, presumed pdf or binning methods can be easily extended to the stochastic field formulation.

Generalized Lagrange Jacobi Gauss-Lobatto (GLJGL) Collocation Method for Solving Linear and Nonlinear Fokker-Planck Equations

NASA Astrophysics Data System (ADS)

Parand, K.; Latifi, S.; Moayeri, M. M.; Delkhosh, M.

2018-05-01

In this study, we have constructed a new numerical approach for solving the time-dependent linear and nonlinear Fokker-Planck equations. In fact, we have discretized the time variable with Crank-Nicolson method and for the space variable, a numerical method based on Generalized Lagrange Jacobi Gauss-Lobatto (GLJGL) collocation method is applied. It leads to in solving the equation in a series of time steps and at each time step, the problem is reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. One can observe that the proposed method is simple and accurate. Indeed, one of its merits is that it is derivative-free and by proposing a formula for derivative matrices, the difficulty aroused in calculation is overcome, along with that it does not need to calculate the General Lagrange basis and matrices; they have Kronecker property. Linear and nonlinear Fokker-Planck equations are given as examples and the results amply demonstrate that the presented method is very valid, effective, reliable and does not require any restrictive assumptions for nonlinear terms.

Distributed Fault-Tolerant Control of Networked Uncertain Euler-Lagrange Systems Under Actuator Faults.

PubMed

Chen, Gang; Song, Yongduan; Lewis, Frank L

2016-05-03

This paper investigates the distributed fault-tolerant control problem of networked Euler-Lagrange systems with actuator and communication link faults. An adaptive fault-tolerant cooperative control scheme is proposed to achieve the coordinated tracking control of networked uncertain Lagrange systems on a general directed communication topology, which contains a spanning tree with the root node being the active target system. The proposed algorithm is capable of compensating for the actuator bias fault, the partial loss of effectiveness actuation fault, the communication link fault, the model uncertainty, and the external disturbance simultaneously. The control scheme does not use any fault detection and isolation mechanism to detect, separate, and identify the actuator faults online, which largely reduces the online computation and expedites the responsiveness of the controller. To validate the effectiveness of the proposed method, a test-bed of multiple robot-arm cooperative control system is developed for real-time verification. Experiments on the networked robot-arms are conduced and the results confirm the benefits and the effectiveness of the proposed distributed fault-tolerant control algorithms.

Photograph of nearly full moon taken from Apollo 8

NASA Image and Video Library

1968-12-22

AS08-14-2506 (21-27 Dec. 1968) --- This photograph of a nearly full moon was taken from the Apollo 8 spacecraft at a point above 70 degrees east longitude. (Hold picture with moon's dark portion at left). Mare Crisium, the circular, dark-colored area near the center, is near the eastern edge of the moon as viewed from Earth. Mare Nectaris is the circular mare near the terminator. The large, irregular maira are Tranquillitatis and Fecunditatis. The terminator at left side of picture crosses Mare Tranquillitatis and highlands to the south. Lunar farside features occupy most of the right half of the picture. The large, dark-colored crater Tsiolkovsky is near the limb at the lower right. Conspicuous bright rays radiate from two large craters, one to the north of Tsiolkovsky, the other near the limb in the upper half of the picture. These rayed craters were not conspicuous in Lunar Orbiter photography due to the low sun elevations when the Lunar Orbiter photography was made. The crater Langrenus is near the center of the picture at the eastern edge of Mare Fecunditatis. The lunar surface probably has less pronounced color that indicated by this print.

Radio Astronomy on and Around the Moon

NASA Astrophysics Data System (ADS)

Falcke, Heino; Klein Wolt, Mark; Ping, Jinsong; Chen, Linjie

2018-06-01

The exploration of remote places on other planets has now become a major goal in current space flight scenarios. On the other hand, astronomers have always sought the most remote and isolated sites to place their observatories and to make their most precise and most breath taking discoveries. Especially for radio astronomy, lunar exploration offers a complete new window to the universe. The polar region and the far-side of the moon are acknowledged as unique locations for a low-frequency radio telescope providing scientific data at wavelengths that cannot be obtained from the Earth nor from single satellites. Scientific areas to be covered range from radio surveys, to solar-system studies, exo-planet detection, and astroparticle physics. The key science area, however, is the detection and measurement of cosmological 21 cm hydrogen emission from the still unexplored dark ages of the universe. Developing a lunar radio facility can happen in steps and may involve small satellites, rover-based radio antennas, of free- flying constellations around the moon. A first such step could be the Netherlands-Chinese Long Wavelength Explorer (NCLE), which is supposed to be launched in 2018 as part of the ChangE’4 mission to the moon-earth L2 point.

Derivation of the Torque Associated to Tesseral Resonances

NASA Astrophysics Data System (ADS)

El Moutamid, Maryame

2018-04-01

A so-called m+1:m Tesseral Resonance is simply equivalent to an inner m+1:m Lindblad Resonance or an outer Lindblad Resonance, where m is an integer. They are generated between a gravity anomaly that rotates with the primary and a test particle evolving around this primary, instead of being caused by a secondary, meaning that in this case the particle and the secondary do not share the same orbit. We show in this work that the torque is stronger for small values of |m|; as |m| tends to infinity, the torque tends to zero and that the Lagrange points are displaced away from the usual triangular configuration. These simple results have interesting implications on Saturn, Chariklo and Mars.

Distributed optical fiber-based monitoring approach of spatial seepage behavior in dike engineering

NASA Astrophysics Data System (ADS)

Su, Huaizhi; Ou, Bin; Yang, Lifu; Wen, Zhiping

2018-07-01

The failure caused by seepage is the most common one in dike engineering. As to the characteristics of seepage in dike, such as longitudinal extension engineering, the randomness, strong concealment and small initial quantity order, by means of distributed fiber temperature sensor system (DTS), adopting an improved optical fiber layer layout scheme, the location of initial interpolation point of the saturation line is obtained. With the barycentric Lagrange interpolation collocation method (BLICM), the infiltrated surface of dike full-section is generated. Combined with linear optical fiber monitoring seepage method, BLICM is applied in an engineering case, which shows that a real-time seepage monitoring technique is presented in full-section of dike based on the combination method.

WMAP Observatory Thermal Design and On-Orbit Thermal Performance

NASA Technical Reports Server (NTRS)

Glazer, Stuart D.; Brown, Kimberly D.; Michalek, Theodore J.; Ancarrow, Walter C.

2003-01-01

The Wilkinson Microwave Anisotropy Probe (WMAP) observatory, launched June 30, 2001, is designed to measure the cosmic microwave background radiation with unprecedented precision and accuracy while orbiting the second Lagrange point (L2). The instrument cold stage must be cooled passively to <95K, and systematic thermal variations in selected instrument components controlled to less than 0.5 mK (rms) per spin period. This paper describes the thermal design and testing of the WMAP spacecraft and instrument. Flight thermal data for key spacecraft and instrument components are presented from launch through the first year of mission operations. Effects of solar flux variation due to the Earth's elliptical orbit about the sun, surface thermo-optical property degradations, and solar flares on instrument thermal stability are discussed.

Cryogenic Propellant Storage and Transfer (CPST) Technology Maturation: Establishing a Foundation for a Technology Demonstration Mission (TDM)

NASA Technical Reports Server (NTRS)

Doherty, Michael P.; Meyer, Michael L.; Motil, Susan M.; Ginty, Carol A.

2014-01-01

As part of U.S. National Space Policy, NASA is seeking an innovative path for human space exploration, which strengthens the capability to extend human and robotic presence throughout the solar system. NASA is laying the groundwork to enable humans to safely reach multiple potential destinations, including asteroids, Lagrange points, the Moon and Mars. In support of this, NASA is embarking on the Technology Demonstration Mission Cryogenic Propellant Storage and Transfer (TDM CPST) Project to test and validate key cryogenic capabilities and technologies required for future exploration elements, opening up the architecture for large cryogenic propulsion stages (CPS) and propellant depots. The TDM CPST project will provide an on-orbit demonstration of the capability to store, transfer, and measure cryogenic propellants for a duration which is relevant to enable long term human space exploration missions beyond low Earth orbit (LEO). Recognizing that key cryogenic fluid management technologies anticipated for on-orbit (flight) demonstration needed to be matured to a readiness level appropriate for infusion into the design of the flight demonstration, the NASA Headquarters Space Technology Mission Directorate authorized funding for a one-year (FY12) ground based technology maturation program. The strategy, proposed by the CPST Project Manager, focused on maturation through modeling, studies, and ground tests of the storage and fluid transfer Cryogenic Fluid Management (CFM) technology sub-elements and components that were not already at a Technology Readiness Level (TRL) of 5. A technology maturation plan (TMP) was subsequently approved which described: the CFM technologies selected for maturation, the ground testing approach to be used, quantified success criteria of the technologies, hardware and data deliverables, and a deliverable to provide an assessment of the technology readiness after completion of the test, study or modeling activity. This paper will present the testing, studies, and modeling that occurred in FY12 to mature cryogenic fluid management technologies for propellant storage, transfer, and supply, to examine extensibility to full scale, long duration missions, and to develop and validate analytical models. Finally, the paper will briefly describe an upcoming test to demonstrate Liquid Oxygen (LO2) Zero Boil-Off (ZBO).

Cryogenic Propellant Storage and Transfer (CPST) Technology Maturation: Establishing a Foundation for a Technology Demonstration Mission (TDM)

NASA Technical Reports Server (NTRS)

Doherty, Michael P.; Meyer, Michael L.; Motil, Susan M.; Ginty, Carol A.

2013-01-01

As part of U.S. National Space Policy, NASA is seeking an innovative path for human space exploration, which strengthens the capability to extend human and robotic presence throughout the solar system. NASA is laying the groundwork to enable humans to safely reach multiple potential destinations, including asteroids, Lagrange points, the Moon and Mars. In support of this, NASA is embarking on the Technology Demonstration Mission Cryogenic Propellant Storage and Transfer (TDM CPST) Project to test and validate key cryogenic capabilities and technologies required for future exploration elements, opening up the architecture for large cryogenic propulsion stages (CPS) and propellant depots. The TDM CPST project will provide an on-orbit demonstration of the capability to store, transfer, and measure cryogenic propellants for a duration which is relevant to enable long term human space exploration missions beyond low Earth orbit (LEO). Recognizing that key cryogenic fluid management technologies anticipated for on-orbit (flight) demonstration needed to be matured to a readiness level appropriate for infusion into the design of the flight demonstration, the NASA Headquarters Space Technology Mission Directorate authorized funding for a one-year (FY12) ground based technology maturation program. The strategy, proposed by the CPST Project Manager, focused on maturation through modeling, studies, and ground tests of the storage and fluid transfer Cryogenic Fluid Management (CFM) technology sub-elements and components that were not already at a Technology Readiness Level (TRL) of 5. A technology maturation plan (TMP) was subsequently approved which described: the CFM technologies selected for maturation, the ground testing approach to be used, quantified success criteria of the technologies, hardware and data deliverables, and a deliverable to provide an assessment of the technology readiness after completion of the test, study or modeling activity. This paper will present the testing, studies, and modeling that occurred in FY12 to mature cryogenic fluid management technologies for propellant storage, transfer, and supply, to examine extensibility to full scale, long duration missions, and to develop and validate analytical models. Finally, the paper will briefly describe an upcoming test to demonstrate Liquid Oxygen (LO2) Zero Boil- Off (ZBO).

Calibration Image of Earth by Mars Color Imager

NASA Image and Video Library

2005-08-22

Three days after the Mars Reconnaissance Orbiter Aug. 12, 2005, launch, the NASA spacecraft was pointed toward Earth and the Mars Color Imager camera was powered up to acquire a suite of color and ultraviolet images of Earth and the Moon.

Modelling of charged satellite motion in Earth's gravitational and magnetic fields

NASA Astrophysics Data System (ADS)

Abd El-Bar, S. E.; Abd El-Salam, F. A.

2018-05-01

In this work Lagrange's planetary equations for a charged satellite subjected to the Earth's gravitational and magnetic force fields are solved. The Earth's gravity, and magnetic and electric force components are obtained and expressed in terms of orbital elements. The variational equations of orbit with the considered model in Keplerian elements are derived. The solution of the problem in a fully analytical way is obtained. The temporal rate of changes of the orbital elements of the spacecraft are integrated via Lagrange's planetary equations and integrals of the normalized Keplerian motion obtained by Ahmed (Astron. J. 107(5):1900, 1994).

A note on libration point orbits, temporary capture and low-energy transfers

NASA Astrophysics Data System (ADS)

Fantino, E.; Gómez, G.; Masdemont, J. J.; Ren, Y.

2010-11-01

In the circular restricted three-body problem (CR3BP) the weak stability boundary (WSB) is defined as a boundary set in the phase space between stable and unstable motion relative to the second primary. At a given energy level, the boundaries of such region are provided by the stable manifolds of the central objects of the L1 and L2 libration points, i.e., the two planar Lyapunov orbits. Besides, the unstable manifolds of libration point orbits (LPOs) around L1 and L2 have been identified as responsible for the weak or temporary capture around the second primary of the system. These two issues suggest the existence of natural dynamical channels between the Earth's vicinity and the Sun-Earth libration points L1 and L2. Furthermore, it has been shown that the Sun-Earth L2 central unstable manifolds can be linked, through an heteroclinic connection, to the central stable manifolds of the L2 point in the Earth-Moon three-body problem. This concept has been applied to the design of low energy transfers (LETs) from the Earth to the Moon. In this contribution we consider all the above three issues, i.e., weak stability boundaries, temporary capture and low energy transfers, and we discuss the role played by the invariant manifolds of LPOs in each of them. The study is made in the planar approximation.

Planetary maps

USGS Publications Warehouse

,

1992-01-01

An important goal of the USGS planetary mapping program is to systematically map the geology of the Moon, Mars, Venus, and Mercury, and the satellites of the outer planets. These geologic maps are published in the USGS Miscellaneous Investigations (I) Series. Planetary maps on sale at the USGS include shaded-relief maps, topographic maps, geologic maps, and controlled photomosaics. Controlled photomosaics are assembled from two or more photographs or images using a network of points of known latitude and longitude. The images used for most of these planetary maps are electronic images, obtained from orbiting television cameras, various optical-mechanical systems. Photographic film was only used to map Earth's Moon.

Cold-trapped organic compounds at the poles of the Moon and Mercury: Implications for origins

NASA Astrophysics Data System (ADS)

Zhang, Jo Ann; Paige, David A.

2009-08-01

We have calculated evaporation rates for a range of organic compounds that may be cold-trapped at the poles of the Moon and Mercury. Organics vary widely in their volatilities and thus can be stable to evaporation at higher and lower temperatures than water. The detection of cold-trapped organics would point to volatile delivery by impacts, as comets and asteroids are the only plausible sources for organic molecules. The characterization of cold-trapped organics on both bodies may provide constraints on the thermal evolution of cold traps over time and the history of volatiles in the inner solar system.

Orbit Maintenance and Navigation of Human Spacecraft at Cislunar Near Rectilinear Halo Orbits

NASA Technical Reports Server (NTRS)

Davis, Diane; Bhatt, Sagar; Howell, Kathleen; Jang, Jiann-Woei; Whitley, Ryan; Clark, Fred; Guzzetti, Davide; Zimovan, Emily; Barton, Gregg

2017-01-01

Multiple studies have concluded that Earth-Moon libration point orbits are attractive candidates for staging operations. The Near Rectilinear Halo Orbit (NRHO), a member of the Earth-Moon halo orbit family, has been singularly demonstrated to meet multi-mission architectural constraints. In this paper, the challenges associated with operating human spacecraft in the NRHO are evaluated. Navigation accuracies and human vehicle process noise effects are applied to various station keeping strategies in order to obtain a reliable orbit maintenance algorithm. Additionally, the ability to absorb missed burns, construct phasing maneuvers to avoid eclipses and conduct rendezvous and proximity operations are examined.

A Real-Time Marker-Based Visual Sensor Based on a FPGA and a Soft Core Processor

PubMed Central

Tayara, Hilal; Ham, Woonchul; Chong, Kil To

2016-01-01

This paper introduces a real-time marker-based visual sensor architecture for mobile robot localization and navigation. A hardware acceleration architecture for post video processing system was implemented on a field-programmable gate array (FPGA). The pose calculation algorithm was implemented in a System on Chip (SoC) with an Altera Nios II soft-core processor. For every frame, single pass image segmentation and Feature Accelerated Segment Test (FAST) corner detection were used for extracting the predefined markers with known geometries in FPGA. Coplanar PosIT algorithm was implemented on the Nios II soft-core processor supplied with floating point hardware for accelerating floating point operations. Trigonometric functions have been approximated using Taylor series and cubic approximation using Lagrange polynomials. Inverse square root method has been implemented for approximating square root computations. Real time results have been achieved and pixel streams have been processed on the fly without any need to buffer the input frame for further implementation. PMID:27983714

MAP Attitude Control System Design and Analysis

NASA Technical Reports Server (NTRS)

Andrews, S. F.; Campbell, C. E.; Ericsson-Jackson, A. J.; Markley, F. L.; ODonnell, J. R., Jr.

1997-01-01

The Microwave Anisotropy Probe (MAP) is a follow-on to the Differential Microwave Radiometer (DMR) instrument on the Cosmic Background Explorer (COBE) spacecraft. The MAP spacecraft will perform its mission in a Lissajous orbit around the Earth-Sun L(sub 2) Lagrange point to suppress potential instrument disturbances. To make a full-sky map of cosmic microwave background fluctuations, a combination fast spin and slow precession motion will be used. MAP requires a propulsion system to reach L(sub 2), to unload system momentum, and to perform stationkeeping maneuvers once at L(sub 2). A minimum hardware, power and thermal safe control mode must also be provided. Sufficient attitude knowledge must be provided to yield instrument pointing to a standard deviation of 1.8 arc-minutes. The short development time and tight budgets require a new way of designing, simulating, and analyzing the Attitude Control System (ACS). This paper presents the design and analysis of the control system to meet these requirements.

A Novel Model to Simulate Flexural Complements in Compliant Sensor Systems

PubMed Central

Tang, Hongyan; Zhang, Dan; Guo, Sheng; Qu, Haibo

2018-01-01

The main challenge in analyzing compliant sensor systems is how to calculate the large deformation of flexural complements. Our study proposes a new model that is called the spline pseudo-rigid-body model (spline PRBM). It combines dynamic spline and the pseudo-rigid-body model (PRBM) to simulate the flexural complements. The axial deformations of flexural complements are modeled by using dynamic spline. This makes it possible to consider the nonlinear compliance of the system using four control points. Three rigid rods connected by two revolute (R) pins with two torsion springs replace the three lines connecting the four control points. The kinematic behavior of the system is described using Lagrange equations. Both the optimization and the numerical fitting methods are used for resolving the characteristic parameters of the new model. An example is given of a compliant mechanism to modify the accuracy of the model. The spline PRBM is important in expanding the applications of the PRBM to the design and simulation of flexural force sensors. PMID:29596377

A Real-Time Marker-Based Visual Sensor Based on a FPGA and a Soft Core Processor.

PubMed

Tayara, Hilal; Ham, Woonchul; Chong, Kil To

2016-12-15

This paper introduces a real-time marker-based visual sensor architecture for mobile robot localization and navigation. A hardware acceleration architecture for post video processing system was implemented on a field-programmable gate array (FPGA). The pose calculation algorithm was implemented in a System on Chip (SoC) with an Altera Nios II soft-core processor. For every frame, single pass image segmentation and Feature Accelerated Segment Test (FAST) corner detection were used for extracting the predefined markers with known geometries in FPGA. Coplanar PosIT algorithm was implemented on the Nios II soft-core processor supplied with floating point hardware for accelerating floating point operations. Trigonometric functions have been approximated using Taylor series and cubic approximation using Lagrange polynomials. Inverse square root method has been implemented for approximating square root computations. Real time results have been achieved and pixel streams have been processed on the fly without any need to buffer the input frame for further implementation.

Trajectory planning of mobile robots using indirect solution of optimal control method in generalized point-to-point task

NASA Astrophysics Data System (ADS)

Nazemizadeh, M.; Rahimi, H. N.; Amini Khoiy, K.

2012-03-01

This paper presents an optimal control strategy for optimal trajectory planning of mobile robots by considering nonlinear dynamic model and nonholonomic constraints of the system. The nonholonomic constraints of the system are introduced by a nonintegrable set of differential equations which represent kinematic restriction on the motion. The Lagrange's principle is employed to derive the nonlinear equations of the system. Then, the optimal path planning of the mobile robot is formulated as an optimal control problem. To set up the problem, the nonlinear equations of the system are assumed as constraints, and a minimum energy objective function is defined. To solve the problem, an indirect solution of the optimal control method is employed, and conditions of the optimality derived as a set of coupled nonlinear differential equations. The optimality equations are solved numerically, and various simulations are performed for a nonholonomic mobile robot to illustrate effectiveness of the proposed method.

Cubature versus Fekete-Gauss nodes for spectral element methods on simplicial meshes

NASA Astrophysics Data System (ADS)

Pasquetti, Richard; Rapetti, Francesca

2017-10-01

In a recent JCP paper [9], a higher order triangular spectral element method (TSEM) is proposed to address seismic wave field modeling. The main interest of this TSEM is that the mass matrix is diagonal, so that an explicit time marching becomes very cheap. This property results from the fact that, similarly to the usual SEM (say QSEM), the basis functions are Lagrange polynomials based on a set of points that shows both nice interpolation and quadrature properties. In the quadrangle, i.e. for the QSEM, the set of points is simply obtained by tensorial product of Gauss-Lobatto-Legendre (GLL) points. In the triangle, finding such an appropriate set of points is however not trivial. Thus, the work of [9] follows anterior works that started in 2000's [2,6,11] and now provides cubature nodes and weights up to N = 9, where N is the total degree of the polynomial approximation. Here we wish to evaluate the accuracy of this cubature nodes TSEM with respect to the Fekete-Gauss one, see e.g.[12], that makes use of two sets of points, namely the Fekete points and the Gauss points of the triangle for interpolation and quadrature, respectively. Because the Fekete-Gauss TSEM is in the spirit of any nodal hp-finite element methods, one may expect that the conclusions of this Note will remain relevant if using other sets of carefully defined interpolation points.

Using Lunar Observations to Validate Pointing Accuracy and Geolocation, Detector Sensitivity Stability and Static Point Response of the CERES Instruments

NASA Technical Reports Server (NTRS)

Daniels, Janet L.; Smith, G. Louis; Priestley, Kory J.; Thomas, Susan

2014-01-01

Validation of in-orbit instrument performance is a function of stability in both instrument and calibration source. This paper describes a method using lunar observations scanning near full moon by the Clouds and Earth Radiant Energy System (CERES) instruments. The Moon offers an external source whose signal variance is predictable and non-degrading. From 2006 to present, these in-orbit observations have become standardized and compiled for the Flight Models -1 and -2 aboard the Terra satellite, for Flight Models-3 and -4 aboard the Aqua satellite, and beginning 2012, for Flight Model-5 aboard Suomi-NPP. Instrument performance measurements studied are detector sensitivity stability, pointing accuracy and static detector point response function. This validation method also shows trends per CERES data channel of 0.8% per decade or less for Flight Models 1-4. Using instrument gimbal data and computed lunar position, the pointing error of each detector telescope, the accuracy and consistency of the alignment between the detectors can be determined. The maximum pointing error was 0.2 Deg. in azimuth and 0.17 Deg. in elevation which corresponds to an error in geolocation near nadir of 2.09 km. With the exception of one detector, all instruments were found to have consistent detector alignment from 2006 to present. All alignment error was within 0.1o with most detector telescopes showing a consistent alignment offset of less than 0.02 Deg.

Apollo 15 Lunar eclipse views

NASA Image and Video Library

1971-08-01

S71-58222 (31 July-2 Aug. 1971) --- During the lunar eclipse that occurred during the Apollo 15 lunar landing mission, astronaut Alfred M. Worden, command module pilot, used a 35mm Nikon camera to obtain a series of 15 photographs while the moon was entering and exiting Earth's umbra. Although it might seem that there should be no light on the moon when it is in Earth's shadow, sunlight is scattered into this region by Earth's atmosphere. This task was an attempt to measure by photographic photometry the amount of scattered light reaching the moon. The four views from upper left to lower right were selected to show the moon as it entered Earth's umbra. The first is a four-second exposure which was taken at the moment when the moon had just entered umbra; the second is a 15-second exposure taken two minutes after entry; the third, a 30-second exposure three minutes after entry; and the fourth is a 60-second exposure four minutes after entry. In all cases the light reaching the moon was so bright on the very high speed film (Eastman Kodak type 2485 emulsion) that the halation obscures the lunar image, which should be about one-third as big as the circle of light. The background star field is clearly evident, and this is very important for these studies. The spacecraft was in full sunlight when these photographs were taken, and it was pointed almost directly away from the sun so that the windows and a close-in portion of the camera's line-of-sight were in shadow. The environment around the vehicle at this time appears to be very "clean" with no light scattering particles noticeable.

Radioactivity of the moon and planets

NASA Astrophysics Data System (ADS)

Surkov, Iu. A.

The major results of studies of the radioactivity of the moon and terrestrial planets are reviewed. Measurements of the cosmogenic and natural radioactivity of the moon and Mars were obtained from planetary orbiter measurements, and those of Venus by in situ measurements, in addition to measurements of lunar samples brought back to earth. For the case of the moon, the Western maria on the near side are found to be the most radioactive areas, with highlands on both sides of the moon exhibiting lower radioactivity than the maria and lunar radioactivity levels in general less than those of the earth, which is correlated with different chemical compositions of the two bodies. The potassium, uranium and thorium contents of the landing sites of Veneras 8, 9 and 10 are shown to differ from each other, but be similar to those of terrestrial basalts, which they also resemble in density. Gamma-radiation and X-ray fluorescence measurements of Mars indicate the content of natural radioelements to be similar to that of the eruptive rocks of the earth crust, with Martian rocks of volcanic formations similar to terrestrial and lunar basalts, and those of the ancient terra formations more closely resembling the anorthosite-norite-troctolite association of the lunar highlands. It is pointed out that natural radioelements contents of all the bodies examined indicate a single chemical differentiation process, while cosmogenic radiation contents can aid in determining cosmic ray intensities as well as the sequences of geological events.

An Alternative view of Earth's Tectonics : The Moon's explosive origin out of SE Asia.

NASA Astrophysics Data System (ADS)

Coleman, P. F.

2017-12-01

A lunar birth scar is typically considered untenable, under the standard paradigm (GTS-4.6-0 Ga, Giant Impact/Plate Tectonics), since it would have been erased by a combination of Wilson recycling, and erosion. This paradigm, while supported by robust, absolute dating, is still provisional, and, like all scientifc paradigms, is nonetheless open to refutation. It cannot, a priori, rule out such a scar. If empirical evidence were to be discovered, in favor of a lunar birthmark, it would have profound implications for the standard view. Coleman (2015) proposed an alternative paradigm based on an internal explosion of Proto-Earth (PE) that ejected the Moon into orbit and left coeval global signatures, such as; ocean-continent antipodality, the global geoid, origin of water, continents, trenches, fault lines, LIPs, hotspots, seamount chains, from the high TP shock/seismic waves. The abrupt deceleration also led to inertial effects of PE's crustal layers, possibly explaining subduction/obduction and fold and thrust fold belts. One major, first order, line of evidence is the actual fission signature ( 4000+ km long) where the Moon was explosively thrust tangentially (to the core) through ductile mantle (see Fig B) to escape into orbit. The proposed path, (locus Moon's center) is from (0°, 78.5°E) (Fig A), near present day India, to (+14.4°, 119°E) out of SE Asia (See Fig C). Possible evidence in favor of this path (but not limited to) include: the Indian Geoid Anomaly Low ( Moon's exhumation?), the Himalayas and Tibetan Plateau (generated by the Moon's NE collisional movement and temporary hole and mantle rebound), SE Asia with many minor plates and back arc basins ( the Moon's exit zone), the East African Rifts (EARs) form a NE-directed pull apart region (explained as a set explosive crustal fragments or "plates") moving towards this relic unconsolidated Asian sink hole (See Fig D). The existence of a fossilised lunar birth points to a recent Earth-Moon, since insufficient time has elapsed, to break up the scar, by "plate" movement, or erosion. The present tectonic/ volcanic activity, (eg earthquakes/eruptions along the Pacific Ring of Fire) is further evidence of this "smoking gun". Coleman P.F., 2015, Alternative Models of the Moon, Physics Today, 68,4,8.

Triggering Factor of Strong Earthquakes and Its Prediction Verification

NASA Astrophysics Data System (ADS)

Ren, Z. Q.; Ren, S. H.

After 30 yearsS research, we have found that great earthquakes are triggered by tide- generation force of the moon. ItSs not the tide-generation force in classical view- points, but is a non-classical viewpoint tide-generation force. We call it as TGFR (Tide-Generation ForcesS Resonance). TGFR strongly depends on the tide-generation force at time of the strange astronomical points (SAP). The SAP mostly are when the moon and another celestial body are arranged with the earth along a straight line (with the same apparent right ascension or 180o difference), the other SAP are the turning points of the moonSs relatively motion to the earth. Moreover, TGFR have four different types effective areas. Our study indicates that a majority of earthquakes are triggering by the rare superimposition of TGFRsS effective areas. In China the great earthquakes in the plain area of Hebei Province, Taiwan, Yunnan Province and Sichuan province are trigger by the decompression TGFR; Other earthquakes are trig- gered by compression TGFR which are in Gansu Province, Ningxia Provinces and northwest direction of Beijing. The great earthquakes in Japan, California, southeast of Europe also are triggered by compression of the TGFR. and in the other part of the world like in Philippines, Central America countries, and West Asia, great earthquakes are triggered by decompression TGFR. We have carried out examinational immediate prediction cooperate TGFR method with other earthquake impending signals such as suggested by Professor Li Junzhi. The successful ratio is about 40%(from our fore- cast reports to the China Seismological Administration). Thus we could say the great earthquake can be predicted (include immediate earthquake prediction). Key words: imminent prediction; triggering factor; TGFR (Tide-Generation ForcesS Resonance); TGFR compression; TGFR compression zone; TGFR decompression; TGFR decom- pression zone

NASA's Space Launch System: Deep-Space Opportunities for SmallSats

NASA Technical Reports Server (NTRS)

Robinson, Kimberly F.; Schorr, Andrew A.

2017-01-01

Designed for human exploration missions into deep space, NASA's Space Launch System (SLS) represents a new spaceflight infrastructure asset, enabling a wide variety of unique utilization opportunities. While primarily focused on launching the large systems needed for crewed spaceflight beyond Earth orbit, SLS also offers a game-changing capability for the deployment of small satellites to deep-space destinations, beginning with its first flight. Currently, SLS is making rapid progress toward readiness for its first launch in two years, using the initial configuration of the vehicle, which is capable of delivering 70 metric tons (t) to Low Earth Orbit (LEO). On its first flight test of the Orion spacecraft around the moon, accompanying Orion on SLS will be small-satellite secondary payloads, which will deploy in cislunar space. The deployment berths are sized for "6U" CubeSats, and on EM-1 the spacecraft will be deployed into cislunar space following Orion separate from the SLS Interim Cryogenic Propulsion Stage. Payloads in 6U class will be limited to 14 kg maximum mass. Secondary payloads on EM-1 will be launched in the Orion Stage Adapter (OSA). Payload dispensers will be mounted on specially designed brackets, each attached to the interior wall of the OSA. For the EM-1 mission, a total of fourteen brackets will be installed, allowing for thirteen payload locations. The final location will be used for mounting an avionics unit, which will include a battery and sequencer for executing the mission deployment sequence. Following the launch of EM-1, deployments of the secondary payloads will commence after sufficient separation of the Orion spacecraft to the upper stage vehicle to minimize any possible contact of the deployed cubesats to Orion. Currently this is estimated to require approximately 4 hours. The allowed deployment window for the cubesats will be from the time the upper stage disposal maneuvers are complete to up to 10 days after launch. The upper stage will fly past the moon at a perigee of approximately 100km, and this closest approach will occur about 5 days after launch. The limiting factor for the latest deployment time is the available power in the sequencer system. Several NASA Mission Directorates were involved in the development of programs for the competition, selection, and development of EM-1 payloads that support directorate priorities. CubeSat payloads on EM-1 will include both NASA research experiments and spacecraft developed by industry, international and potentially academia partners. The Human Exploration and Operations Mission Directorate (HEOMD) Advanced Exploration Systems (AES) Division was allocated five payload opportunities on the EM-1 mission. Near Earth Asteroid (NEA) Scout is designed to rendezvous with and characterize a candidate NEA. A solar sail, an innovation the spacecraft will demonstrated for the CubeSat class, will provide propulsion. Lunar Flashlight will use a green propellant system and will search for potential ice deposits in the moon's permanently shadowed craters. BioSentinel is a yeast radiation biosensor, planned to measure the effects of space radiation on deoxyribonucleic acid (DNA). Lunar Icecube, a collaboration with Morehead State University, will prospect for water in ice, liquid, and vapor forms as well as other lunar volatiles from a low-perigee, highly inclined lunar orbit using a compact Infrared spectrometer. Skyfire, a partnership with Lockheed Martin, is a technology demonstration mission that will perform a lunar flyby, collecting spectroscopy, and thermography data to address questions related to surface characterization, remote sensing, and site selection. NASA's Space Technology Mission Directorate (STMD) was allocated three payload opportunities on the EM-1 mission. These slots will be filled via the 2 Centennial Challenges Program, NASA's flagship program for technology prize competitions, which directly engages the public, academia, and industry in open prize competitions to stimulate innovation. The NASA Science Mission Directorate (SMD) was allocated two payload opportunities on the EM-1 mission. The CubeSat Mission to Study Solar Particles (CuSP) payload will study the sources and acceleration mechanisms of solar and interplanetary particles in near-Earth orbit, support space weather research by determining proton radiation levels during Solar Energetic Particle (SEP) events and identifying suprathermal properties that could help predict geomagnetic storms. The LunaH-Map payload will help scientists understand the quantity of H-bearing materials in lunar cold traps (10 km), determine the concentration of H-bearing materials with 1m depth, and constrain the vertical distribution of H-bearing materials. The final three payload opportunities for the EM-1 mission were allocated for NASA's international space agency counterparts. The flight opportunities are intended to benefit the international space agency and NASA as well as further the collective space exploration goals. ArgoMoon is sponsored by ESA/ASI and will fly along with the ICPS on its disposal trajectory to perform proximity operations with the ICPS post-disposal, take external imagery of engineering and historical significance, and perform an optical communications demonstration. EQUULEUS, sponsored by JAXA, will fly to a libration orbit around the Earth-Moon L2 point and demonstrate trajectory control techniques within the Sun-Earth-Moon region for the first time by a nano spacecraft. The mission will also contribute to the future human exploration scenario by understanding the radiation environment in geospace and deep space, characterizing the flux of impacting meteors on the far side of the moon, and demonstrating the future deep space exploration scenario using the "deep space port" at Lagrange points. OMOTENASHI, also sponsored by JAXA, will land the smallest lunar lander to date on the lunar surface to demonstrate the feasibility of the hardware for distributed cooperative exploration system. Small landers will enable multi-point exploration, which is complimentary with large-scale human exploration. Once on the lunar surface, the OMOTENASHI spacecraft will observe the radiation and soil environments of the lunar surface by active radiation measurements and soil shear measurements. Following EM-1, Space Launch System will evolve to the more-powerful Block 1B configuration, which uses a new Exploration Upper Stage to increase the vehicle's LEO payload capability from 70 t to 105 t. With that transition, the Orion Stage Adapter, which will carry the secondary payloads on EM-1, will be phased out, and a new Universal Stage Adapter will be introduced, creating opportunities for flying larger secondary payloads. This paper will provide a brief status of SLS progress toward first launch; an overview of smallsat accommodations, integration, and operations on EM-1; information about the specific payloads flying on that launch; and a discussion of future accommodations and opportunities for secondary payloads on SLS for Exploration Mission-2 and beyond.

NASA's Space Launch System: Deep-Space Delivery for Smallsats

NASA Technical Reports Server (NTRS)

Robinson, Kimberly F.; Norris, George

2017-01-01

Designed for human exploration missions into deep space, NASA's Space Launch System (SLS) represents a new spaceflight infrastructure asset, enabling a wide variety of unique utilization opportunities. While primarily focused on launching the large systems needed for crewed spaceflight beyond Earth orbit, SLS also offers a game-changing capability for the deployment of small satellites to deep-space destinations, beginning with its first flight. Currently, SLS is making rapid progress toward readiness for its first launch in two years, using the initial configuration of the vehicle, which is capable of delivering 70 metric tons (t) to Low Earth Orbit (LEO). On its first flight test of the Orion spacecraft around the moon, accompanying Orion on SLS will be small-satellite secondary payloads, which will deploy in cislunar space. The deployment berths are sized for "6U" CubeSats, and on EM-1 the spacecraft will be deployed into cislunar space following Orion separate from the SLS Interim Cryogenic Propulsion Stage. Payloads in 6U class will be limited to 14 kg maximum mass. Secondary payloads on EM-1 will be launched in the Orion Stage Adapter (OSA). Payload dispensers will be mounted on specially designed brackets, each attached to the interior wall of the OSA. For the EM-1 mission, a total of fourteen brackets will be installed, allowing for thirteen payload locations. The final location will be used for mounting an avionics unit, which will include a battery and sequencer for executing the mission deployment sequence. Following the launch of EM-1, deployments of the secondary payloads will commence after sufficient separation of the Orion spacecraft to the upper stage vehicle to minimize any possible contact of the deployed CubeSats to Orion. Currently this is estimated to require approximately 4 hours. The allowed deployment window for the CubeSats will be from the time the upper stage disposal maneuvers are complete to up to 10 days after launch. The upper stage will fly past the moon at a perigee of approximately 100km, and this closest approach will occur about 5 days after launch. The limiting factor for the latest deployment time is the available power in the sequencer system. Several NASA Mission Directorates were involved in the development of programs for the competition, selection, and development of EM-1 payloads that support directorate priorities. CubeSat payloads on EM-1 will include both NASA research experiments and spacecraft developed by industry, international and potentially academia partners. The Human Exploration and Operations Mission Directorate (HEOMD) Advanced Exploration Systems (AES) Division was allocated five payload opportunities on the EM-1 mission. Near Earth Asteroid (NEA) Scout is designed to rendezvous with and characterize a candidate NEA. A solar sail, an innovation the spacecraft will demonstrated for the CubeSat class, will provide propulsion. Lunar Flashlight will use a green propellant system and will search for potential ice deposits in the moon's permanently shadowed craters. BioSentinel is a yeast radiation biosensor, planned to measure the effects of space radiation on deoxyribonucleic acid (DNA). Lunar Icecube, a collaboration with Morehead State University, will prospect for water in ice, liquid, and vapor forms as well as other lunar volatiles from a low-perigee, highly inclined lunar orbit using a compact Infrared spectrometer. Skyfire, a partnership with Lockheed Martin, is a technology demonstration mission that will perform a lunar flyby, collecting spectroscopy, and thermography data to address questions related to surface characterization, remote sensing, and site selection. NASA's Space Technology Mission Directorate (STMD) was allocated three payload opportunities on the EM-1 mission. These slots will be filled via the Centennial Challenges Program, NASA's flagship program for technology prize competitions, which directly engages the public, academia, and industry in open prize competitions to stimulate innovation. The NASA Science Mission Directorate (SMD) was allocated two payload opportunities on the EM-1 mission. The CubeSat Mission to Study Solar Particles (CuSP) payload will study the sources and acceleration mechanisms of solar and interplanetary particles in near-Earth orbit, support space weather research by determining proton radiation levels during Solar Energetic Particle (SEP) events and identifying suprathermal properties that could help predict geomagnetic storms. The LunaH-Map payload will help scientists understand the quantity of H-bearing materials in lunar cold traps (10 km), determine the concentration of H-bearing materials with 1m depth, and constrain the vertical distribution of H-bearing materials. The final three payload opportunities for the EM-1 mission were allocated for NASA's international space agency counterparts. The flight opportunities are intended to benefit the international space agency and NASA as well as further the collective space exploration goals. ArgoMoon is sponsored by ESA/ASI and will fly along with the ICPS on its disposal trajectory to perform proximity operations with the ICPS post-disposal, take external imagery of engineering and historical significance, and perform an optical communications demonstration. EQUULEUS, sponsored by JAXA, will fly to a libration orbit around the Earth-Moon L2 point and demonstrate trajectory control techniques within the Sun-Earth- Moon region for the first time by a nano spacecraft. The mission will also contribute to the future human exploration scenario by understanding the radiation environment in geospace and deep space, characterizing the flux of impacting meteors on the far side of the moon, and demonstrating the future deep space exploration scenario using the "deep space port" at Lagrange points. OMOTENASHI, also sponsored by JAXA, will land the smallest lunar lander to date on the lunar surface to demonstrate the feasibility of the hardware for distributed cooperative exploration system. Small landers will enable multi-point exploration, which is complimentary with large-scale human exploration. Once on the lunar surface, the OMOTENASHI spacecraft will observe the radiation and soil environments of the lunar surface by active radiation measurements and soil shear measurements. Following EM-1, Space Launch System will evolve to the more-powerful Block 1B configuration, which uses a new Exploration Upper Stage to increase the vehicle's LEO payload capability from 70 t to 105 t. With that transition, the Orion Stage Adapter, which will carry the secondary payloads on EM-1, will be phased out, and a new Universal Stage Adapter will be introduced, creating opportunities for flying larger secondary payloads. This paper will provide a brief status of SLS progress toward first launch; an overview of smallsat accommodations, integration, and operations on EM-1; information about the specific payloads flying on that launch; and a discussion of future accommodations and opportunities for secondary payloads on SLS for Exploration Mission-2 and beyond.

[The mathematical theory of acupoints].

PubMed

Zhuo, Lian-Shi

2013-12-01

The ancient medical classics were retrieved to explore narrative on acupoints. And the relevant content of legal calendar in Shiji (Historical Records) and Hanshu (History of the Former Han Dynasty) were taken as a reference. The result showed that the total number of acu-points were based on the number of 365 days of a year. And the corrupts can be restored with the theory of numerology. The 59 heat point originated from the phase of moon, while the 57 water points originated from the number or year related with diasters. Although acupoints are considered to be related with numerology, the recognition of hot points and water points are held to be associated with experiential points in clinic.

Cis-Lunar Base Camp

NASA Technical Reports Server (NTRS)

Merrill, Raymond G.; Goodliff, Kandyce E.; Mazanek, Daniel D.; Reeves, John D., Jr.

2012-01-01

Historically, when mounting expeditions into uncharted territories, explorers have established strategically positioned base camps to pre-position required equipment and consumables. These base camps are secure, safe positions from which expeditions can depart when conditions are favorable, at which technology and operations can be tested and validated, and facilitate timely access to more robust facilities in the event of an emergency. For human exploration missions into deep space, cis-lunar space is well suited to serve as such a base camp. The outer regions of cis-lunar space, such as the Earth-Moon Lagrange points, lie near the edge of Earth s gravity well, allowing equipment and consumables to be aggregated with easy access to deep space and to the lunar surface, as well as more distant destinations, such as near-Earth Asteroids (NEAs) and Mars and its moons. Several approaches to utilizing a cis-lunar base camp for sustainable human exploration, as well as some possible future applications are identified. The primary objective of the analysis presented in this paper is to identify options, show the macro trends, and provide information that can be used as a basis for more detailed mission development. Compared within are the high-level performance and cost of 15 preliminary cis-lunar exploration campaigns that establish the capability to conduct crewed missions of up to one year in duration, and then aggregate mass in cis-lunar space to facilitate an expedition from Cis-Lunar Base Camp. Launch vehicles, chemical propulsion stages, and electric propulsion stages are discussed and parametric sizing values are used to create architectures of in-space transportation elements that extend the existing in-space supply chain to cis-lunar space. The transportation options to cis-lunar space assessed vary in efficiency by almost 50%; from 0.16 to 0.68 kg of cargo in cis-lunar space for every kilogram of mass in Low Earth Orbit (LEO). For the 15 cases, 5-year campaign costs vary by only 15% from 0.36 to 0.51 on a normalized scale across all campaigns. Thus the development and first flight costs of assessed transportation options are similar. However, the cost of those options per flight beyond the initial operational capability varies by 70% from 0.3 to 1.0 on a normalized scale. The 10-year campaigns assessed begin to show the effect of this large range of cost beyond initial operational capability as they vary approximately 25% with values from 0.75 to 1.0 on the normalized campaign scale. Therefore, it is important to understand both the cost of implementation and first use as well as long term utilization. Finally, minimizing long term recurring costs is critical to the affordability of future human space exploration missions. Finally minimizing long term recurring costs is critical to the affordability of future human space exploration missions.

Designating Earth's Moon as a United Nations World Heritage Site - Permanently Protected from Commercial or Military Uses

NASA Astrophysics Data System (ADS)

Steiner, R. G.

2002-01-01

This paper proposes that Earth's Moon, in its entirety, be designated a United Nations World Heritage Site (WHS), permanently protected from any and all commercial or military utilization and reserved exclusively for scientific and aesthetic purposes. The paper discusses: 1) the extraordinary importance of the Moon for science, culture, and religion - past, present and future; 2) the history of proposals to exploit the Moon for commercial and military purposes and the shortcomings of this colonial, exploitation paradigm; and 3) the necessity, policy mechanisms, and political dynamics of designating the Moon as a World Heritage Site, permanently protected from commercial and/or military uses. The first part of the paper discusses the extraordinary importance of the Moon as it exists today - as a scientific laboratory, a source of beauty and inspiration throughout human evolution, a source for artistic expression, and as an object that is considered sacred by many cultures. Next, the paper traces the history of specific proposals for the exploitation of the Moon for commercial and/or military purposes - including plans by the U.S. Air Force in 1959 to detonate a nuclear explosion on the Moon, proposals to strip-mine the lunar regolith for helium-3 and rocket-fuel hydrogen; construction of solar power plants to transmit energy to Earth, and proposals to use the lunar surface as a billboard upon which to project commercial advertisements visible from Earth. The profound ethical, legal, and scientific shortcomings of this exploitation paradigm are described as an emerging Extraterrestrial Manifest Destiny that we have a collective obligation to challenge and constrain. The paper proposes that space exploration be infused with an ethical commitment to compassion, reverence, conservation, and non-interference to abiotic and biotic systems alike; as opposed to the expansion and extraterrestrial imposition of the colonization, exploitation, domination, and despoliation paradigm that has characterized 19th and 20th century western civilization on Earth. The World Heritage process, and how Earth's Moon clearly satisfies necessary criteria, is described, as are the political challenges this proposal presents, including the 'national sovereignty' issue. The 1972 United Nations World Heritage Convention (signed by 167 countries), provides for the protection of cultural and natural properties deemed to be of "outstanding universal value", including value "from the point of view of science, conservation, or natural beauty" and places them under "a collective responsibility." The Moon clearly meets several criteria for WHS designation, as follow: a. "be outstanding examples representing major stages of Earth's history...significant on-going geological processes in the development of landforms, or significant geomorphic or physiographic features"; b. "contain superlative natural phenomena or areas of exceptional natural beauty and aesthetic importance"; and c. the Moon qualifies within the Convention as an "associative cultural landscape" which designates areas "by virtue of their powerful religious, artistic or cultural associations of the natural element." To facilitate WHS site designation for the Moon, it is proposed that the 1979 "Moon Treaty" (Agreement Governing the Activities of States on the Moon and Other Celestial Bodies, entered into force 7/11/84) be amended and broadly ratified internationally. Specifically, Article 11 - which presently provides for 'the establishment of an international regime to govern the exploitation of the natural resources of the moon, encourage the development of the natural resources of the moon, the management and expansion of opportunities in the use of those resources' - should be amended to provide a clear and unequivocal declaration of the extraordinary, irreplaceable cultural and natural value of the Moon, and designation of the Moon in its entirety as an inviolate World Heritage Site reserved exclusively for scientific purposes and aesthetic/religious appreciation under the collective responsibility of all humankind.

Silicon PV cell production on the Moon as the basis for a new architecture for space exploration

NASA Astrophysics Data System (ADS)

Duke, Michael B.; Ignatiev, Alex; Freundlich, Alex; Rosenberg, Sanders D.; Makel, Darby

2001-02-01

A method is described by which silicon photovoltaic (PV) devices can be directly deposited onto the lunar regolith using primarily lunar materials. In sequence, a robotic ``crawler'' moving at slow speed sequentially melts the top layer of regolith and deposits a conducting layer, a doped silicon, a top conducting grid, and an antireflective coating by vacuum evaporation techniques. Concentrated solar energy is utilized as the energy source. Development of this capability would significantly lower the cost of electrical energy on the Moon and would enable a range of other activities, including lower cost propellant production, human outposts with complete food-growth capabilities, and advanced materials production. Low cost energy could affect the economics of propellants in space by allowing the extraction of solar wind hydrogen from the lunar regolith. This would allow the economical export of propellants and other materials to space, first to an Earth-Moon Lagrangian Point and potentially to low Earth orbit. .

Design of fast earth-return trajectories from a lunar base

NASA Astrophysics Data System (ADS)

Anhorn, Walter

1991-09-01

The Apollo Lunar Program utilized efficient transearth trajectories which employed parking orbits in order to minimize energy requirements. This thesis concentrates on a different type of transearth trajectory. These are direct-ascent, hyperbolic trajectories which omit the parking orbits in order to achieve short flight times to and from a future lunar base. The object of the thesis is the development of a three-dimensional transearth trajectory model and associated computer program for exploring trade-offs between flight-time and energy, given various mission constraints. The program also targets the Moon with a hyperbolic trajectory, which can be used for targeting Earth impact points. The first-order model is based on an Earth-centered conic and a massless spherical Moon, using MathCAD version 3.0. This model is intended as the basis for future patched-conic formulations for the design of fast Earth-return trajectories. Applications include placing nuclear deterrent arsenals on the Moon, various space support related activities, and finally protection against Earth-threatening asteroids and comets using lunar bases.

Geologic evolution of the terrestrial planets

NASA Technical Reports Server (NTRS)

Head, J. W.; Mutch, T. A.; Wood, C. A.

1977-01-01

The paper presents a geologic comparison of the terrestrial planets Mercury, Venus, Earth, the Moon and Mars, in the light of the recent photogeologic and other evidence gathered by satellites, and discusses the relationships between their regional terrain types, ages, and planetary evolution. The importance of the two fundamental processes, impact cratering and volcanism, which had formed these planets are stressed and the factors making the earth unique, such as high planetary evolution index (PEI), dynamic geological agents and the plate tectonics, are pointed out. The igneous processes which dominate earth and once existed on the others are outlined together with the planetary elevations of the earth which has a bimodal distribution, the moon which has a unimodal Gaussian distribution and Mars with a distribution intermediate between the earth and moon. Questions are raised concerning the existence of a minimum planetary mass below which mantle convection will not cause lithospheric rifting, and as to whether each planet follows a separate path of evolution depending on its physical properties and position within the solar system.

The role of binocular viewing in a spacing illusion arising in a darkened surround.

PubMed

Suzuki, K

1998-01-01

A study is reported of the binocular-oculomotor hypothesis of the moon illusion. In a dark hall, a pair of light points was presented straight ahead horizontally, and another pair was presented at the same distance but 50 degrees upward. Twenty subjects compared the spacings of these two pairs. Half of the subjects viewed the stimuli first monocularly and then binocularly, and the other half viewed them in the reverse order. Eye position was also systematically varied, either level or elevated. A spacing illusion was consistently obtained during binocular viewing (with the upper spacing seen as smaller), but no illusion arose during monocular viewing unless it was preceded by binocular viewing. Furthermore, an enhancement of the illusion due to eye elevation was found only during binocular viewing. These findings replicate the report of Taylor and Boring (1942 American Journal of Psychology 55 189-201), in which the moon was used as the stimulus, and support the binocular-oculomotor hypothesis as a partial explanation for the moon illusion.

Milagro Contributions to XXVI International Cosmic Ray Conference

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hoffman, C.M.; Haines, T.J.; Sinnis, G.

1999-08-01

Milagrito, a prototype for the Milagro detector, operated for 15 months in 1997--8 and collected 8.9 x 10{sup 9} events. It was the first extensive air shower (EAS) array sensitive to showers initiated by primaries with energy below 1 TeV. The shadows of the sun and moon observed with cosmic rays can be used to study systematic pointing shifts and measure the angular resolution of EAS arrays. Below a few TeV, the paths of cosmic rays coming toward the earth are bent by the helio- and geo-magnetic fields. This is expected to distort and displace the shadows of the sunmore » and the moon. The moon shadow, offset from the nominal (unreflected) position, has been observed with high statistical significance in Milagrito. This can be used to establish energy calibrations, as well as to search for the anti-matter content of the VHE cosmic ray flux. The shadow of the sun has also been observed with high significance.« less

Spacecraft formation keeping near the libration points of the Sun-Earth/Moon system

NASA Astrophysics Data System (ADS)

Marchand, Belinda G.

Multi-spacecraft formations, evolving near the vicinity of the libration points of the Sun-Earth/Moon system, have drawn increased interest for a variety of applications. This is particularly true for space based interferometry missions such as Terrestrial Planet Finder (TPF) and the Micro Arcsecond X-Ray Imaging Mission (MAXIM). Recent studies in formation flight have focused, primarily, on the control of formations that evolve in the immediate vicinity of the Earth. However, the unique dynamical structure near the libration points requires that the effectiveness and feasibility of these methods be re-examined. The present study is divided into two main topics. First, a dynamical systems approach is employed to develop a better understanding of the natural uncontrolled formation dynamics in this region of space. The focus is formations that evolve near halo orbits and Lissajous trajectories, near the L1 and L2 libration points of the Sun-Earth/Moon system. This leads to the development of a Floquet controller designed to simplify the process of identifying naturally existing formations as well as the associated stable manifolds for deployment. The initial analysis is presented in the Circular Restricted Three-Body Problem, but the results are later transitioned into the more complete Ephemeris model. The next subject of interest in this investigation is non-natural formations. That is, formations that are not consistent with the natural dynamical flow near the libration points. Mathematically, precise formation keeping of a given nominal configuration requires continuous control. Hence, a detailed analysis is presented to contrast the effectiveness and issues associated with linear optimal control and feedback linearization methods. Of course, continuous operation of the thrusters, may not represent a feasible option for a particular mission. If discrete formation keeping is implemented, however, the formation keeping goal will be subject to increased tracking errors relative to the nominal path. With this in mind, the final phase of the analysis presented here is centered on discrete formation keeping. The initial analysis is devoted to both linear state and radial targeters. The results from these two methodologies are later employed as a starting solution for an optimal impulsive control algorithm.

Zeros of Schrödinger's Radial Function Rnl(r) and Kummer's Function 1F1(-a c; z) and Their ``Angle'' Distributions

NASA Astrophysics Data System (ADS)

Tarasov, V. F.

In the present paper exact formulae for the calculation of zeros of Rnl(r) and 1F1(-a c; z), where z = 2 λ r, a = n - l - 1 >= 0 and c = 2l + 2 >= 2 are presented. For a <= 4 the method due to Tartallia and Cardono, and that due to L. Ferrai, L. Euler and J. L. Lagrange are used. In other cases (a > 4) numerical methods are employed to obtain the results (to within 10-15). For greater geometrical obviousness of the irregulary distribution (as a > 3) of zeros xk = zk - (c + a - 1) on the axis y = 0, the circular diagrams with the radius Ra = (a - 1) √ {c + a - 1} are presented for the first time. It is possible to notice some singularities of distribution of these zeros and their images - the points Tk - on the circle. For a = 3 and 4 their exact ``angle'' asymptotics (as c --> ∞) are obtained. It is shown that in the basis of the L. Ferrari, L. Euler and J.-L. Lagrange methods, using for solving the equation 1F1(-4 c; z) = 0, one Common for all these methods. equation is obtained viz., the cubic resolvent equation of FEL-type. Calculating of zeros xk of the Rnl(r) and 1F1(z) functions enable us to show the ``singular'' cases (a, c) = (4, 6), (6, 4), (8, 14), ...

Bright Evening Star Seen from Mars is Earth

NASA Image and Video Library

2014-02-06

This view of the twilight sky and Martian horizon taken by NASA Curiosity Mars rover includes Earth as the brightest point of light in the night sky. Earth is a little left of center in the image, and our moon is just below Earth.

Using Lunar Observations to Validate In-Flight Calibrations of Clouds and Earth Radiant Energy System Instruments

NASA Technical Reports Server (NTRS)

Daniels, Janet L.; Smith, G. Louis; Priestley, Kory J.; Thomas, Susan

2014-01-01

The validation of in-orbit instrument performance requires stability in both instrument and calibration source. This paper describes a method of validation using lunar observations scanning near full moon by the Clouds and Earth Radiant Energy System (CERES) instruments. Unlike internal calibrations, the Moon offers an external source whose signal variance is predictable and non-degrading. From 2006 to present, in-orbit observations have become standardized and compiled for the Flight Models-1 and -2 aboard the Terra satellite, for Flight Models-3 and -4 aboard the Aqua satellite, and beginning 2012, for Flight Model-5 aboard Suomi-NPP. Instrument performance parameters which can be gleaned are detector gain, pointing accuracy and static detector point response function validation. Lunar observations are used to examine the stability of all three detectors on each of these instruments from 2006 to present. This validation method has yielded results showing trends per CERES data channel of 1.2% per decade or less.

Optimal Low Energy Earth-Moon Transfers

NASA Technical Reports Server (NTRS)

Griesemer, Paul Ricord; Ocampo, Cesar; Cooley, D. S.

2010-01-01

The optimality of a low-energy Earth-Moon transfer is examined for the first time using primer vector theory. An optimal control problem is formed with the following free variables: the location, time, and magnitude of the transfer insertion burn, and the transfer time. A constraint is placed on the initial state of the spacecraft to bind it to a given initial orbit around a first body, and on the final state of the spacecraft to limit its Keplerian energy with respect to a second body. Optimal transfers in the system are shown to meet certain conditions placed on the primer vector and its time derivative. A two point boundary value problem containing these necessary conditions is created for use in targeting optimal transfers. The two point boundary value problem is then applied to the ballistic lunar capture problem, and an optimal trajectory is shown. Additionally, the ballistic lunar capture trajectory is examined to determine whether one or more additional impulses may improve on the cost of the transfer.

Solar Warning Architecture for Manned Missions to Mars

DTIC Science & Technology

2011-06-01

public discussions of manned missions to return to the Moon, explore near-earth asteroids , and even visit Mars, a deep-space solar weather warning...mission planning, and libration points. In addition, the limited previous analysis on this problem was mined for information. 2.2 Radiation Effects...behind the Earth, on its orbital path. These two libration points are stable along all 3 axes, leading some to theorize there may be asteroids or

Thermal model for impact breccia lithification - Manicouagan and the moon

NASA Technical Reports Server (NTRS)

Simonds, C. H.; Warner, J. L.; Phinney, W. C.; Mcgee, P. E.

1976-01-01

The thermal model of Simonds (1975) is extended to the full spectrum of impact-produced rocks ranging from fragmental breccias to impact melts, with reference to the Manicouagan impact structure in Quebec. This is done by relating the basic textural features of impact-lithified rocks to variations in the mixture of superheated impact-fused material originating near the point of impact and much cooler fragmented debris originating farther from the point of impact.

Development of the program visualizing the lunar physical libration with Visual Basic

NASA Astrophysics Data System (ADS)

Zagidullin, Arthur; Petrova, Natalia

Study of the Moon, of its spin-orbital characteristics and parameters of the lunar interior is one of the traditional fields of the Kazan astronomical school. However, despite the incredible successes in space investigations of the planets and of the Moon, in last years the interest to celestial mechanics, ephemerides astronomy and astrometry is significantly decreased, especially among the young scientists and students. Therefore, it is encouraging to see the work of the third-year student, which is devoted to the study of the physical libration of the Moon. This report presents the results of the first stage of the above study associated with the study of Cassini's laws in the rotation of the Moon and the visualization of these laws by means the programming language Visual Basic. The Earth moves on the Moon's orbit in selenocentric frame. Dynamic coordinate system is based on the principal axes of inertia of the Moon. The x-axis is directed along the largest principal axis of inertia A, the axis z is a dynamic pole of the Moon associated with the smallest principal axis of inertia C. According to the first Cassini’s law the lunar pole is inclined at a constant angle approximately equal to 1.5 degree. The ascending node of the orbit is coincides with descending node of the lunar equator (the second Cassini’s law) and, as a result, the ecliptic pole lies between the orbit pole and spin pole. Therefore the three vectors directed from the lunar centre of mass to orbit pole, ecliptic pole and spin pole form a single plane. The third Cassini’s law reflects the uniform rotation of the Moon synchronised with orbital motion of the Moon around the Earth (in the selenocentric frame the Earth moves around the Moon). It’s necessary a significant time to calculate the corresponding coordinates of points, which move synchronously on the orbit and on the equator. In any time t the Earth moves with the mean velocity n and forms the angle n*t in the orbit plane. At the same time, according to the third law, the axis x forms the same angle varphi = n*t in equatorial plane. In other words the longest axis of the Moon is always "looking" at the Earth. The latter action, which the developed program executes, is a demonstration of the effects of several, the most powerful, harmonics of the physical libration. Unfortunately, Visual Basic opportunities are severely limited for creating three-dimensional images. Because of this we could not to support real scale in angles and time. This work was supported by RFBR grant No. 13-02-00792.

Impact landing ends SMART-1 mission to the Moon

NASA Astrophysics Data System (ADS)

2006-09-01

SMART-1 scientists, engineers and space operations experts witnessed the final moments of the spacecraft’s life in the night between Saturday 2 and Sunday 3 September at ESA’s European Space Operations Centre (ESOC), in Darmstadt, Germany. The confirmation of the impact reached ESOC at 07:42:22 CEST (05:42:22 UT) when ESA’s New Norcia ground station in Australia suddenly lost radio contact with the spacecraft. SMART-1 ended its journey in the Lake of Excellence, in the point situated at 34.4º South latitude and 46.2º West longitude. The SMART-1 impact took place on the near side of the Moon, in a dark area just near the terminator (the line separating the day side from the night side), at a “grazing” angle of about one degree and a speed of about 2 kilometres per second. The impact time and location was planned to favour observations of the impact event from telescopes on Earth, and was achieved by a series of orbit manoeuvres and corrections performed during the course of summer 2006, the last of which was on 1 September. Professional and amateur ground observers all around the world - from South Africa to the Canary Islands, South America, the continental United States, Hawaii, and many other locations - were watching before and during the small SMART-1 impact, hoping to spot the faint impact flash and to obtain information about the impact dynamics and about the lunar surface excavated by the spacecraft. The quality of the data and images gathered from the ground observatories - a tribute to the end of the SMART-1 mission and a possible additional contribution to lunar science - will be assessed in the days to come. For the last 16 months and until its final orbits, SMART-1 has been studying the Moon, gathering data about the morphology and mineralogical composition of the surface in visible, infrared and X-ray light. “The legacy left by the huge wealth of SMART-1 data, to be analysed in the months and years to come, is a precious contribution to lunar science at a time when the exploration of the Moon is once again getting the world’s interest” said Bernard Foing, ESA SMART-1 Project Scientist. “The measurements by SMART-1 call into question the theories concerning the Moon’s violent origin and evolution,” he added. The Moon may have formed from the impact of a Mars-size asteroid with the Earth 4500 million years ago. “SMART-1 has mapped large and small impact craters, studied the volcanic and tectonic processes that shaped the Moon, unveiled the mysterious poles, and investigated sites for future exploration,” Foing concluded. “ESA’s decision to extend the SMART-1 scientific mission by a further year ( it was initially planned to last only six months around the Moon) allowed the instrument scientists to extensively use a number of innovative observing modes at the Moon,” added Gerhard Schwehm, ESA’s SMART-1 Mission Manager. In addition to plain nadir observations (looking down on the ‘vertical’ line for lunar surveys), they included targeted observations, moon-spot pointing and ‘push-broom’ observations (a technique SMART-1 used to obtain colour images). “This was tough work for the mission planners, but the lunar data archive we are now building is truly impressive.” “SMART-1 has been an enormous success also from a technological point of view,” said Giuseppe Racca, ESA SMART-1 Project Manager. The major goal of the mission was to test an ion engine (solar electric propulsion) in space for the first time for interplanetary travel, and capture a spacecraft into orbit around another celestial body, in combination with gravity assist manoeuvres. SMART-1 also tested future deep-space communication techniques for spacecraft, techniques to achieve autonomous spacecraft navigation, and miniaturised scientific instruments, used for the first time around the Moon. “It is a great satisfaction to see how well the mission achieved its technological objectives, and did great lunar science at the same time,” Racca concluded. “Operating SMART-1 has been an extremely complex but rewarding task,” said Octavio Camino-Ramos, ESA SMART-1 Spacecraft Operations Manager. “The long spiralling trajectory around Earth to test solar electric propulsion (a low-thrust approach), the long exposure to radiation, the strong perturbations of the gravity fields of the Earth-Moon system and then the reaching of a lunar orbit optimised for the scientific investigations, have allowed us to gain valuable expertise in navigation techniques for low-thrust propulsion and innovative operations concepts: telemetry distribution and alerting through the internet, and a high degree of ground operations automation - a remarkable benchmark for the future,” he explained. “For ESA’s Science Programme, SMART-1 represents a great success and a very good return on investment, both from the technological and the scientific point of view,” said Professor Southwood, ESA’s Director of Science. “It seems that right now everyone in the world is planning on going to the Moon. Future scientific missions will greatly benefit from the technological and operational experience gained thanks to this small spacecraft, while the set of scientific data gathered by SMART-1 is already helping to update our current picture of the Moon.” Note to editors More images and further updates on the SMART-1 mission end can be found at:www.esa.int/smart-1 SMART-1, (Small Mission for Advanced Research and Technology) is the first European mission to the Moon. It was launched on 27 September 2003 on board an Ariane 5 rocket, from the CSG, Europe’s Spaceport in Kourou, French Guiana and reached its destination in November 2004 after following a long spiralling trajectory around Earth. In this phase, the spacecraft successfully tested for the first time in space the series of advanced technologies it carried on board. The technology demonstration part of the mission was declared successfully concluded when SMART-1 reached the Moon and was captured by the lunar gravity field in mid-November 2004. SMART-1 started its scientific observations of the Moon in March 2005, running on an elliptical polar orbit that ranged from about 500 to 3000 kilometres over the lunar surface. The instruments on board included a miniaturised imaging camera (AMIE), an X-ray telescope (D-CIXS) to identify the key chemical elements in the lunar surface, an infrared spectrometer (SIR) to chart the Moon’s minerals and an X-ray solar monitor (XSM) to complement the D-CIXS measurements and study the solar variability. SMART-1 was a small unmanned satellite weighing 366 kilograms and roughly fitting into a cube just 1 metre across, excluding its 14-metre solar panels. It was manufactured by the Swedish Space Corporation, Solna, leading a consortium of more than 20 European industrial teams.

Using multi-dimensional Smolyak interpolation to make a sum-of-products potential

DOE Office of Scientific and Technical Information (OSTI.GOV)

Avila, Gustavo, E-mail: Gustavo-Avila@telefonica.net; Carrington, Tucker, E-mail: Tucker.Carrington@queensu.ca

2015-07-28

We propose a new method for obtaining potential energy surfaces in sum-of-products (SOP) form. If the number of terms is small enough, a SOP potential surface significantly reduces the cost of quantum dynamics calculations by obviating the need to do multidimensional integrals by quadrature. The method is based on a Smolyak interpolation technique and uses polynomial-like or spectral basis functions and 1D Lagrange-type functions. When written in terms of the basis functions from which the Lagrange-type functions are built, the Smolyak interpolant has only a modest number of terms. The ideas are tested for HONO (nitrous acid)

A Fluid Structure Algorithm with Lagrange Multipliers to Model Free Swimming

NASA Astrophysics Data System (ADS)

Sahin, Mehmet; Dilek, Ezgi

2017-11-01

A new monolithic approach is prosed to solve the fluid-structure interaction (FSI) problem with Lagrange multipliers in order to model free swimming/flying. In the present approach, the fluid domain is modeled by the incompressible Navier-Stokes equations and discretized using an Arbitrary Lagrangian-Eulerian (ALE) formulation based on the stable side-centered unstructured finite volume method. The solid domain is modeled by the constitutive laws for the nonlinear Saint Venant-Kirchhoff material and the classical Galerkin finite element method is used to discretize the governing equations in a Lagrangian frame. In order to impose the body motion/deformation, the distance between the constraint pair nodes is imposed using the Lagrange multipliers, which is independent from the frame of reference. The resulting algebraic linear equations are solved in a fully coupled manner using a dual approach (null space method). The present numerical algorithm is initially validated for the classical FSI benchmark problems and then applied to the free swimming of three linked ellipses. The authors are grateful for the use of the computing resources provided by the National Center for High Performance Computing (UYBHM) under Grant Number 10752009 and the computing facilities at TUBITAK-ULAKBIM, High Performance and Grid Computing Center.

Prediction of a Densely Loaded Particle-Laden Jet using a Euler-Lagrange Dense Spray Model

NASA Astrophysics Data System (ADS)

Pakseresht, Pedram; Apte, Sourabh V.

2017-11-01

Modeling of a dense spray regime using an Euler-Lagrange discrete-element approach is challenging because of local high volume loading. A subgrid cluster of droplets can lead to locally high void fractions for the disperse phase. Under these conditions, spatio-temporal changes in the carrier phase volume fractions, which are commonly neglected in spray simulations in an Euler-Lagrange two-way coupling model, could become important. Accounting for the carrier phase volume fraction variations, leads to zero-Mach number, variable density governing equations. Using pressure-based solvers, this gives rise to a source term in the pressure Poisson equation and a non-divergence free velocity field. To test the validity and predictive capability of such an approach, a round jet laden with solid particles is investigated using Direct Numerical Simulation and compared with available experimental data for different loadings. Various volume fractions spanning from dilute to dense regimes are investigated with and without taking into account the volume displacement effects. The predictions of the two approaches are compared and analyzed to investigate the effectiveness of the dense spray model. Financial support was provided by National Aeronautics and Space Administration (NASA).

Efficient Numerical Methods for Nonlinear-Facilitated Transport and Exchange in a Blood-Tissue Exchange Unit

PubMed Central

Poulain, Christophe A.; Finlayson, Bruce A.; Bassingthwaighte, James B.

2010-01-01

The analysis of experimental data obtained by the multiple-indicator method requires complex mathematical models for which capillary blood-tissue exchange (BTEX) units are the building blocks. This study presents a new, nonlinear, two-region, axially distributed, single capillary, BTEX model. A facilitated transporter model is used to describe mass transfer between plasma and intracellular spaces. To provide fast and accurate solutions, numerical techniques suited to nonlinear convection-dominated problems are implemented. These techniques are the random choice method, an explicit Euler-Lagrange scheme, and the MacCormack method with and without flux correction. The accuracy of the numerical techniques is demonstrated, and their efficiencies are compared. The random choice, Euler-Lagrange and plain MacCormack method are the best numerical techniques for BTEX modeling. However, the random choice and Euler-Lagrange methods are preferred over the MacCormack method because they allow for the derivation of a heuristic criterion that makes the numerical methods stable without degrading their efficiency. Numerical solutions are also used to illustrate some nonlinear behaviors of the model and to show how the new BTEX model can be used to estimate parameters from experimental data. PMID:9146808

Towards the Next International Lunar Decade

NASA Astrophysics Data System (ADS)

Beldavs, Vidvuds

2016-07-01

The idea of an International Lunar Decade (ILD) germinated in work underway in the International Lunar Working Group (ILEWG) coordinated by ESA starting before 2000. Envisioned was an International Geophysical Year (IGY) inspired global collaborative undertaking to better understand the Moon, its origins and resources as a step towards lunar development and possible human settlement. By 2006 the ILD idea had evolved sufficiently that the ILEWG endorsed it and endorsement was also received from COSPAR [1] The Planetary Society under the leadership of Louis Friedman championed the ILD idea, received a grant from the Secure World Foundation to promote it at various conferences as well as to the United Nations Committee on the Peaceful Uses of Outer Space (COPUOS). Friedman made a presentation about ILD to COPUOS in February, 2007 [2]. Despite positive interest in the idea no member state of COPUOS chose to promote it. The ILD agenda was adopted by ILEWG and largely fulfilled by the member space agencies in the decade from 2007-2014, but without UN endorsement as a global initiative. In 2013 an idea for an International Lunar Decade took hold among a group of space activists that included ideas for an International Lunar Research Park [3], an International Lunar Geophysical Year and other elements including an article published by V. Beldavs in the Space Review on January 14, 2014 [4]. These various thought streams were brought to focus at the conference "The Next Giant Leap: Leveraging Lunar Assets for Sustainable Pathways to Space", November 9-13, 2014 in Hawaii that resulted in the International Lunar Decade Declaration [3] and the formation of the working group (ILDWG) to promote implementation of ILD. In 2015 numerous organizations and influential persons were approached and informed about the idea of a framework for international collaboration sustained over a decade to gain an understanding of the Moon and its resources and to develop the technologies and infrastructure that would make lunar development feasible. Presentations, posters and papers were presented at about a dozen conferences in 2015 and the idea of ILD continued to evolve. Where initially launch was anticipated in 2017 commemorating the 60th anniversary of the IGY and the of launch of Sputnik other possibilities have been discussed including launch on July 20, 2019 commemorating the 50th anniversary of the Apollo 11 landing. Current thinking is that the ILD will span the timeframe from 2020 to 2030 aiming towards achieving breakthrough to a self-sustaining space economy beyond Earth orbit. Key to this would be technologies for ISRU as well as markets for products derived from lunar resources and the policies that needed for private investment in lunar resource ventures. The international collaboration envisioned in ILD will coordinate action in lunar exploration, technology development and infrastructure construction and deployment in cislunar space and on the Moon to enable lunar operations, including manned facilities on the Moon as well as at E-M Lagrange points and facilities in Earth orbit. The ILD concept is increasingly including consideration of specific building block elements such as the proposed energy, communication and navigation lunar utility [5]. In 2016 it is anticipated that ILD will be presented at ten more conferences and that key organizations will include ILD in their plans. We anticipate worldwide celebrations commemorating the launch of Sputnik and the dawn of the space age in 2017. A major goal is that ILD become a theme of the UNISPACE +50 conference in 2018. The 50th anniversary of the landing of Apollo 11 on the Moon on July 20, 2019 will mark the launch of ILD itself marking the decade 2020-2030 as a paradigm shift from government-centric, budget driven deep space initiatives to a self-sustaining space economy with the expectation of significant expansion of space exploration along with profit-making space business. References: [1] http://www.planetary.org/press-room/releases/2006/0708_Planetary_Society_Calls_for.html [2] http://www.unoosa.org/pdf/pres/stsc2007/tech-19.pdf [3] Pittman, B 2011 "Been there, never done this", Ad Astra, http://www.nss.org/adastra/volume23/beenthere.html [4] Beldavs, V 2014 "The International Lunar Decade", The Space Review, http://www.thespacereview.com/article/2431/1 [5] Beldavs, V, Dunlap, D, Crisafulli, J, and Foing, B 2015 "The lunar electrical power utility", The Space Review, http://www.thespacereview.com/article/2860/1

Moon and Sun shadowing effect in the MACRO detector

NASA Astrophysics Data System (ADS)

Ambrosio, M.; Antolini, R.; Baldini, A.; Barbarino, G. C.; Barish, B. C.; Battistoni, G.; Becherini, Y.; Bellotti, R.; Bemporad, C.; Bernardini, P.; Bilokon, H.; Bower, C.; Brigida, M.; Bussino, S.; Cafagna, F.; Calicchio, M.; Campana, D.; Carboni, M.; Caruso, R.; Cecchini, S.; Cei, F.; Chiarella, V.; Chiarusi, T.; Choudhary, B. C.; Coutu, S.; Cozzi, M.; De Cataldo, G.; Dekhissi, H.; De Marzo, C.; De Mitri, I.; Derkaoui, J.; De Vincenzi, M.; Di Credico, A.; Erriquez, O.; Favuzzi, C.; Forti, C.; Fusco, P.; Giacomelli, G.; Giannini, G.; Giglietto, N.; Giorgini, M.; Grassi, M.; Grillo, A.; Gustavino, C.; Habig, A.; Hanson, K.; Heinz, R.; Katsavounidis, E.; Katsavounidis, I.; Kearns, E.; Kim, H.; Kumar, A.; Kyriazopoulou, S.; Lamanna, E.; Lane, C.; Levin, D. S.; Lipari, P.; Longley, N. P.; Longo, M. J.; Loparco, F.; Maaroufi, F.; Mancarella, G.; Mandrioli, G.; Manzoor, S.; Margiotta, A.; Marini, A.; Martello, D.; Marzari-Chiesa, A.; Mazziotta, M. N.; Michael, D. G.; Monacelli, P.; Montaruli, T.; Monteno, M.; Mufson, S.; Musser, J.; Nicolò, D.; Nolty, R.; Orth, C.; Osteria, G.; Palamara, O.; Patrizii, L.; Pazzi, R.; Peck, C. W.; Perrone, L.; Petrera, S.; Popa, V.; Rainò, A.; Reynoldson, J.; Ronga, F.; Satriano, C.; Scapparone, E.; Scholberg, K.; Sioli, M.; Sirri, G.; Sitta, M.; Spinelli, P.; Spinetti, M.; Spurio, M.; Steinberg, R.; Stone, J. L.; Sulak, L. R.; Surdo, A.; Tarlè, G.; Togo, V.; Vakili, M.; Walter, C. W.; Webb, R.

2003-11-01

Using data collected by the MACRO experiment from 1989 to the end of its operations in 2000, we have studied in the underground muon flux the shadowing effects due to both the Moon and the Sun. We have observed the shadow cast by the Moon at its apparent position with a significance of 6.5 σ. The Moon shadowing effect has been used to verify the pointing capability of the detector and to determine the instrument resolution for the search of muon excesses from any direction of the celestial sphere. The dependence of the effect on the geomagnetic field is clearly shown by splitting the data sample in day and night observations. The Sun shadow, observed with a significance of 4.6 σ is displaced by about 0.6° from its apparent position. In this case however the explanation resides in the configuration of the Solar and Interplanetary Magnetic Fields, which affect the propagation of cosmic ray particles between the Sun, and the Earth. The displacement of the Sun shadow with respect to the real Sun position has been used to establish an upper limit on the antimatter flux in cosmic rays of about 48% at 68% c.l. and primary energies of about 20 TeV.

The Electrostatic Environments of Mars and the Moon

NASA Technical Reports Server (NTRS)

Calle, Carlos I.

2011-01-01

The electrical activity present in the environment near the surfaces of Mars and the moon has very different origins and presents a challenge to manned and robotic planetary exploration missions. Mars is covered with a layer of dust that has been redistributed throughout the entire planet by global dust storms. Dust, levitated by these storms as well as by the frequent dust devils, is expected to be electrostatically charged due to the multiple grain collisions in the dust-laden atmosphere. Dust covering the surface of the moon is expected to be electrostatically charged due to the solar wind, cosmic rays, and the solar radiation itself through the photoelectric effect. Electrostatically charged dust has a large tendency to adhere to surfaces. NASA's Mars exploration rovers have shown that atmospheric dust falling on solar panels can decrease their efficiency to the point of rendering the rover unusable. And as the Apollo missions to the moon showed, lunar dust adhesion can hinder manned and unmanned lunar exploration activities. Taking advantage of the electrical activity on both planetary system bodies, dust removal technologies are now being developed that use electrostatic and dielectrophoretic forces to produce controlled dust motion. This paper presents a short review of the theoretical and semiempirical models that have been developed for the lunar and Martian electrical environments.

Timing of Crystallisation of the Lunar Magma Ocean Constrained by the Oldest Zircon

NASA Technical Reports Server (NTRS)

Nemchin, A.; Timms, N.; Pidgeon, R.; Geisler, T.; Reddy, S.; Meyer, C.

2009-01-01

The presently favoured concept for the early evolution of the Moon involves consolidation of debris from a giant impact of a Mars sized body with Earth forming a primitive Moon with a thick global layer of melt referred to as the Lunar Magma Ocean1 . It is widely accepted that many significant features observed on the Moon today are the result of crystallisation of this magma ocean. However, controversy exists over the precise timing and duration of the crystallisation process. Resolution of this problem depends on the establishment of precise and robust key crystallisation time points. We report a 4417 6 Myr old zircon in lunar breccia sample 72215,195, which provides a precisely determined younger limit for the solidification of the Lunar Magma Ocean. A model based on these data, together with the age of the Moon forming giant impact, defines an exponential time frame for crystallisation and suggests formation of anorthositic crust after about 80-85% of the magma ocean was solidified. In combination with other zircon ages the 4417 +/- 6 Myr age also suggests that the very small (less than a few per cent) residual portion of the magma ocean continued to solidify during the following 300-500 m.y.

A new preconditioner update strategy for the solution of sequences of linear systems in structural mechanics: application to saddle point problems in elasticity

NASA Astrophysics Data System (ADS)

Mercier, Sylvain; Gratton, Serge; Tardieu, Nicolas; Vasseur, Xavier

2017-12-01

Many applications in structural mechanics require the numerical solution of sequences of linear systems typically issued from a finite element discretization of the governing equations on fine meshes. The method of Lagrange multipliers is often used to take into account mechanical constraints. The resulting matrices then exhibit a saddle point structure and the iterative solution of such preconditioned linear systems is considered as challenging. A popular strategy is then to combine preconditioning and deflation to yield an efficient method. We propose an alternative that is applicable to the general case and not only to matrices with a saddle point structure. In this approach, we consider to update an existing algebraic or application-based preconditioner, using specific available information exploiting the knowledge of an approximate invariant subspace or of matrix-vector products. The resulting preconditioner has the form of a limited memory quasi-Newton matrix and requires a small number of linearly independent vectors. Numerical experiments performed on three large-scale applications in elasticity highlight the relevance of the new approach. We show that the proposed method outperforms the deflation method when considering sequences of linear systems with varying matrices.

User's guide to four-body and three-body trajectory optimization programs

NASA Technical Reports Server (NTRS)

Pu, C. L.; Edelbaum, T. N.

1974-01-01

A collection of computer programs and subroutines written in FORTRAN to calculate 4-body (sun-earth-moon-space) and 3-body (earth-moon-space) optimal trajectories is presented. The programs incorporate a variable step integration technique and a quadrature formula to correct single step errors. The programs provide capability to solve initial value problem, two point boundary value problem of a transfer from a given initial position to a given final position in fixed time, optimal 2-impulse transfer from an earth parking orbit of given inclination to a given final position and velocity in fixed time and optimal 3-impulse transfer from a given position to a given final position and velocity in fixed time.

Power transmission by laser beam from lunar-synchronous satellite

NASA Technical Reports Server (NTRS)

Williams, M. D.; Deyoung, R. J.; Schuster, G. L.; Choi, S. H.; Dagle, J. E.; Coomes, E. P.; Antoniak, Z. I.; Bamberger, J. A.; Bates, J. M.; Chiu, M. A.

1993-01-01

The possibility of beaming power from synchronous lunar orbits (the L1 and L2 Lagrange points) to a manned long-range lunar rover is addressed. The rover and two versions of a satellite system (one powered by a nuclear reactor, the other by photovoltaics) are described in terms of their masses, geometries, power needs, missions, and technological capabilities. Laser beam power is generated by a laser diode array in the satellite and converted to 30 kW of electrical power at the rover. Present technological capabilities, with some extrapolation to near future capabilities, are used in the descriptions. The advantages of the two satellite/rover systems over other such systems and over rovers with onboard power are discussed along with the possibility of enabling other missions.

Analysis of heliographic missions complementary to ISPM. [International Solar Polar Mission

NASA Technical Reports Server (NTRS)

Driver, J. M.

1984-01-01

Five concepts were formulated, analyzed, and compared for satisfying heliographic science mission objectives both with and without a concurrent International Solar Polar Mission (ISPM) Spacecraft. Key astrodynamic constraints and performance factors are known from literature for the Lagrange point mission and the sun-synchronous earth orbit mission, but are set forth in this paper for the three solar orbiting missions concepts considered. Any of these five missions should be doable at modest cost since no strong cost drivers were encountered in the analyses. The mission to be flown depends on mission capability to meet science measurement needs more than on strong economic factors. Each mission offers special advantages for particular measurement emphasis. Based on selected qualitative mission discriminators, an overall 'best mission' was selected and described in some detail.

Order Reduction, Projectability and Constraints of Second-Order Field Theories and Higher-Order Mechanics

NASA Astrophysics Data System (ADS)

Gaset, Jordi; Román-Roy, Narciso

2016-12-01

The projectability of Poincaré-Cartan forms in a third-order jet bundle J3π onto a lower-order jet bundle is a consequence of the degenerate character of the corresponding Lagrangian. This fact is analyzed using the constraint algorithm for the associated Euler-Lagrange equations in J3π. The results are applied to study the Hilbert Lagrangian for the Einstein equations (in vacuum) from a multisymplectic point of view. Thus we show how these equations are a consequence of the application of the constraint algorithm to the geometric field equations, meanwhile the other constraints are related with the fact that this second-order theory is equivalent to a first-order theory. Furthermore, the case of higher-order mechanics is also studied as a particular situation.

Analytic theory of orbit contraction and ballistic entry into planetary atmospheres

NASA Technical Reports Server (NTRS)

Longuski, J. M.; Vinh, N. X.

1980-01-01

A space object traveling through an atmosphere is governed by two forces: aerodynamic and gravitational. On this premise, equations of motion are derived to provide a set of universal entry equations applicable to all regimes of atmospheric flight from orbital motion under the dissipate force of drag through the dynamic phase of reentry, and finally to the point of contact with the planetary surface. Rigorous mathematical techniques such as averaging, Poincare's method of small parameters, and Lagrange's expansion, applied to obtain a highly accurate, purely analytic theory for orbit contraction and ballistic entry into planetary atmospheres. The theory has a wide range of applications to modern problems including orbit decay of artificial satellites, atmospheric capture of planetary probes, atmospheric grazing, and ballistic reentry of manned and unmanned space vehicles.

Observation of two new L4 Neptune Trojans in the Dark Energy Survey supernova fields

DOE PAGES

Gerdes, D. W.

2016-01-28

We report the discovery of the eighth and ninth known Trojans in stable orbits around Neptune's leading Lagrange point, L4. The objects 2014 QO 441 and 2014 QP 441 were detected in data obtained during the 2013-14 and 2014-15 observing seasons by the Dark Energy Survey, using the Dark Energy Camera (DECam) on the 4-meter Blanco telescope at Cerro Tololo Inter- American Observatory. Both are in high-inclination orbits (18.8° and 19.4° respectively). Furthermore, with an eccentricity of 0.104, 2014 QO 441 has the most eccentric orbit of the eleven known stable Neptune Trojans. We describe the search procedure and investigatemore » the objects' long-term dynamical stability and physical properties.« less

The James Webb Space Telescope

NASA Technical Reports Server (NTRS)

Mather, John C.

2004-01-01

The James Webb Space Telescope (JWST) will extend the discoveries of the Hubble Space Telescope (HST) and the Spitzer Space Telescope (SST) by deploying a large cooled infrared telescope around the Sun-Earth Lagrange point L2. With a 6 m aperture and three instruments covering the wavelength range from 0.6 to 28 microns, it will provide sensitivities orders of magnitude better than any other facilities. It is intended to observe the light from the first galaxies and the first supernovae, the assembly of galaxies, and the formation and evolution of stars and planetary systems. In this talk I will review the scientific objectives and the ability of the system to meet them. I will close with a summary of possible future IR space missions, ranging from the far IR to planet-finding coronagraphs and interferometers

Next Generation Space Telescope

NASA Technical Reports Server (NTRS)

Mather, John; Stockman, H. S.; Fisher, Richard R. (Technical Monitor)

2000-01-01

The Next Generation Space Telescope (NGST), planned for launch in 2009, will be an 8-m class radiatively cooled infrared telescope at the Lagrange point L2. It will cover the wavelength range from 0.6 to 28 microns with cameras and spectrometers, to observe the first luminous objects after the Big Bang, and the formation, growth, clustering, and evolution of galaxies, stars, and protoplanetary clouds, leading to better understanding of our own Origins. It will seek evidence of the cosmic dark matter through its gravitational effects. With an aperture three times greater than the Hubble Space Telescope, it will provide extraordinary advances in capabilities and enable the discovery of many new phenomena. It is a joint project of the NASA, ESA, and CSA, and scientific operations will be provided by the Space Telescope Science Institute.

James Webb Space Telescope Status

NASA Technical Reports Server (NTRS)

Mather, John C.

2005-01-01

The James Webb Space Telescope (JWST) is the first deployable infrared to millimeter wave space telescopes. We will describe the progress on JWST and introduce other speakers in the session. The JWST will operate at the Sun-Earth Lagrange point L2, where radiative cooling lowers the telescope and instrument temperatures to about 35 K. It will have an 18-segment beryllium primary mirror with a 25 m2 area fitting inside a 6.6m circumscribed circle, and will provide spectroscopy and imaging over the wavelength range from 0.6 to 28 microns. It is planned for launch in 2011 on an Ariane 5 rocket. The project is a partnership of NASA, ESA, and CSA, and the prime contractor is Northrop Grumman. See http://www.jwst.nasa.gov for more details on JWST.

Comparison of transform coding methods with an optimal predictor for the data compression of digital elevation models

NASA Technical Reports Server (NTRS)

Lewis, Michael

1994-01-01

Statistical encoding techniques enable the reduction of the number of bits required to encode a set of symbols, and are derived from their probabilities. Huffman encoding is an example of statistical encoding that has been used for error-free data compression. The degree of compression given by Huffman encoding in this application can be improved by the use of prediction methods. These replace the set of elevations by a set of corrections that have a more advantageous probability distribution. In particular, the method of Lagrange Multipliers for minimization of the mean square error has been applied to local geometrical predictors. Using this technique, an 8-point predictor achieved about a 7 percent improvement over an existing simple triangular predictor.

Digital elevation modeling via curvature interpolation for lidar data

USDA-ARS?s Scientific Manuscript database

Digital elevation model (DEM) is a three-dimensional (3D) representation of a terrain's surface - for a planet (including Earth), moon, or asteroid - created from point cloud data which measure terrain elevation. Its modeling requires surface reconstruction for the scattered data, which is an ill-p...

Trajectory analysis of transfers between L4 and L5 and low lunar orbit

NASA Technical Reports Server (NTRS)

1988-01-01

The flight characteristics and spacecraft performance during missions involving flight between the equilateral libration points and the Moon are discussed. The conclusions drawn will show that a minimum energy trajectory is the most efficient transfer technique for this type of flight.

California State Waters Map Series: offshore of Half Moon Bay, California

USGS Publications Warehouse

Cochrane, Guy R.; Dartnell, Peter; Greene, H. Gary; Johnson, Samuel Y.; Golden, Nadine E.; Hartwell, Stephen R.; Dieter, Bryan E.; Manson, Michael W.; Sliter, Ray W.; Ross, Stephanie L.; Watt, Janet T.; Endris, Charles A.; Kvitek, Rikk G.; Phillips, Eleyne L.; Erdey, Mercedes D.; Chin, John L.; Bretz, Carrie K.

2014-01-01

In 2007, the California Ocean Protection Council initiated the California Seafloor Mapping Program (CSMP), designed to create a comprehensive seafloor map of high-resolution bathymetry, marine benthic habitats, and geology within the 3-nautical-mile limit of California’s State Waters. The CSMP approach is to create highly detailed seafloor maps through collection, integration, interpretation, and visualization of swath sonar data, acoustic backscatter, seafloor video, seafloor photography, high-resolution seismic-reflection profiles, and bottom-sediment sampling data. The map products display seafloor morphology and character, identify potential marine benthic habitats, and illustrate both the surficial seafloor geology and shallow (to about 100 m) subsurface geology. The Offshore of Half Moon Bay map area is located in northern California, on the Pacific coast of the San Francisco Peninsula about 40 kilometers south of the Golden Gate. The city of Half Moon Bay, which is situated on the east side of the Half Moon Bay embayment, is the nearest significant onshore cultural center in the map area, with a population of about 11,000. The Pillar Point Harbor at the north edge of Half Moon Bay offers a protected landing for boats and provides other marine infrastructure. The map area lies offshore of the Santa Cruz Mountains, part of the northwest-trending Coast Ranges that run roughly parallel to the San Andreas Fault Zone. The Santa Cruz Mountains lie between the San Andreas Fault Zone and the San Gregorio Fault system. The flat coastal area, which is the most recent of numerous marine terraces, was formed by wave erosion about 105 thousand years ago. The higher elevation of this same terrace west of the Half Moon Bay Airport is caused by uplift on the Seal Cove Fault, a splay of the San Gregorio Fault Zone. Although originally incised into the rising terrain horizontally, the ancient terrace surface has been gently folded into a northwest-plunging syncline by compression related to right-lateral strike-slip movement along the San Gregorio Fault Zone. The lowest elevation coincides with the deepest part of Half Moon Bay; the terrace surface rises both to the north and to the south. Uplift in this map area has resulted in relatively shallow water depths within California’s State Waters and, thus, little accommodation space for sediment accumulation. Sediment is observed in the shelter of Half Moon Bay and on the outer half of the California’s State Waters shelf. Sediment in the area is mobile, often forming dunes and sand waves. A westward bend in the San Andreas Fault Zone, southeast of the map area, coupled with right-lateral movement along the Seal Cove Fault, which comes ashore in Pillar Point Harbor, has resulted in the folding and uplifting of sedimentary rocks of the Purisima Formation in the offshore. Differential erosion of these folded and faulted layers of the Purisima Formation has exposed the parallel curved-rock ridges that are visible on the seafloor from the headland at Pillar Point. During the winter, strong North Pacific storms generate large, long-period waves that shoal and break over this bedrock reef at the world-famous surfing location known as Mavericks. The Offshore of Half Moon Bay map area lies within the cold-temperate biogeographic zone that is called either the “Oregonian province” or the “northern California ecoregion.” This biogeographic province is maintained by the long-term stability of the southward-flowing California Current, an eastern limb of the North Pacific subtropical gyre that flows from Oregon to Baja California. At its midpoint off central California, the California Current transports subarctic surface (0–500 m deep) waters southward, about 150 to 1,300 km from shore. Seasonal northwesterly winds that are, in part, responsible for the California Current, generate coastal upwelling. The south end of the Oregonian province is at Point Conception (about 365 km south of the map area), although its associated phylogeographic group of marine fauna may extend beyond to the area offshore of Los Angeles in southern California. The ocean off central California has experienced a warming over the last 50 years that is driving an ecosystem shift away from the productive subarctic regime towards a depopulated subtropical environment. Seafloor habitats in the Offshore of Half Moon Bay map area, which lies within the Shelf (continental shelf) megahabitat, range from significant rocky outcrops that support kelp-forest communities nearshore to rocky-reef communities in deep water. Biological productivity resulting from coastal upwelling supports populations of sea birds such as Sooty Shearwater, Western Gull, Common Murre, Cassin’s Auklet, and many other less populous bird species. In addition, an observable recovery of Humpback and Blue Whales has occurred in the area; both species are dependent on coastal upwelling to provide nutrients. The large extent of exposed inner shelf bedrock supports large forests of “bull kelp,” which is well adapted for high wave-energy environments. Common fish species found in the kelp beds and rocky reefs include lingcod and various species of rockfish and greenling.

Evaluation of the new radiation belt AE9/AP9/SPM model for a cislunar mission

NASA Astrophysics Data System (ADS)

Badavi, Francis F.; Walker, Steven A.; Santos Koos, Lindsey M.

2014-09-01

Space mission planners continue to experience challenges associated with human space flight. Concerned with the omnipresence of harmful ionizing radiation in space, at the mission design stage, mission planners must evaluate the amount of exposure the crew of a spacecraft is subjected to during the transit trajectory from low Earth orbit (LEO) to geosynchronous orbit (GEO) and beyond (free space). The Earth's geomagnetic field is located within the domain of LEO-GEO and, depending on latitude, extends out some 40,000-60,000 km. This field contains the Van Allen trapped electrons, protons, and low-energy plasmas, such as the nuclei of hydrogen, helium, oxygen, and to a lesser degree other atoms. In addition, there exist the geomagnetically attenuated energetic galactic cosmic rays (GCR). These particles are potentially harmful to improperly shielded crew members and onboard subsystems. Mitigation strategies to limit the exposure due to free space GCR and sporadic solar energetic particles (SEP) such as flare and coronal mass ejection (CME) must also be exercised beyond the trapped field. Presented in this work is the exposure analysis for a multi-vehicle mission planned for the epoch of February 2020 from LEO to the Earth-moon Lagrange-point two (L2), located approximately 63,000 km beyond the orbit of the Earth-moon binary system. Space operation at L2 provides a gravitationally stable orbit for a vehicle and partially eliminates the need for periodic thrust-vectoring to maintain orbital stability. In the cislunar (Earth-moon) space of L2, the mission trajectory and timeline in this work call for a cargo vehicle to rendezvous with a crew vehicle. This is followed by 15 days of space activities at L2 while the cargo and crew vehicles are docked after which the crew returns to Earth. The mission epoch of 2020 is specifically chosen as it is anticipated that the next solar minimum (i.e. end of cycle 24) in the Sun's approximate 11 years cycle will take place around this time. From a mission planning point of view, this date is ideal as the predictable GCR exposure will be at a maximum, while the sporadic SEP will be at a minimum. In addition, it is anticipated that by 2020 a vehicle capable of launching a crew of four will be operationally ready. During the LEO-GEO transit, the crew and cargo vehicles will encounter exposure from trapped particles and attenuated GCR, followed by free space exposure due to GCR and SEP during solar active times. Within the trapped field, a challenge arises from properly calculating the amount of exposure acquired. Within this field, in the absence of SEP (i.e. solar quiet times), the vehicles will have to transit through an inner proton belt, an inner and outer electron belts, and an attenuated GCR field. There exist a number of models to define the intensities of the trapped particles during the quiet and active SEP. Among the more established trapped models are the historic and popular electron/proton AE8/AP8 model dating back to the 1980s, the historic and less popular electron/proton CRRES model dating back to 1990s, and the recently released electron/proton/space plasma AE9/AP9/SPM model. The AE9/AP9/SPM model is a major improvement over the older AE8/AP8 and CRRES models. This model is derived from numerous measurements acquired over four solar cycles dating back to the 1970s, roughly representing 40 years of data collection. In contrast, the older AE8/AP8 and CRRES models were limited to only a few months of measurements taken during the prior solar minima and maxima. In this work, within the trapped field, along the design trajectory of the crew vehicle, the AE9/AP9/SPM model is evaluated against the older AE8/AP8 model during solar quiet times. The analysis is then extended to the GCR dominated en-route, cislunar L2 space and return trajectories in order to provide cumulative exposure estimates to the crew vehicle for the duration of the entire mission.

Laser observations of the moon - Normal points for 1972

NASA Technical Reports Server (NTRS)

Shelus, P. J.; Mulholland, J. D.; Silverberg, E. C.

1975-01-01

The lunar laser observations taken at the McDonald Observatory during 1972 are presented in the form of compressed normal points, using the technique of an earlier paper. Refinements in the knowledge of the lunar motion have permitted corresponding increases in the ability to discriminate observations contaminated by equipment malfunctions; a list of amendments is given for the 1969-1971 data. The geometry of the telescope must be taken into account in the application of these data.

Development and validation of a learning progression for change of seasons, solar and lunar eclipses, and moon phases

NASA Astrophysics Data System (ADS)

Testa, Italo; Galano, Silvia; Leccia, Silvio; Puddu, Emanuella

2015-12-01

In this paper, we report about the development and validation of a learning progression about the Celestial Motion big idea. Existing curricula, research studies on alternative conceptions about these phenomena, and students' answers to an open questionnaire were the starting point to develop initial learning progressions about change of seasons, solar and lunar eclipses, and Moon phases; then, a two-tier multiple choice questionnaire was designed to validate and improve them. The questionnaire was submitted to about 300 secondary students of different school levels (14 to 18 years old). Item response analysis and curve integral method were used to revise the hypothesized learning progressions. Findings support that spatial reasoning is a key cognitive factor for building an explanatory framework for the Celestial Motion big idea, but also suggest that causal reasoning based on physics mechanisms underlying the phenomena, as light flux laws or energy transfers, may significantly impact a students' understanding. As an implication of the study, we propose that the teaching of the three discussed astronomy phenomena should follow a single teaching-learning path along the following sequence: (i) emphasize from the beginning the geometrical aspects of the Sun-Moon-Earth system motion; (ii) clarify consequences of the motion of the Sun-Moon-Earth system, as the changing solar radiation flow on the surface of Earth during the revolution around the Sun; (iii) help students moving between different reference systems (Earth and space observer's perspective) to understand how Earth's rotation and revolution can change the appearance of the Sun and Moon. Instructional and methodological implications are also briefly discussed.

Annular and Total Solar Eclipses of 2003

NASA Technical Reports Server (NTRS)

Espenak, Fred; Anderson, Jay

2002-01-01

On Saturday, 2003 May 31, an annular eclipse of the Sun will be visible from a broad corridor that traverses the North Atlantic. The path of the Moon's antumbral shadow begins in northern Scotland, crosses Iceland and central Greenland, and ends at sunrise in Baffin Bay (Canada). A partial eclipse will be seen within the much broader path of the Moon's penumbral shadow, which includes most of Europe, the Middle East, central and northern Asia, and northwestern North America. The trajectory of the Moon's shadow is quite unusual during this event. The shadow axis passes to the far north where it barely grazes Earth's surface. In fact, the northern edge of the antumbra actually misses Earth so that one path limit is defined by the day/night terminator rather than by the shadow's upper edge. As a result, the track of annularity has a peculiar "D" shape that is nearly 1200 kilometers wide. Since the eclipse occurs just three weeks prior to the northern summer solstice, Earth's northern axis is pointed sunwards by 22.8 deg. As seen from the Sun, the antumbral shadow actually passes between the North Pole and the terminator. As a consequence of this extraordinary geometry, the path of annularity runs from east to west rather than the more typical west to east. The event transpires near the Moon's ascending node in Taurus five degrees north of Aldebaran. Since apogee occurs three days earlier (May 28 at 13 UT), the Moon's apparent diameter (29.6 arc-minutes) is still too small to completely cover the Sun (31.6 arc-minutes) resulting in an annular eclipse.

Zero, minimum and maximum relative radial acceleration for planar formation flight dynamics near triangular libration points in the Earth-Moon system

NASA Astrophysics Data System (ADS)

Salazar, F. J. T.; Masdemont, J. J.; Gómez, G.; Macau, E. E.; Winter, O. C.

2014-11-01

Assume a constellation of satellites is flying near a given nominal trajectory around L4 or L5 in the Earth-Moon system in such a way that there is some freedom in the selection of the geometry of the constellation. We are interested in avoiding large variations of the mutual distances between spacecraft. In this case, the existence of regions of zero and minimum relative radial acceleration with respect to the nominal trajectory will prevent from the expansion or contraction of the constellation. In the other case, the existence of regions of maximum relative radial acceleration with respect to the nominal trajectory will produce a larger expansion and contraction of the constellation. The goal of this paper is to study these regions in the scenario of the Circular Restricted Three Body Problem by means of a linearization of the equations of motion relative to the periodic orbits around L4 or L5. This study corresponds to a preliminar planar formation flight dynamics about triangular libration points in the Earth-Moon system. Additionally, the cost estimate to maintain the constellation in the regions of zero and minimum relative radial acceleration or keeping a rigid configuration is computed with the use of the residual acceleration concept. At the end, the results are compared with the dynamical behavior of the deviation of the constellation from a periodic orbit.

Temperature Gradient on Martian Moon Phobos

NASA Image and Video Library

2017-10-04

This image combines two products from the first pointing at the Martian moon Phobos by the Thermal Emission Imaging System (THEMIS) camera on NASA's Mars Odyssey orbiter, on Sept. 29, 2017. Surface-temperature information from observation in thermal-infrared wavelengths is overlaid on a more detailed image from a visible-light observation. The left edge of the small moon was in darkness, and the right edge in morning sunlight. Phobos has an oblong shape with average diameter of about 14 miles (22 kilometers). The distance to Phobos from Odyssey during the observation was about 3,424 miles (5,511 kilometers). Researchers will analyze the surface-temperature information from this observation and possible future THEMIS observations to learn how quickly the surface warms after sunup or cools after sundown. That could provide information about surface materials, because larger rocks heat or cool more slowly than smaller particles do. The thermal information in this image is from merging observations made in four thermal-infrared wavelength bands, centered from 11.04 microns to 14.88 microns. Researchers have been using THEMIS to examine Mars since early 2002, but the maneuver turning the orbiter around to point the camera at Phobos was developed only recently. Odyssey orbits Mars at an altitude of about 250 miles (400 kilometers), much closer to the planet than to Phobos, which orbits about 3,700 miles (6,000 kilometers) above the surface of Mars. https://photojournal.jpl.nasa.gov/catalog/PIA22057

The Lunar Polesitter

NASA Technical Reports Server (NTRS)

West, John L.

2008-01-01

Here-to-fore, sailcraft mission and system studies have focused on sailcraft applications in support of NASA's science missions and, in a few studies, on the needs of other federal agencies such as the National Oceanic and Atmospheric Administration (NOAA) and Department of Defense (DoD). These studies have identified numerous promising applications for solar sails, leading NASA to support proposal efforts for three NASA New Millennium Program (NMP) flight demonstration opportunities (the Space Technology-5, -7, and -9 opportunities) as well as an extensive three-year ground development program in FY 2003-2005 sponsored by the NASA In-Space Propulsion Technology (ISPT) Program. What has not been done to date, however, is to investigate how the technology might also benefit the nation's (and NASA's) emerging interest in the Human Exploration Initiative (HEI). This paper reports on the first effort to address this shortfall in mission applications studies in support of HEI: the use of solar-sail-propelled Lunar Polesitter spacecraft which make use of the natural properties of the Earth-Moon L2 point and solar sail propulsion to enable their positioning near the Lunar poles to serve as communications relay stations. Suitably positioned, such spacecraft enable continuous communications to and from the Earth from any point on the lunar far side. The paper shows that a viable sailcraft system design exists permitting station-keeping of a Lunar Polesitter relay station at 40 Lunar radii from the Moon in the anti-Earth direction, displaced 6-8 Lunar radii below the Earth- Moon plane.

Addressing Children's Alternative Frameworks of the Moon's Phases and Eclipses.

ERIC Educational Resources Information Center

Barnett, Michael; Morran, Judy

2002-01-01

Analyzes a project-based space science curriculum designed to support elementary school students in understanding complex, inter-related astronomy concepts. Uses pre- and post-interviews, examines student work, and has students complete a pre- and post-astronomy conceptual survey to assess conceptual change. Points out that instruction should…

Rendezvous with Toutatis from the Moon: The Chang'e-2 mission

NASA Astrophysics Data System (ADS)

Huang, J.; Tang, X.; Meng, L.

2014-07-01

Chang'e-2 probe was the second lunar probe of China, with the main objectives to demonstrate some key features of the new lunar soft landing technology, and its applications to future exploration missions. After completing the planned mission successfully, Chang'e-2 flew away from the Moon and entered into the interplanetary space. Later, at a distance of 7 million km from the Earth, Chang'e-2 encountered asteroid (4179) Toutatis with a very close fly-by distance and obtained colorful images with a 3-m resolution. Given some surplus velocity increment as well as the promotion of autonomous flight ability and improvement of control, propulsion, and thermal systems in the initial design, Chang'e-2 had the capabilities necessary for escaping from the Moon. By taking advantage of the unique features of the Lagrangian point, the first close fly-by of asteroid Toutatis was realized despite the tight constraints of propellant allocation, spacecraft-Earth communication, and coordination of execution sequences. Chang'e-2 realized the Toutatis flyby with a km-level distance at closest approach. In the absence of direct measurement method, based on the principle of relative navigation and through the use of the sequence of target images, we calculated the rendezvous parameters such as relative distance and image resolution. With the help of these parameters, some fine and new scientific discoveries about the asteroid were obtained by techniques of optical measurements and image processing. Starting with an innovative design, followed by high-fidelity testing and demonstration, elaborative implementation, and optimal usage of residual propellant, Chang'e-2 has for the first time successfully explored the Moon, L2 point and an asteroid, while achieving the purpose of 'faster, better, cheaper'. What Chang'e-2 has accomplished was far beyond our expectations. *J. Huang is the chief designer (PI) of Chang'e-2 probe, planned Chang'e-2's multi-objective and multitasking exploration mission.

Dynamics and Control of Constrained Multibody Systems modeled with Maggi's equation: Application to Differential Mobile Robots Part I

NASA Astrophysics Data System (ADS)

Amengonu, Yawo H.; Kakad, Yogendra P.

2014-07-01

Quasivelocity techniques such as Maggi's and Boltzmann-Hamel's equations eliminate Lagrange multipliers from the beginning as opposed to the Euler-Lagrange method where one has to solve for the n configuration variables and the multipliers as functions of time when there are m nonholonomic constraints. Maggi's equation produces n second-order differential equations of which (n-m) are derived using (n-m) independent quasivelocities and the time derivative of the m kinematic constraints which add the remaining m second order differential equations. This technique is applied to derive the dynamics of a differential mobile robot and a controller which takes into account these dynamics is developed.

Augmented Lagrange Programming Neural Network for Localization Using Time-Difference-of-Arrival Measurements.

PubMed

Han, Zifa; Leung, Chi Sing; So, Hing Cheung; Constantinides, Anthony George

2017-08-15

A commonly used measurement model for locating a mobile source is time-difference-of-arrival (TDOA). As each TDOA measurement defines a hyperbola, it is not straightforward to compute the mobile source position due to the nonlinear relationship in the measurements. This brief exploits the Lagrange programming neural network (LPNN), which provides a general framework to solve nonlinear constrained optimization problems, for the TDOA-based localization. The local stability of the proposed LPNN solution is also analyzed. Simulation results are included to evaluate the localization accuracy of the LPNN scheme by comparing with the state-of-the-art methods and the optimality benchmark of Cramér-Rao lower bound.

Domain decomposition methods for nonconforming finite element spaces of Lagrange-type

NASA Technical Reports Server (NTRS)

Cowsar, Lawrence C.

1993-01-01

In this article, we consider the application of three popular domain decomposition methods to Lagrange-type nonconforming finite element discretizations of scalar, self-adjoint, second order elliptic equations. The additive Schwarz method of Dryja and Widlund, the vertex space method of Smith, and the balancing method of Mandel applied to nonconforming elements are shown to converge at a rate no worse than their applications to the standard conforming piecewise linear Galerkin discretization. Essentially, the theory for the nonconforming elements is inherited from the existing theory for the conforming elements with only modest modification by constructing an isomorphism between the nonconforming finite element space and a space of continuous piecewise linear functions.

From LEO, to the Moon and then Mars: Developing a Global Strategy for Exploration Risk Reduction

NASA Technical Reports Server (NTRS)

Laurini, Kathleen C.; Hufenbach, Bernard

2009-01-01

Most nations currently involved in human spaceflight, or with such ambitions, believe that space exploration will capture the imagination of our youth resulting in future engineers and scientists, advance technologies which will improve life on earth, increase the knowledge of our solar system, and strengthen bonds and relationships across the globe. The Global Exploration Strategy, published in 2007 by 14 space agencies, eloquently makes this case and presents a vision for space exploration. It argues that in order for space exploration to be sustainable, nations must work together to address the challenges and share the burden of costs. This paper will examine Mars mission scenarios developed by NASA, ESA and other agencies and show resulting conclusions regarding key challenges, needed technologies and associated mission risks. It will discuss the importance of using the International Space Station as a platform for exploration risk reduction and how the global exploration community will develop lunar exploration elements and architectures that enable the long term goal of human missions to Mars. The International Space Station (ISS) is a critical first step both from a technology and capability demonstration point of view, but also from a partnership point of view. There is much work that can be done in low earth orbit for exploration risk reduction. As the current "outpost at the edge of the frontier", the ISS is a place where we can demonstrate certain technologies and capabilities that will substantially reduce the risk of deploying an outpost on the lunar surface and Mars mission scenarios. The ISS partnership is strong and has fulfilled mission needs. Likewise, the partnerships we build on the moon will provide a strong foundation for establishing partnerships for the human Mars missions. On the moon, we build a permanently manned outpost and deploy technologies and capabilities to allow humans to stay for long periods of time. The moon is interesting from a scientific point of view, but it is extremely important for development and demonstration the technologies and capabilities needed for human missions to Mars. This paper will show the logic and strategy for addressing technological, operational and programmatic challenges by using low earth orbit and lunar missions to enable the long term goal of exploration of our solar system.

Trajectory design for Saturnian Ocean Worlds orbiters using multidimensional Poincaré maps

NASA Astrophysics Data System (ADS)

Davis, Diane Craig; Phillips, Sean M.; McCarthy, Brian P.

2018-02-01

Missions based on low-energy orbits in the vicinity of planetary moons, such as Titan or Enceladus, involve significant end-to-end trajectory design challenges due to the gravitational effects of the distant larger primary. To address these challenges, the current investigation focuses on the visualization and use of multidimensional Poincaré maps to perform preliminary design of orbits with significant out-of-plane components, including orbits that provide polar coverage. Poincaré maps facilitate the identification of families of solutions to a given orbit problem and provide the ability to easily respond to changing inputs and requirements. A visual-based design process highlights a variety of trajectory options near Saturn's ocean worlds, including both moon-centered orbits and libration point orbits.

SKITTER/implement mechanical interface

NASA Technical Reports Server (NTRS)

Cash, John Wilson, III; Cone, Alan E.; Garolera, Frank J.; German, David; Lindabury, David Peter; Luckado, Marshall Cleveland; Murphey, Craig; Rowell, John Bryan; Wilkinson, Brad

1988-01-01

SKITTER (Spacial Kinematic Inertial Translatory Tripod Extremity Robot) is a three-legged transport vehicle designed to perform under the unique environment of the moon. The objective of this project was to design a mechanical interface for SKITTER. This mechanical latching interface will allow SKITTER to use a series of implements such as drills, cranes, etc., and perform different tasks on the moon. The design emphasized versatility and detachability; that is, the interface design is the same for all implements, and connection and detachment is simple. After consideration of many alternatives, a system of three identical latches at each of the three interface points was chosen. The latching mechanism satisfies the design constraints because it facilitates connection and detachment. Also, the moving parts are protected from the dusty environment by housing plates.

Solar System Exploration Augmented by In-Situ Resource Utilization: Human Planetary Base Issues for Mercury and Saturn

NASA Technical Reports Server (NTRS)

Palaszewski, Bryan A.

2017-01-01

Human and robotic missions to Mercury and Saturn are presented and analyzed with a range of propulsion options. Historical studies of space exploration, planetary spacecraft, and astronomy, in-situ resource utilization (ISRU), and industrialization all point to the vastness of natural resources in the solar system. Advanced propulsion benefitted from these resources in many ways. While advanced propulsion systems were proposed in these historical studies, further investigation of nuclear options using high power nuclear thermal and nuclear pulse propulsion as well as advanced chemical propulsion can significantly enhance these scenarios. Updated analyses based on these historical visions are presented. Nuclear thermal propulsion and ISRU enhanced chemical propulsion landers are assessed for Mercury missions. At Saturn, nuclear pulse propulsion with alternate propellant feed systems and Saturn moon exploration with chemical propulsion and nuclear electric propulsion options are discussed. Issues with using in-situ resource utilization on Mercury missions are discussed. At Saturn, the best locations for exploration and the use of the moons Titan and Enceladus as central locations for Saturn moon exploration is assessed.

Inflight Calibration of the Lunar Reconnaissance Orbiter Camera Wide Angle Camera

NASA Astrophysics Data System (ADS)

Mahanti, P.; Humm, D. C.; Robinson, M. S.; Boyd, A. K.; Stelling, R.; Sato, H.; Denevi, B. W.; Braden, S. E.; Bowman-Cisneros, E.; Brylow, S. M.; Tschimmel, M.

2016-04-01

The Lunar Reconnaissance Orbiter Camera (LROC) Wide Angle Camera (WAC) has acquired more than 250,000 images of the illuminated lunar surface and over 190,000 observations of space and non-illuminated Moon since 1 January 2010. These images, along with images from the Narrow Angle Camera (NAC) and other Lunar Reconnaissance Orbiter instrument datasets are enabling new discoveries about the morphology, composition, and geologic/geochemical evolution of the Moon. Characterizing the inflight WAC system performance is crucial to scientific and exploration results. Pre-launch calibration of the WAC provided a baseline characterization that was critical for early targeting and analysis. Here we present an analysis of WAC performance from the inflight data. In the course of our analysis we compare and contrast with the pre-launch performance wherever possible and quantify the uncertainty related to various components of the calibration process. We document the absolute and relative radiometric calibration, point spread function, and scattered light sources and provide estimates of sources of uncertainty for spectral reflectance measurements of the Moon across a range of imaging conditions.

The new moon illusion and the role of perspective in the perception of straight and parallel lines.

PubMed

Rogers, Brian; Naumenko, Olga

2015-01-01

In the new moon illusion, the sun does not appear to be in a direction perpendicular to the boundary between the lit and dark sides of the moon, and aircraft jet trails appear to follow curved paths across the sky. In both cases, lines that are physically straight and parallel to the horizon appear to be curved. These observations prompted us to investigate the neglected question of how we are able to judge the straightness and parallelism of extended lines. To do this, we asked observers to judge the 2-D alignment of three artificial "stars" projected onto the dome of the Saint Petersburg Planetarium that varied in both their elevation and their separation in horizontal azimuth. The results showed that observers make substantial, systematic errors, biasing their judgments away from the veridical great-circle locations and toward equal-elevation settings. These findings further demonstrate that whenever information about the distance of extended lines or isolated points is insufficient, observers tend to assume equidistance, and as a consequence, their straightness judgments are biased toward the angular separation of straight and parallel lines.

The formulation of dynamical contact problems with friction in the case of systems of rigid bodies and general discrete mechanical systems—Painlevé and Kane paradoxes revisited

NASA Astrophysics Data System (ADS)

Charles, Alexandre; Ballard, Patrick

2016-08-01

The dynamics of mechanical systems with a finite number of degrees of freedom (discrete mechanical systems) is governed by the Lagrange equation which is a second-order differential equation on a Riemannian manifold (the configuration manifold). The handling of perfect (frictionless) unilateral constraints in this framework (that of Lagrange's analytical dynamics) was undertaken by Schatzman and Moreau at the beginning of the 1980s. A mathematically sound and consistent evolution problem was obtained, paving the road for many subsequent theoretical investigations. In this general evolution problem, the only reaction force which is involved is a generalized reaction force, consistently with the virtual power philosophy of Lagrange. Surprisingly, such a general formulation was never derived in the case of frictional unilateral multibody dynamics. Instead, the paradigm of the Coulomb law applying to reaction forces in the real world is generally invoked. So far, this paradigm has only enabled to obtain a consistent evolution problem in only some very few specific examples and to suggest numerical algorithms to produce computational examples (numerical modeling). In particular, it is not clear what is the evolution problem underlying the computational examples. Moreover, some of the few specific cases in which this paradigm enables to write down a precise evolution problem are known to show paradoxes: the Painlevé paradox (indeterminacy) and the Kane paradox (increase in kinetic energy due to friction). In this paper, we follow Lagrange's philosophy and formulate the frictional unilateral multibody dynamics in terms of the generalized reaction force and not in terms of the real-world reaction force. A general evolution problem that governs the dynamics is obtained for the first time. We prove that all the solutions are dissipative; that is, this new formulation is free of Kane paradox. We also prove that some indeterminacy of the Painlevé paradox is fixed in this formulation.

Lagrange constraint neural network for audio varying BSS

NASA Astrophysics Data System (ADS)

Szu, Harold H.; Hsu, Charles C.

2002-03-01

Lagrange Constraint Neural Network (LCNN) is a statistical-mechanical ab-initio model without assuming the artificial neural network (ANN) model at all but derived it from the first principle of Hamilton and Lagrange Methodology: H(S,A)= f(S)- (lambda) C(s,A(x,t)) that incorporates measurement constraint C(S,A(x,t))= (lambda) ([A]S-X)+((lambda) 0-1)((Sigma) isi -1) using the vector Lagrange multiplier-(lambda) and a- priori Shannon Entropy f(S) = -(Sigma) i si log si as the Contrast function of unknown number of independent sources si. Szu et al. have first solved in 1997 the general Blind Source Separation (BSS) problem for spatial-temporal varying mixing matrix for the real world remote sensing where a large pixel footprint implies the mixing matrix [A(x,t)] necessarily fill with diurnal and seasonal variations. Because the ground truth is difficult to be ascertained in the remote sensing, we have thus illustrated in this paper, each step of the LCNN algorithm for the simulated spatial-temporal varying BSS in speech, music audio mixing. We review and compare LCNN with other popular a-posteriori Maximum Entropy methodologies defined by ANN weight matrix-[W] sigmoid-(sigma) post processing H(Y=(sigma) ([W]X)) by Bell-Sejnowski, Amari and Oja (BSAO) called Independent Component Analysis (ICA). Both are mirror symmetric of the MaxEnt methodologies and work for a constant unknown mixing matrix [A], but the major difference is whether the ensemble average is taken at neighborhood pixel data X's in BASO or at the a priori sources S variables in LCNN that dictates which method works for spatial-temporal varying [A(x,t)] that would not allow the neighborhood pixel average. We expected the success of sharper de-mixing by the LCNN method in terms of a controlled ground truth experiment in the simulation of variant mixture of two music of similar Kurtosis (15 seconds composed of Saint-Saens Swan and Rachmaninov cello concerto).

Lunar Lander project: A study on future manned missions to the Moon

NASA Technical Reports Server (NTRS)

1966-01-01

This project is based on designing a small lunar probe which will conduct research relating to future manned missions to the moon. The basic design calls for two experiments to be run. The first of these experiments is an enclosed environment section which will be exposed to solar radiation while on the moon. The purpose of this experiment is to determine the effect of radiation on an enclosed environment and how different shielding materials can be used to moderate this effect. The eight compartments will have the following covering materials: glass, polarized glass, plexiglass, polyurethane, and boron impregnated versions of the polyurethane and plexiglass. The enclosed atmosphere will be sampled by a mass spectrometer to determine elemental breakdown of its primary constituents. This is needed so that an accurate atmospheric processing system can be designed for a manned mission. The second experiment is a seismic study of the moon. A small penetrating probe will be shot into the lunar surface and data will be collected onboard the lander by an electronic seismograph which will store the data in the data storage unit for retrieval and transmission once every twenty-three hours. The project is designed to last ten years with possible extended life for an additional nine years at which point power requirements prevent proper functioning of the various systems.

The Use of Standards on the LADEE Mission

NASA Technical Reports Server (NTRS)

Gundy-Burlet, Karen

2015-01-01

The Lunar Atmosphere Dust Environment Explorer (LADEE) was a small explorer class mission that launched Sept 7, 2013 and successfully de-orbited and impacted the moon's surface on April 17, 2014. The spacecraft was the first to launch from a Minotaur 5 and was the first deep space mission to launch from the Wallops flight facility. Figure 1 shows the famous image of a frog unlucky enough to be launched from the facility at the same time as LADEE. The science mission for the spacecraft was to determine the density, composition and variability of the lunar exosphere. In addition, it performed a first-of-a-kind demonstration of laser-based communications from deep space that exhibited a record downlink rate of 622 megabits per second from the moon. In order to perform the lunar dust surveys, the spacecraft was placed in a retrograde equatorial orbit with periapsis between 20 and 60 kilometers. The mission was granted an extension in which final science surveys were performed at altitudes as low as 2 kilometers over the moon's surface. The cadence for spacecraft operations was demanding: the moon's highly inhomogeneous gravity field distorted the orbit, the regular maneuvers were subject to strict payload-induced pointing requirements, and there were periodic attitude changes to keep the spacecraft thermally safe. This led to a need for high reliability in the operation of the spacecraft while obeying strict budget and schedule guidelines.

Uranus moon - 1985U1

NASA Technical Reports Server (NTRS)

1986-01-01

Several craters are seen on the surface of 1985U1, one of several small moons of Uranus discovered by Voyager 2. The spacecraft acquired this single image -- the only close-up it obtained of any of the new moons -- on Jan. 24, 1986. At the time, Voyager was at a distance of about 500,000 kilometers (300,000 miles) from 1985U1, yielding a resolution of about 10 km (6 mi) in this clear-filter, narrow-angle image. The moon was found Dec. 3O, 1985; it was the first and largest of nearly a dozen satellites discovered by the spacecraft cameras. This image shows 1985U1 to be a dark, nearly spherical object, with a diameter of about 150 km (90 mi); the dark surface reflects only 7 percent of the incident light. The picture was inserted into the Voyager encounter sequence late in its development. This image has had a complex history, having been recorded on the spacecraft tape recorder and first played back during the late afternoon of Jan. 24. An antenna-pointing problem at one of the Australian tracking stations led to loss of the data, so the image had to be transmitted a second time. It was successfully received shortly before 6 p.m. PST Jan. 26. The Voyager project is managed for NASA by the Jet Propulsion Laboratory.

Solar Eclipse, STEREO Style

NASA Technical Reports Server (NTRS)

2007-01-01

There was a transit of the Moon across the face of the Sun - but it could not be seen from Earth. This sight was visible only from the STEREO-B spacecraft in its orbit about the sun, trailing behind the Earth. NASA's STEREO mission consists of two spacecraft launched in October, 2006 to study solar storms. The transit starts at 1:56 am EST and continued for 12 hours until 1:57 pm EST. STEREO-B is currently about 1 million miles from the Earth, 4.4 times farther away from the Moon than we are on Earth. As the result, the Moon will appear 4.4 times smaller than what we are used to. This is still, however, much larger than, say, the planet Venus appeared when it transited the Sun as seen from Earth in 2004. This alignment of STEREO-B and the Moon is not just due to luck. It was arranged with a small tweak to STEREO-B's orbit last December. The transit is quite useful to STEREO scientists for measuring the focus and the amount of scattered light in the STEREO imagers and for determining the pointing of the STEREO coronagraphs. The Sun as it appears in these the images and each frame of the movie is a composite of nearly simultaneous images in four different wavelengths of extreme ultraviolet light that were separated into color channels and then recombined with some level of transparency for each.

Motions about a fixed point by hypergeometric functions: new non-complex analytical solutions and integration of the herpolhode

NASA Astrophysics Data System (ADS)

Mingari Scarpello, Giovanni; Ritelli, Daniele

2018-06-01

The present study highlights the dynamics of a body moving about a fixed point and provides analytical closed form solutions. Firstly, for the symmetrical heavy body, that is the Lagrange-Poisson case, we compute the second (precession, ψ ) and third (spin, φ) Euler angles in explicit and real form by means of multiple hypergeometric (Lauricella) functions. Secondly, releasing the weight assumption but adding the complication of the asymmetry, by means of elliptic integrals of third kind, we provide the precession angle ψ completing the treatment of the Euler-Poinsot case. Thirdly, by integrating the relevant differential equation, we reach the finite polar equation of a special motion trajectory named the herpolhode. Finally, we keep the symmetry of the first problem, but without weight, and take into account a viscous dissipation. The use of motion first integrals—adopted for the first two problems—is no longer practicable in this situation; therefore, the Euler equations, faced directly, are driving to particular occurrences of Bessel functions of order - 1/2.

Fractional spectral and pseudo-spectral methods in unbounded domains: Theory and applications

NASA Astrophysics Data System (ADS)

Khosravian-Arab, Hassan; Dehghan, Mehdi; Eslahchi, M. R.

2017-06-01

This paper is intended to provide exponentially accurate Galerkin, Petrov-Galerkin and pseudo-spectral methods for fractional differential equations on a semi-infinite interval. We start our discussion by introducing two new non-classical Lagrange basis functions: NLBFs-1 and NLBFs-2 which are based on the two new families of the associated Laguerre polynomials: GALFs-1 and GALFs-2 obtained recently by the authors in [28]. With respect to the NLBFs-1 and NLBFs-2, two new non-classical interpolants based on the associated- Laguerre-Gauss and Laguerre-Gauss-Radau points are introduced and then fractional (pseudo-spectral) differentiation (and integration) matrices are derived. Convergence and stability of the new interpolants are proved in detail. Several numerical examples are considered to demonstrate the validity and applicability of the basis functions to approximate fractional derivatives (and integrals) of some functions. Moreover, the pseudo-spectral, Galerkin and Petrov-Galerkin methods are successfully applied to solve some physical ordinary differential equations of either fractional orders or integer ones. Some useful comments from the numerical point of view on Galerkin and Petrov-Galerkin methods are listed at the end.

Passive remote sensing of altitude and optical depth of dust plumes using the oxygen A and B bands: First results from EPIC/DSCOVR at Lagrange-1 point

NASA Astrophysics Data System (ADS)

Xu, Xiaoguang; Wang, Jun; Wang, Yi; Zeng, Jing; Torres, Omar; Yang, Yuekui; Marshak, Alexander; Reid, Jeffrey; Miller, Steve

2017-07-01

We presented an algorithm for inferring aerosol layer height (ALH) and optical depth (AOD) over ocean surface from radiances in oxygen A and B bands measured by the Earth Polychromatic Imaging Camera (EPIC) on the Deep Space Climate Observatory (DSCOVR) orbiting at Lagrangian-1 point. The algorithm was applied to EPIC imagery of a 2 day dust outbreak over the North Atlantic Ocean. Retrieved ALHs and AODs were evaluated against counterparts observed by Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP), Moderate Resolution Imaging Spectroradiometer, and Aerosol Robotic Network. The comparisons showed 71.5% of EPIC-retrieved ALHs were within ±0.5 km of those determined from CALIOP and 74.4% of EPIC AOD retrievals fell within a ± (0.1 + 10%) envelope of MODIS retrievals. This study demonstrates the potential of EPIC measurements for retrieving global aerosol height multiple times daily, which are essential for evaluating aerosol profile simulated in climate models and for better estimating aerosol radiative effects.

Total Transfer Capability Assessment Incorporating Corrective Controls for Transient Stability using TSCOPF

NASA Astrophysics Data System (ADS)

Hakim, Lukmanul; Kubokawa, Junji; Yorino, Naoto; Zoka, Yoshifumi; Sasaki, Yutaka

Advancements have been made towards inclusion of both static and dynamic security into transfer capability calculation. However, to the authors' knowledge, work on considering corrective controls into the calculation has not been reported yet. Therefore, we propose a Total Transfer Capability (TTC) assessment considering transient stability corrective controls. The method is based on the Newton interior point method for nonlinear programming and transfer capability is approached as a maximization of power transfer with both static and transient stability constraints are incorporated into our Transient Stability Constrained Optimal Power Flow (TSCOPF) formulation. An interconnected power system is simulated to be subjected to a severe unbalanced 3-phase 4-line to ground fault and following the fault, generator and load are shed in a pre-defined sequence to mimic actual corrective controls. In a deregulated electricity market, both generator companies and large load customers are encouraged to actively participate in maintaining power system stability as corrective controls upon agreement of compensation for being shed following a disturbance. Implementation of this proposal on the actual power system operation should be carried out through combining it with the existing transient stabilization controller system. Utilization of these corrective controls results in increasing TTC as suggested in our numerical simulation. As Lagrange multipliers can also describe sensitivity of both inequality and equality constraints to the objective function, then selection of which generator or load to be shed can be carried out on the basis of values of Lagrange multipliers of its respective generator's rotor angle stability and active power balance equation. Hence, the proposal in this paper can be utilized by system operator to assess the maximum TTC for specific loads and network conditions.

Quantum canonical ensemble: A projection operator approach

NASA Astrophysics Data System (ADS)

Magnus, Wim; Lemmens, Lucien; Brosens, Fons

2017-09-01

Knowing the exact number of particles N, and taking this knowledge into account, the quantum canonical ensemble imposes a constraint on the occupation number operators. The constraint particularly hampers the systematic calculation of the partition function and any relevant thermodynamic expectation value for arbitrary but fixed N. On the other hand, fixing only the average number of particles, one may remove the above constraint and simply factorize the traces in Fock space into traces over single-particle states. As is well known, that would be the strategy of the grand-canonical ensemble which, however, comes with an additional Lagrange multiplier to impose the average number of particles. The appearance of this multiplier can be avoided by invoking a projection operator that enables a constraint-free computation of the partition function and its derived quantities in the canonical ensemble, at the price of an angular or contour integration. Introduced in the recent past to handle various issues related to particle-number projected statistics, the projection operator approach proves beneficial to a wide variety of problems in condensed matter physics for which the canonical ensemble offers a natural and appropriate environment. In this light, we present a systematic treatment of the canonical ensemble that embeds the projection operator into the formalism of second quantization while explicitly fixing N, the very number of particles rather than the average. Being applicable to both bosonic and fermionic systems in arbitrary dimensions, transparent integral representations are provided for the partition function ZN and the Helmholtz free energy FN as well as for two- and four-point correlation functions. The chemical potential is not a Lagrange multiplier regulating the average particle number but can be extracted from FN+1 -FN, as illustrated for a two-dimensional fermion gas.

Stargazing

ERIC Educational Resources Information Center

Mayes, Valynda

2010-01-01

In 2009, we had the year of astronomy. Even President Obama hosted an astronomy night on the White House lawn. Your explorations of nature need not be limited to daylight hours--though it is important to point our when celestial objects like the Moon are visible during the day to counter misconceptions. This year, introduce your students to the…

International Priorities for Teacher Education. World Assembly 1969.

ERIC Educational Resources Information Center

International Council on Education for Teaching, Washington, DC.

Four papers are included in this pamphlet, the proceedings of the World Assembly at Abidjan, Ivory Coast. The keynote address, "A Turning Point in History" by Jaime Benitez, President of the University of Puerto Rico, discusses the Apollo 11 moon landing as an object lesson on values with international implications for shifting…

Retrieval operations with SPARTAN 201

NASA Image and Video Library

1994-09-15

STS064-74-052 (9-20 Sept. 1994) --- Astronauts onboard the space shuttle Discovery used a 70mm camera to capture this photograph of the retrieval operations with the Shuttle Pointed Autonomous Research Tool for Astronomy 201 (SPARTAN 201). A gibbous moon can be seen in the background. Photo credit: NASA or National Aeronautics and Space Administration

Investigation of Loop Heat Pipe Survival and Restart After Extreme Cold Environment Exposure

NASA Technical Reports Server (NTRS)

Golliher, Eric; Ku, Jentung; Licari, Anthony; Sanzi, James

2010-01-01

NASA plans human exploration near the South Pole of the Moon, and other locations where the environment is extremely cold. This paper reports on the heat transfer performance of a loop heat pipe (LHP) exposed to extreme cold under the simulated reduced gravitational environment of the Moon. A common method of spacecraft thermal control is to use a LHP with ammonia working fluid. Typically, a small amount of heat is provided either by electrical heaters or by environmental design, such that the LHP condenser temperature never drops below the freezing point of ammonia. The concern is that a liquid-filled, frozen condenser would not restart, or that a thawing condenser would damage the tubing due to the expansion of ammonia upon thawing. This paper reports the results of an experimental investigation of a novel approach to avoid these problems. The LHP compensation chamber (CC) is conditioned such that all the ammonia liquid is removed from the condenser and the LHP is nonoperating. The condenser temperature is then reduced to below that of the ammonia freezing point. The LHP is then successfully restarted.

DSCOVR Science Data and Retrospective Access

NASA Astrophysics Data System (ADS)

Rowland, W. F.; Codrescu, S.; Tilton, M.; Cartwright, J.; Redmon, R. J.; Loto'aniu, P. T. M.; Mccullough, H.; Denig, W. F.

2016-12-01

On July 27, 2016 the Deep Space Climate Observatory (DSCOVR) became the first operational satellite at the first Lagrange point (L1). This vantage, approximately one percent of the distance from the Earth to the Sun along the Earth-Sun line, means that DSCOVR data provide critical advanced warning of impending space weather events. As such, DSCOVR data are essential for forecasters, modelers, and the scientific community. The National Oceanic and Atmospheric Administration's National Centers for Environmental Information (NOAA/NCEI) archives the retrospective data and shares them with the public. We examine the data available, with a focus on some of the more interesting events that have occurred. We also discuss mechanisms created to facilitate search and access for those data, including a user-driven interface that allows one to dynamically generate plots and order relevant data of interest.

Rotational Properties of Jupiter Trojan 1173 Anchises

NASA Astrophysics Data System (ADS)

Chatelain, Joseph; Henry, Todd; French, Linda; Trilling, David

2015-11-01

Anchises (1173) is a large Trojan asteroid librating about Jupiter’s L5 Lagrange point. Here we examine its rotational and lightcurve properties by way of data collected over a 3.5 year observing campaign. The length of the campaign means that data were gathered for more than a quarter of Anchises' full orbital revolution which allows for accurate determinations of pole orientation and bulk shape properties for the asteroid that can then be compared to results of previous work (i.e. French 1987, Horner et al. 2012). In addition to light curves, photometric data taken during this campaign could potentially detect color differences between hemispheres as the viewing geometry changes over time. Understanding these details about a prominent member of the Jupiter Trojans may help us better understand the history of this fascinating and important group of asteroids.

Real-time Kp predictions from ACE real time solar wind

NASA Astrophysics Data System (ADS)

Detman, Thomas; Joselyn, Joann

1999-06-01

The Advanced Composition Explorer (ACE) spacecraft provides nearly continuous monitoring of solar wind plasma, magnetic fields, and energetic particles from the Sun-Earth L1 Lagrange point upstream of Earth in the solar wind. The Space Environment Center (SEC) in Boulder receives ACE telemetry from a group of international network of tracking stations. One-minute, and 1-hour averages of solar wind speed, density, temperature, and magnetic field components are posted on SEC's World Wide Web page within 3 to 5 minutes after they are measured. The ACE Real Time Solar Wind (RTSW) can be used to provide real-time warnings and short term forecasts of geomagnetic storms based on the (traditional) Kp index. Here, we use historical data to evaluate the performance of the first real-time Kp prediction algorithm to become operational.

Martian Moon Phobos in Thermal Infrared Image

NASA Image and Video Library

2017-10-04

Colors in this image of the Martian moon Phobos indicate a range of surface temperatures detected by observing the moon on Sept. 29, 2017, with the Thermal Emission Imaging System (THEMIS) camera on NASA's Mars Odyssey orbiter. The left edge of the small moon was in darkness, and the right edge in morning sunlight. Phobos has an oblong shape with average diameter of about 14 miles (22 kilometers). Temperature information was derived from thermal-infrared imaging such as the grayscale image shown smaller at lower left with the moon in the same orientation. The color-coding merges information from THEMIS observations made in four thermal-infrared wavelength bands, centered from 11.04 microns to 14.88 microns. The scale bar correlates color-coding to the temperature range on the Kelvin scale, from 130 K (minus 226 degrees Fahrenheit) for dark purple to 270 K (26 degrees F) for red. Researchers will analyze the surface-temperature information from this observation and possible future THEMIS observations to learn how quickly the surface warms after sunup or cools after sundown. That could provide information about surface materials, because larger rocks heat or cool more slowly than smaller particles do. Researchers have been using THEMIS to examine Mars since early 2002, but the maneuver turning the orbiter around to point the camera at Phobos was developed only recently. Odyssey orbits Mars at an altitude of about 250 miles (400 kilometers), much closer to the planet than to Phobos, which orbits about 3,700 miles (6,000 kilometers) above the surface of Mars. The distance to Phobos from Odyssey during the observation was about 3,424 miles (5,511 kilometers). https://photojournal.jpl.nasa.gov/catalog/PIA21858

Shallow Lunar Seismic Activity and the Current Stress State of the Moon

NASA Technical Reports Server (NTRS)

Watters, Thomas R.; Weber, Renee C.; Collins, Geoffrey C.; Johnson, Catherine L.

2017-01-01

A vast, global network of more than 3200 lobate thrust fault scarps has been revealed in high resolution Lunar Reconnaissance Orbiter Camera (LROC) images. The fault scarps are very young, less than 50 Ma, based on their small scale and crisp appearance, crosscutting relations with small-diameter impact craters, and rates of infilling of associated small, shallow graben and may be actively forming today. The population of young thrust fault scarps provides a window into the recent stress state of the Moon and offers insight into the origin of global lunar stresses. The distribution of orientations of the fault scarps is non-random, inconsistent with isotropic stresses from late-stage global contraction as the sole source of stress. Modeling shows that tidal stresses contribute significantly to the current stress state of the lunar crust. Tidal stresses (orbital recession and diurnal tides) superimposed on stresses from global contraction result in non-isotropic compressional stress and may produce thrust faults consistent with lobate scarp orientations. At any particular point on the lunar surface, peak compressive stress will be reached at a certain time in the diurnal cycle. Coseismic slip events on currently active thrust faults are expected to be triggered when peak stresses are reached. Analysis of the timing of the 28 the shallow moonquakes recorded by the Apollo seismic network shows that 19 indeed occur when the Moon is closer to apogee, while only 9 shallow events occur when the Moon is closer to perigee. Here we report efforts to refine the model for the current stress state of the Moon by investigating the contribution of polar wander. Progress on relocating the epicentral locations of the shallow moonquakes using an algorithm designed for sparse networks is also reported.

Establishing the moon as a spectral radiance standard

USGS Publications Warehouse

Kieffer, H.H.; Wildey, R.L.

1996-01-01

A new automated observatory dedicated to the radiometry of the moon has been constructed to provide new radiance information for calibration of earth-orbiting imaging instruments, particularly Earth Observing System instruments. Instrumentation includes an imaging photometer with 4.5-in. resolution on a fully digital mount and a full-aperture radiance calibration source. Interference filters within 0.35-0.95 ??m correspond to standard stellar magnitude systems, accommodate wavelengths of lunar spectral contrast, and approximate some band-passes of planned earth-orbiting instruments (ASTER, Landsat-7 ETM, MISR, MODIS, and SeaWIFS). The same equipment is used for lunar and stellar observations, with the use of an aperture stop in lunar imaging to comply with Nyquist's theorem and lengthen exposure times to avoid scintillation effects. A typical robotic night run involves observation of about 60 photometric standard stars and the moon; about 10 of the standard stars are observed repeatedly to determine atmospheric extinction, and the moon is observed several times. Observations are to be made on every photometric night during the bright half of the month for at least 4.5 years to adequately cover phase and libration variation. Each lunar image is reduced to absolute exoatmospheric radiance and reprojected to a fixed selenographic grid system. The collection of these images at various librations and phase angles will be reduced to photometric models for each of the approximately 120 000 points in the lunar grid for each filter. Radiance models of the moon can then be produced for the precise geometry of an orbiting instrument observation. Expected errors are under 1% relative and 2.5% absolute. A second telescope operating from 1.0 to 2.5 ??m is planned.

RESOLVE - Starting Point for Partnerships in Lunar and Mars Resource Characterization

NASA Technical Reports Server (NTRS)

Sanders, Gerald B.; Rosenbaum, Bernard; Simon, Thomas; Larson, William E.; Luecke, Dale; Captain, Jainine; Sacksteder, Kurt; Johnson, Kenneth R.; Boucher, Dale; Taylor, Jeffrey

2007-01-01

The mystery and controversy surrounding the possibility of finding water/ice at the lunar poles of the Moon based on the interpretation of neutron spectrometer data from Lunar Prospector and radar data from Clementine raises questions that both Science and the Human Exploration proponents want answered. From the Science perspective, the determination of lunar volatiles and in particular the increased hydrogen concentration detected at the lunar poles was identified as an important objectives for lunar exploration and understanding the history of the Moon, Sun, and the solar system. From the Human Exploration perspective, the potential for large concentrations of accessible water opens up possibilities for utilizing in-situ resources, known as In-Situ Resource Utilization (ISRU), to implement a sustained and affordable human exploration program of the Moon and beyond through production of propellants, fuel cell reagents, and life support consumables for lunar surface operations and mobility, and Earth-Moon transportation. Both the Science and Human Exploration proponents agree that a mission to the lunar poles to obtain ground truth data is the only means to conclusively answer the questions of whether water/ice exists, how much, what form, and where did it come from. In 2005, NASA initiated the Regolith and Environment Science & Oxygen and Lunar Volatiles Extraction (RESOLVE) project, and is currently developing hardware under the NASA Exploration Technology Development Program (ETDP). The purpose of the project was to begin developing technologies and operations that would answer the fundamental science questions, such as What resources are available on the Moon, where are they, what form, and where did they come from? as well as critical engineering questions, such as How will we mine these resources, what chemical extraction processes are the most practical and efficient, and what are the engineering challenges to be faced in this environment? .

Lunar Global Heat Flow: Predictions and Constraints

NASA Astrophysics Data System (ADS)

Siegler, M.; Williams, J. P.; Paige, D. A.; Feng, J.

2017-12-01

The global thermal state of the Moon provides fundamental information on its bulk composition and interior evolution. The Moon is known to have a highly asymmetric surface composition [e.g. Lawrence et al., 2003] and crustal thickness [Wieczorek et al.,2012], which is suspected to result from interior asymmetries [Wieczorek and Phillips, 2000; Laneuville et al., 2013]. This is likely to cause a highly asymmetric surface heat flux, both past and present. Our understanding the thermal evolution and composition of the bulk moon therefore requires a global picture of the present lunar thermal state, well beyond our two-point Apollo era measurement. As on the on the Earth, heat flow measurements need to be taken in carefully selected locations to truly characterize the state of the planet's interior. Future surface heat flux and seismic observations will be affected by the presence of interior temperature and crustal radiogenic anomalies, so placement of such instruments is critically important for understanding the lunar interior. The unfortunate coincidence that Apollo geophysical measurements lie areas within or directly abutting the highly radiogenic, anomalously thin-crusted Procellarum region highlights the importance of location for in situ geophysical study [e.g. Siegler and Smrekar, 2014]. Here we present the results of new models of global lunar geothermal heat flux. We synthesize data from several recent missions to constrain lunar crustal composition, thickness and density to provide global predictions of the surface heat flux of the Moon. We also discuss implications from new surface heat flux constraints from the LRO Diviner Lunar Radiometer Experiment and Chang'E 2 Microwave Radiometer. We will identify areas with the highest uncertainty to provide insight on the placement of future landed geophysical missions, such as the proposed Lunar Geophysical Network, to better aim our future exploration of the Moon.

More Sophisticated Fits of the Oribts of Haumea's Interacting Moons

NASA Astrophysics Data System (ADS)

Oldroyd, William Jared; Ragozzine, Darin; Porter, Simon

2018-04-01

Since the discovery of Haumea's moons, it has been a challenge to model the orbits of its moons, Hi’iaka and Namaka. With many precision HST observations, Ragozzine & Brown 2009 succeeded in calculating a three-point mass model which was essential because Keplerian orbits were not a statistically acceptable fit. New data obtained in 2010 could be fit by adding a J2 and spin pole to Haumea, but new data from 2015 was far from the predicted locations, even after an extensive exploration using Bayesian Markov Chain Monte Carlo methods (using emcee). Here we report on continued investigations as to why our model cannot fit the full 10-year baseline of data. We note that by ignoring Haumea and instead examining the relative motion of the two moons in the Hi’iaka centered frame leads to adequate fits for the data. This suggests there are additional parameters connected to Haumea that will be required in a full model. These parameters are potentially related to photocenter-barycenter shifts which could be significant enough to affect the fitting process; these are unlikely to be caused by the newly discovered ring (Ortiz et al. 2017) or by unknown satellites (Burkhart et al. 2016). Additionally, we have developed a new SPIN+N-bodY integrator called SPINNY that self-consistently calculates the interactions between n-quadrupoles and is designed to test the importance of other possible effects (Haumea C22, satellite torques on the spin-pole, Sun, etc.) on our astrometric fits. By correctly determining the orbit of Haumea’s satellites we develop a better understanding of the physical properties of each of the objects with implications for the formation of Haumea, its moons, and its collisional family.

On the photo-gravitational restricted four-body problem with variable mass

NASA Astrophysics Data System (ADS)

Mittal, Amit; Agarwal, Rajiv; Suraj, Md Sanam; Arora, Monika

2018-05-01

This paper deals with the photo-gravitational restricted four-body problem (PR4BP) with variable mass. Following the procedure given by Gascheau (C. R. 16:393-394, 1843) and Routh (Proc. Lond. Math. Soc. 6:86-97, 1875), the conditions of linear stability of Lagrange triangle solution in the PR4BP are determined. The three radiating primaries having masses m1, m2 and m3 in an equilateral triangle with m2=m3 will be stable as long as they satisfy the linear stability condition of the Lagrangian triangle solution. We have derived the equations of motion of the mentioned problem and observed that there exist eight libration points for a fixed value of parameters γ (m at time t/m at initial time, 0<γ≤1 ), α (the proportionality constant in Jeans' law (Astronomy and Cosmogony, Cambridge University Press, Cambridge, 1928), 0≤α≤2.2), the mass parameter μ=0.005 and radiation parameters qi, (0< qi≤1, i=1, 2, 3). All the libration points are non-collinear if q2≠ q3. It has been observed that the collinear and out-of-plane libration points also exist for q2=q3. In all the cases, each libration point is found to be unstable. Further, zero velocity curves (ZVCs) and Newton-Raphson basins of attraction are also discussed.

An Introduction to Lagrangian Differential Calculus.

ERIC Educational Resources Information Center

Schremmer, Francesca; Schremmer, Alain

1990-01-01

Illustrates how Lagrange's approach applies to the differential calculus of polynomial functions when approximations are obtained. Discusses how to obtain polynomial approximations in other cases. (YP)

Comments on "The multisynapse neural network and its application to fuzzy clustering".

PubMed

Yu, Jian; Hao, Pengwei

2005-05-01

In the above-mentioned paper, Wei and Fahn proposed a neural architecture, the multisynapse neural network, to solve constrained optimization problems including high-order, logarithmic, and sinusoidal forms, etc. As one of its main applications, a fuzzy bidirectional associative clustering network (FBACN) was proposed for fuzzy-partition clustering according to the objective-functional method. The connection between the objective-functional-based fuzzy c-partition algorithms and FBACN is the Lagrange multiplier approach. Unfortunately, the Lagrange multiplier approach was incorrectly applied so that FBACN does not equivalently minimize its corresponding constrained objective-function. Additionally, Wei and Fahn adopted traditional definition of fuzzy c-partition, which is not satisfied by FBACN. Therefore, FBACN can not solve constrained optimization problems, either.

Spherical Pendulum Small Oscillations for Slewing Crane Motion

PubMed Central

Perig, Alexander V.; Stadnik, Alexander N.; Deriglazov, Alexander I.

2014-01-01

The present paper focuses on the Lagrange mechanics-based description of small oscillations of a spherical pendulum with a uniformly rotating suspension center. The analytical solution of the natural frequencies' problem has been derived for the case of uniform rotation of a crane boom. The payload paths have been found in the inertial reference frame fixed on earth and in the noninertial reference frame, which is connected with the rotating crane boom. The numerical amplitude-frequency characteristics of the relative payload motion have been found. The mechanical interpretation of the terms in Lagrange equations has been outlined. The analytical expression and numerical estimation for cable tension force have been proposed. The numerical computational results, which correlate very accurately with the experimental observations, have been shown. PMID:24526891

Variational tricomplex of a local gauge system, Lagrange structure and weak Poisson bracket

NASA Astrophysics Data System (ADS)

Sharapov, A. A.

2015-09-01

We introduce the concept of a variational tricomplex, which is applicable both to variational and nonvariational gauge systems. Assigning this tricomplex with an appropriate symplectic structure and a Cauchy foliation, we establish a general correspondence between the Lagrangian and Hamiltonian pictures of one and the same (not necessarily variational) dynamics. In practical terms, this correspondence allows one to construct the generating functional of a weak Poisson structure starting from that of a Lagrange structure. As a byproduct, a covariant procedure is proposed for deriving the classical BRST charge of the BFV formalism by a given BV master action. The general approach is illustrated by the examples of Maxwell’s electrodynamics and chiral bosons in two dimensions.

Four Galileo Views of Amalthea

NASA Technical Reports Server (NTRS)

1997-01-01

These four images of Jupiter's moon, Amalthea, were taken by Galileo's solid state imaging system at various times between February and June 1997. North is approximately up in all cases. Amalthea, whose longest dimension is approximately 247 kilometers (154 miles) across, is tidally locked so that the same side of the satellite always points towards Jupiter, similar to how the nearside of our own Moon always points toward Earth. In such a tidally locked state, one side of Amalthea always points in the direction in which Amalthea moves as it orbits about Jupiter. This is called the 'leading side' of the moon and is shown in the top two images. The opposite side of Amalthea, the 'trailing side,' is shown in the bottom pair of images. The Sun illuminates the surface from the left in the top left image and from the right in the bottom left image. Such lighting geometries, similar to taking a picture from a high altitude at sunrise or sunset, are excellent for viewing the topography of the satellite's surface such as impact craters and hills. In the two images on the right, however, the Sun is almost directly behind the spacecraft. This latter geometry, similar to taking a picture from a high altitude at noon, washes out topographic features and emphasizes Amalthea's albedo (light/dark) patterns. It emphasizes the presence of surface materials that are intrinsically brighter or darker than their surroundings. The bright albedo spot that dominates the top right image is located inside a large south polar crater named Gaea.

The Jet Propulsion Laboratory, Pasadena, CA manages the Galileo mission for NASA's Office of Space Science, Washington, DC. JPL is an operating division of California Institute of Technology (Caltech).

This image and other images and data received from Galileo are posted on the World Wide Web, on the Galileo mission home page at URL http://galileo.jpl.nasa.gov.

Harvest Moon at NASA Goddard

NASA Image and Video Library

2017-12-08

September's Harvest Moon as seen around NASA's Goddard Space Flight Center. According to folklore, every full Moon has a special name. There's the Wolf Moon, the Snow Moon, the Worm Moon, the Sprouting Grass Moon, the Flower Moon, the Strawberry Moon, the Thunder Moon, the Sturgeon Moon, the Harvest Moon, the Hunter's Moon, the Beaver Moon, and the Long Night's Moon. Each name tells us something about the season or month in which the full Moon appears. This month's full Moon is the Harvest Moon. More about the Harvest Moon from NASA: Science 1.usa.gov/16lb1eZ Credit: NASA/Goddard/Debbie Mccallum NASA image use policy. NASA Goddard Space Flight Center enables NASA’s mission through four scientific endeavors: Earth Science, Heliophysics, Solar System Exploration, and Astrophysics. Goddard plays a leading role in NASA’s accomplishments by contributing compelling scientific knowledge to advance the Agency’s mission. Follow us on Twitter Like us on Facebook Find us on Instagram

Harvest Moon at NASA Goddard

NASA Image and Video Library

2013-09-20

September's Harvest Moon as seen around NASA's Goddard Space Flight Center. According to folklore, every full Moon has a special name. There's the Wolf Moon, the Snow Moon, the Worm Moon, the Sprouting Grass Moon, the Flower Moon, the Strawberry Moon, the Thunder Moon, the Sturgeon Moon, the Harvest Moon, the Hunter's Moon, the Beaver Moon, and the Long Night's Moon. Each name tells us something about the season or month in which the full Moon appears. This month's full Moon is the Harvest Moon. More about the Harvest Moon from NASA: Science 1.usa.gov/16lb1eZ Credit: NASA/Goddard/Debbie Mccallum NASA image use policy. NASA Goddard Space Flight Center enables NASA’s mission through four scientific endeavors: Earth Science, Heliophysics, Solar System Exploration, and Astrophysics. Goddard plays a leading role in NASA’s accomplishments by contributing compelling scientific knowledge to advance the Agency’s mission. Follow us on Twitter Like us on Facebook Find us on Instagram

Absolute, SI-traceable lunar irradiance tie-points for the USGS Lunar Model

NASA Astrophysics Data System (ADS)

Brown, Steven W.; Eplee, Robert E.; Xiong, Xiaoxiong J.

2017-10-01

The United States Geological Survey (USGS) has developed an empirical model, known as the Robotic Lunar Observatory (ROLO) Model, that predicts the reflectance of the Moon for any Sun-sensor-Moon configuration over the spectral range from 350 nm to 2500 nm. The lunar irradiance can be predicted from the modeled lunar reflectance using a spectrum of the incident solar irradiance. While extremely successful as a relative exo-atmospheric calibration target, the ROLO Model is not SI-traceable and has estimated uncertainties too large for the Moon to be used as an absolute celestial calibration target. In this work, two recent absolute, low uncertainty, SI-traceable top-of-the-atmosphere (TOA) lunar irradiances, measured over the spectral range from 380 nm to 1040 nm, at lunar phase angles of 6.6° and 16.9° , are used as tie-points to the output of the ROLO Model. Combined with empirically derived phase and libration corrections to the output of the ROLO Model and uncertainty estimates in those corrections, the measurements enable development of a corrected TOA lunar irradiance model and its uncertainty budget for phase angles between +/-80° and libration angles from 7° to 51° . The uncertainties in the empirically corrected output from the ROLO model are approximately 1 % from 440 nm to 865 nm and increase to almost 3 % at 412 nm. The dominant components in the uncertainty budget are the uncertainty in the absolute TOA lunar irradiance and the uncertainty in the fit to the phase correction from the output of the ROLO model.

Transfers between libration-point orbits in the elliptic restricted problem

NASA Astrophysics Data System (ADS)

Hiday, L. A.; Howell, K. C.

The present time-fixed impulsive transfers between 3D libration point orbits in the vicinity of the interior L(1) libration point of the sun-earth-moon barycenter system are 'optimal' in that the total characteristic velocity required for implementation of the transfer exhibits a local minimum. The conditions necessary for a time-fixed, two-impulse transfer trajectory to be optimal are stated in terms of the primer vector, and the conditions necessary for satisfying the local optimality of a transfer trajectory containing additional impulses are addressed by requiring continuity of the Hamiltonian and the derivative of the primer vector at all interior impulses.

Invariant Manifolds, the Spatial Three-Body Problem and Space Mission Design

NASA Technical Reports Server (NTRS)

Gomez, G.; Koon, W. S.; Lo, Martin W.; Marsden, J. E.; Masdemont, J.; Ross, S. D.

2001-01-01

The invariant manifold structures of the collinear libration points for the spatial restricted three-body problem provide the framework for understanding complex dynamical phenomena from a geometric point of view. In particular, the stable and unstable invariant manifold 'tubes' associated to libration point orbits are the phase space structures that provide a conduit for orbits between primary bodies for separate three-body systems. These invariant manifold tubes can be used to construct new spacecraft trajectories, such as 'Petit Grand Tour' of the moons of Jupiter. Previous work focused on the planar circular restricted three-body problem. The current work extends the results to the spatial case.

Are There Oceans Under the Ice of Small Saturnian and Uranian Moons?

NASA Astrophysics Data System (ADS)

England, C.

2003-05-01

Thermal analysis of the large outer-planetary moons (Titan, Callisto, Ganymede) argue strongly for substantial subsurface oceans if they are made up mostly of rock and ice, and if the rock exhibits radioactivity not too different from that of meteoric and lunar material [1]. For Titania, Rhea, Oberon and Iapetus (the TROI moons) with radii just over 700 km, the existence of oceans is less clear. In these bodies, a subsurface ocean may be likely if the rock has sunk to the center of the moon (i.e., the moon is differentiated) and (1) the radiogenic heating rate is on the higher end of that of lunar samples, (2) the bodies experience tidal heating, or (3) the oceans contain compounds such as ammonia that reduce the freezing point of the aqueous environment. A combination of these occurrences would weigh for a subsurface ocean, perhaps of substantial size. That outer-planetary moons with radii larger than about 200 km (e.g.; Enceladus at 250 km) are spherical argues for separation of light and heavy materials, especially in the larger bodies. Otherwise, the moon exhibits an irregular shape (e.g.; Hyperion at 133 km). Primordial radioactivity and collision events may have aided separation. If present-day radiogenicity is that of lunar samples, natural heating is available to maintain global aqueous environments on all of the TROI moons. The ammonia-water eutectics suggested for Titan [2] provide additional margin. The maintenance of oceans in smaller bodies depends on a balance of internal heat generation and thermal isolation by ice or other insulating material. The more important parameter may be the insulating ice, without which an outer-planetary ocean is not possible. The reduced thermal conductivity for impure ice [3] provides even more likelihood for oceans. Calculations for tidal heating within Europa due to orbital resonances [4] suggest that tidal heating amounts to over 40 times its internal radiogenic heating. A value equal only to natural radiogenic heating would be sufficient to maintain aqueous systems within TROI moons. Subsurface aqueous oceans are likely on Titania, Rhea, Oberon and Iapetus, but will be buried more than 300 km under insulating icy layers. Their existence, and that of an environment favorable for life, may be detectable from surface features or from remote surveys of their internal electromagnetic properties. [1] England C, DPS MEETING #34 Abstract #41.08, 9/2002 [2] Lorenz RD, Lunine JI, McKay CP, ENANTIOMER 6 (2-3): 83-96 2001 [3] Lorenz RD and Shandera SE, GEOPHYSICAL RESEARCH LETTERS 28 (2) 215-218 2001 [4] Ross MN, Schubert G, LUNAR AND PLANETARY SCIENCE XVII, PP. 724-725, 1986

A Perspective On The Earth From The Moon

NASA Astrophysics Data System (ADS)

Scott, David R.

``What was most significant about the lunar voyage was not that men set foot on the Moon, but that they set eye on the Earth''. This statement, by Mr. Norman Cousins, Editor of the Saturday Review, summarizes the most significant aspect of the first departure of humans from the environment in which they were born, and in which they must survive. Looking back at the Earth from the Moon, the view is both splendid and overwhelming. This small blue ball in the vastness of black space, dotted with millions of marvellous stars, is an oasis that we must understand and protect. For, if one searches the heavens, one will find no other island for life as we understand it. If we humans do not protect and nurture this environment, it will disappear - just as quickly as the Earth will disappear from behind an outstretched thumb of a man on the Moon. Everything that has meaning disappears: science, history, music, poetry, art, literature, all of it on this small, fragile, and precious little spot out there in the vastness of the universe. From the Moon, we see many new and fascinating visions of the Earth. These views change not only our perspective of the Earth but our value system as well. As an example, from the Earth, we see the Moon track across the sky from horizon to horizon, always the same face, always the same features. But from the Moon, we see the Earth at the same point in the sky, day after day, but always turning, showing us new faces and changing features as the hours pass. We become aware of how much the physical features of the Earth are interrelated. And in a sense, we can ``see the future'' as the Earth turns in our view. From the Moon we see the Earth as a ``whole'' - we see no borders, we see no boundaries, we see all humankind together and interrelated on this single small sphere. This perspective from the Moon makes us realize that the Earth is dynamic and alive and evolving for the human presence - and we realize that if we care not for the life of the Earth itself, we care not for the life of its inhabitants. With this new perspective of the Earth and its place in human life, we must think of bold and visionary ideas to preserve our so limited and fragile environment. Temporary solutions to the problems of our times must be replaced by permanent solutions for future generations. For our generation did not inherit this marvelous environment in which we live, we borrowed it from our children, and children's children. We owe them the best we can achieve; we owe them a conscious and substantial return on their investment in us.

Pre-late heavy bombardment evolution of the Earth's obliquity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Gongjie; Batygin, Konstantin, E-mail: gli@cfa.harvard.edu

2014-11-01

The Earth's obliquity is stabilized by the Moon, which facilitates a rapid precession of the Earth's spin axis, detuning the system away from resonance with orbital modulation. It is, however, likely that the architecture of the solar system underwent a dynamical instability-driven transformation, where the primordial configuration was more compact. Hence, the characteristic frequencies associated with orbital perturbations were likely faster in the past, potentially allowing for secular resonant encounters. In this work, we examine if, at any point in the Earth's evolutionary history, the obliquity varied significantly. Our calculations suggest that even though the orbital perturbations were different, themore » system nevertheless avoided resonant encounters throughout its evolution. This indicates that the Earth obtained its current obliquity during the formation of the Moon.« less

Apollo 17 celebration

NASA Image and Video Library

2012-12-07

Ariana Lyons from Escatawpa Elementary School in Moss Point, Miss., experiences what it feels like to view the world out of a spacesuit during a visit to INFINITY Science Center, a NASA visitors center, Dec. 7. Lyons joined other young visitors to the facility that day in celebrating the 40th anniversary of the Apollo 17 mission to the moon in 1972.

Fine-Grained Sediments; an Annotated Bibliography on Their Dynamic Behavior in Aquatic Systems.

DTIC Science & Technology

1987-09-01

rates would be in- creased less than 15 percent at Moon Island reach and Cow Point, Aberdeen, and South Aberdeen reaches; unchanged in the Crossover... Holstein takes place under influence of the supply of mud by the river Elbe and by erosion of older Holocene deposits on the flats in front of the

Mathematical Investigation of Fluid Flow, Mass Transfer, and Slag-steel Interfacial Behavior in Gas-stirred Ladles

NASA Astrophysics Data System (ADS)

Cao, Qing; Nastac, Laurentiu

2018-06-01

In this study, the Euler-Euler and Euler-Lagrange modeling approaches were applied to simulate the multiphase flow in the water model and gas-stirred ladle systems. Detailed comparisons of the computational and experimental results were performed to establish which approach is more accurate for predicting the gas-liquid multiphase flow phenomena. It was demonstrated that the Euler-Lagrange approach is more accurate than the Euler-Euler approach. The Euler-Lagrange approach was applied to study the effects of the free surface setup, injected bubble size, gas flow rate, and slag layer thickness on the slag-steel interaction and mass transfer behavior. Detailed discussions on the flat/non-flat free surface assumption were provided. Significant inaccuracies in the prediction of the surface fluid flow characteristics were found when the flat free surface was assumed. The variations in the main controlling parameters (bubble size, gas flow rate, and slag layer thickness) and their potential impact on the multiphase fluid flow and mass transfer characteristics (turbulent intensity, mass transfer rate, slag-steel interfacial area, flow patterns, etc.,) in gas-stirred ladles were quantitatively determined to ensure the proper increase in the ladle refining efficiency. It was revealed that by injecting finer bubbles as well as by properly increasing the gas flow rate and the slag layer thickness, the ladle refining efficiency can be enhanced significantly.

Utilizing Solar Power Technologies for On-Orbit Propellant Production

NASA Technical Reports Server (NTRS)

Fikes, John C.; Howell, Joe T.; Henley, Mark W.

2006-01-01

The cost of access to space beyond low Earth orbit may be reduced if vehicles can refuel in orbit. The cost of access to low Earth orbit may also be reduced by launching oxygen and hydrogen propellants in the form of water. To achieve this reduction in costs of access to low Earth orbit and beyond, a propellant depot is considered that electrolyzes water in orbit, then condenses and stores cryogenic oxygen and hydrogen. Power requirements for such a depot require Solar Power Satellite technologies. A propellant depot utilizing solar power technologies is discussed in this paper. The depot will be deployed in a 400 km circular equatorial orbit. It receives tanks of water launched into a lower orbit from Earth, converts the water to liquid hydrogen and oxygen, and stores up to 500 metric tons of cryogenic propellants. This requires a power system that is comparable to a large Solar Power Satellite capable of several 100 kW of energy. Power is supplied by a pair of solar arrays mounted perpendicular to the orbital plane, which rotates once per orbit to track the Sun. The majority of the power is used to run the electrolysis system. Thermal control is maintained by body-mounted radiators; these also provide some shielding against orbital debris. The propellant stored in the depot can support transportation from low Earth orbit to geostationary Earth orbit, the Moon, LaGrange points, Mars, etc. Emphasis is placed on the Water-Ice to Cryogen propellant production facility. A very high power system is required for cracking (electrolyzing) the water and condensing and refrigerating the resulting oxygen and hydrogen. For a propellant production rate of 500 metric tons (1,100,000 pounds) per year, an average electrical power supply of 100 s of kW is required. To make the most efficient use of space solar power, electrolysis is performed only during the portion of the orbit that the Depot is in sunlight, so roughly twice this power level is needed for operations in sunlight (slightly over half of the time). This power level mandates large solar arrays, using advanced Space Solar Power technology. A significant amount of the power has to be dissipated as heat, through large radiators. This paper briefly describes the propellant production facility and the requirements for a high power system capability. The Solar Power technologies required for such an endeavor are discussed.

The Future of Human Exploration

NASA Technical Reports Server (NTRS)

Cooke, Doug

2001-01-01

This slide presentation reviews the near term future of human space exploration in terms of possible mission scenarios, propulsion technologies, orbital dynamics that lead to Low-Energy Transfer from Earth-Moon LI to Solar Libration Points and Return Potential Staging Point for Human Mars Missions. It also examines the required evolution of mission architecture, solar electric propulsion concept, vehicle concepts for future Mars missions, and an overview of a Mars Mission, Also in this presentation are pictures of several historic personages and occasions, and a view of a Mars Meteorite (i.e., ALH84001.0)

Three Dimensional Orbital Stability About the Earth-Moon Equilateral Libration Points.

DTIC Science & Technology

1980-12-01

need to be rotated to the ecliptic . If e is the obliquity of the ecliptic , then the transformation matrix for this is: t F e, ’ C]u 11E -12 IF I) I...the use of the above transformation matrix. The frame for the analysis of the problem will be an Earth-centered ecliptic nonrotating rectangular system...The X-axis will point toward the vernal equinox and the Z-axis will be perpendicular to the ecliptic having the XY-plane coincident with the ecliptic

Ongoing Dynamics and Evolution of Neptune's Ring-Moon System

NASA Astrophysics Data System (ADS)

Showalter, Mark R.; de Pater, Imke; Lissauer, Jack J.; French, Robert S.

2017-06-01

We report results derived from observations of the Neptune system using the Hubble Space Telescope (HST) during August 2016. These observations entail repeated, extremely long exposures through the broadest available filter on the WFC3/UVIS instrument to reveal details of Neptune's faint rings and small, inner moons. The work complements similar observations performed by HST in 2004-2005 and 2009. A principal goal was the recovery of the small moon S/2004 N 1 (henceforth N14), which was first reported in 2009. New images show the moon clearly and make it possible to obtain accurate orbital elements for the first time. A complete analysis of all data 2004-2016 reveals that the mean motion n = 378.90616 +/- 0.00003 degrees per day, corresponding to a semimajor axis a = 105,283 km. Eccentricity and inclination are quite small, with e < 0.001 and i < 0.1 degrees. (This result accounts for the local Laplace Plane tilt of ~ 0.4 degrees). N14 has a physical radius R = 13-15 km, assuming its albedo is 0.09 +/- 0.01, which is the range of Neptune's other inner moons. It orbits interior to the much larger moon Proteus (a = 117,647 km; R = 210 km). Tides are believed to have caused Proteus to spiral outward significantly since its origin, and we find that N14 orbits within the radial zone likely crossed by Proteus. We suggest that N14 may have originated as debris ejected from an impact into Proteus; Proteus subsequently continued to evolve outward but the debris accreted into N14 and remains at its original point of origin. Naiad, the innermost of Neptune's moons, is now orbiting ~ 120 degrees ahead of its published orbital elements. This represents only a 1-sigma correction from its mean motion as derived from Voyager data, but it indicates that later, purported detections of Naiad with the Keck telescope were almost certainly misidentifications. The arcs in the Adams ring show that trends reported previously have continued: the two leading arcs are no longer visible, but the trailing two persist and have been relatively stable. Their mean motion is 820.1119 +/- 0.0003 degrees/day. This value has sufficient precision to rule out any of the previously proposed resonant confinement mechanisms.

The Design and Use of Planetary Science Video Games to Teach Content while Enhancing Spatial Reasoning Skills

NASA Astrophysics Data System (ADS)

Ziffer, Julie; Nadirli, Orkhan; Rudnick, Benjamin; Pinkham, Sunny; Montgomery, Benjamin

2016-10-01

Traditional teaching of Planetary Science requires students to possess well developed spatial reasoning skills (SRS). Recent research has demonstrated that SRS, long known to be crucial to math and science success, can be improved among students who lack these skills (Sorby et al., 2009). Teaching spatial reasoning is particularly valuable to women and minorities who, through societal pressure, often doubt their abilities (Hill et al., 2010). To address SRS deficiencies, our team is developing video games that embed SRS training into Planetary Science content. Our first game, on Moon Phases, addresses the two primary challenges faced by students trying to understand the Sun-Earth-Moon system: 1) visualizing the system (specifically the difference between the Sun-Earth orbital plane and the Earth-Moon orbital plane) and 2) comprehending the relationship between time and the position-phase of the Moon. In our second video game, the student varies an asteroid's rotational speed, shape, and orientation to the light source while observing how these changes effect the resulting light curve. To correctly pair objects to their light curves, students use spatial reasoning skills to imagine how light scattering off a three dimensional rotating object is imaged on a sensor plane and is then reduced to a series of points on a light curve plot. These two games represent the first of our developing suite of high-interest video games designed to teach content while increasing the student's competence in spatial reasoning.

Impact-generated magnetic fields on the Moon : a magnetohydrodynamic numerical investigation

NASA Astrophysics Data System (ADS)

Oran, Rona; Shprits, Yuri; Weiss, Benjamin; Gombosi, Tamas

2015-04-01

Natural remanent magnetization has been identified in lunar rocks, the lunar crust, and a diversity of meteorites. Much of this magnetization is thought to have been produced by cooling a core dynamo mag-netic field. However, the identification of lunar crustal magnetic anomalies at the antipodes of four of the five youngest large (>600 km diameter) impact basins has motivated the alternative hypothesis that the lunar crust could have been magnetized by the impacts. In particular, it has been proposed that highly conducting ionized vapor produced by a basin-forming impact interacts with the ambient solar wind plasma surrounding the Moon to amplify the ambient solar wind magnetic field or any core dynamo field. In this picture, as the ionized vapor cloud expands around the Moon, it pushes and compresses the solar wind plasma into a small region at the antipodal point. The conservation of magnetic flux then leads to an enhanced magnetic field in the compressed plasma. This field can then be recorded as shock remanent magnetization by crustal materials at the antipodal point following the impact of converging basin ejecta. A key requirement for the impact-generated fields hypothesis is that the compressed field be suffi-ciently strong to explain the lunar paleointensities (at least tens of μT) and maintained at the antipodal point for a sufficiently long time (several hours) for the ejecta to arrive and impact the surface. Previous simulations of the expansion of the vapor cloud found that the enhanced field will be strong enough (per-haps reaching hundreds of μT) and will remain at the antipodal site for a sufficiently long time (>1 day) for the arrival of incoming ejecta. However, these studies did not include an explicit calculation of the interaction of the magnetized solar wind plasma with the vapor cloud. Rather, the cloud evolution under the lunar gravity was simulated in the purely hydrodynamic regime. The vapor cloud structure at certain times was used to derive a simplified picture of what the effects would be on an ambient magnetized plasma using general magnetohydrodynamic (MHD) arguments. The solar wind drag acting on the cloud, as well as MHD effects such as field lines stretching and magnetic reconnection were not taken into ac-count. With the advances made in computational MHD models in recent years, we can now revisit these ear-lier important models. Our goal is to perform the first MHD simulations of an impact-generated vapor cloud expanding in the solar wind around the Moon, using BATSRUS, a 3D highly-parallelized versatile MHD code developed at the University of Michigan, in order to self-consistently test the previous estima-tions of the strength and duration of the magnetic field enhancement at the antipodal points. We will con-sider different MHD processes, such as: 1) the finite resistivity of the lunar mantle 2) magnetic diffusion between the solar wind and the initially non-magnetized cloud, 3) magnetic reconnection at the antipode, and 4) viscous drag and the transport of magnetic flux due to solar wind motion, and 4) MHD instabili-ties. This will allow us to systematically examine whether impact-generated fields can indeed be respon-sible for the formation of crustal field enhancements on the Moon.

Analysis of complex elastic structures by a Rayleigh-Ritz component modes method using Lagrange multipliers. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Klein, L. R.

1974-01-01

The free vibrations of elastic structures of arbitrary complexity were analyzed in terms of their component modes. The method was based upon the use of the normal unconstrained modes of the components in a Rayleigh-Ritz analysis. The continuity conditions were enforced by means of Lagrange Multipliers. Examples of the structures considered are: (1) beams with nonuniform properties; (2) airplane structures with high or low aspect ratio lifting surface components; (3) the oblique wing airplane; and (4) plate structures. The method was also applied to the analysis of modal damping of linear elastic structures. Convergence of the method versus the number of modes per component and/or the number of components is discussed and compared to more conventional approaches, ad-hoc methods, and experimental results.

Adapting the Euler-Lagrange equation to study one-dimensional motions under the action of a constant force

NASA Astrophysics Data System (ADS)

Dias, Clenilda F.; Araújo, Maria A. S.; Carvalho-Santos, Vagson L.

2018-01-01

The Euler-Lagrange equations (ELE) are very important in the theoretical description of several physical systems. In this work we have used a simplified form of ELE to study one-dimensional motions under the action of a constant force. From the use of the definition of partial derivative, we have proposed two operators, here called mean delta operators, which may be used to solve the ELE in a simplest way. We have applied this simplification to solve three simple mechanical problems in which the particle is under the action of the gravitational field: a free fall body, the Atwood’s machine and the inclined plan. The proposed simplification can be used to introduce the lagrangian formalism in teaching classical mechanics in introductory physics courses.

A domain decomposition approach to implementing fault slip in finite-element models of quasi-static and dynamic crustal deformation

USGS Publications Warehouse

Aagaard, Brad T.; Knepley, M.G.; Williams, C.A.

2013-01-01

We employ a domain decomposition approach with Lagrange multipliers to implement fault slip in a finite-element code, PyLith, for use in both quasi-static and dynamic crustal deformation applications. This integrated approach to solving both quasi-static and dynamic simulations leverages common finite-element data structures and implementations of various boundary conditions, discretization schemes, and bulk and fault rheologies. We have developed a custom preconditioner for the Lagrange multiplier portion of the system of equations that provides excellent scalability with problem size compared to conventional additive Schwarz methods. We demonstrate application of this approach using benchmarks for both quasi-static viscoelastic deformation and dynamic spontaneous rupture propagation that verify the numerical implementation in PyLith.

Cooperatively surrounding control for multiple Euler-Lagrange systems subjected to uncertain dynamics and input constraints

NASA Astrophysics Data System (ADS)

Chen, Liang-Ming; Lv, Yue-Yong; Li, Chuan-Jiang; Ma, Guang-Fu

2016-12-01

In this paper, we investigate cooperatively surrounding control (CSC) of multi-agent systems modeled by Euler-Lagrange (EL) equations under a directed graph. With the consideration of the uncertain dynamics in an EL system, a backstepping CSC algorithm combined with neural-networks is proposed first such that the agents can move cooperatively to surround the stationary target. Then, a command filtered backstepping CSC algorithm is further proposed to deal with the constraints on control input and the absence of neighbors’ velocity information. Numerical examples of eight satellites surrounding one space target illustrate the effectiveness of the theoretical results. Project supported by the National Basic Research Program of China (Grant No. 2012CB720000) and the National Natural Science Foundation of China (Grant Nos. 61304005 and 61403103).

Evaluation of a transient, simultaneous, arbitrary Lagrange-Euler based multi-physics method for simulating the mitral heart valve.

PubMed

Espino, Daniel M; Shepherd, Duncan E T; Hukins, David W L

2014-01-01

A transient multi-physics model of the mitral heart valve has been developed, which allows simultaneous calculation of fluid flow and structural deformation. A recently developed contact method has been applied to enable simulation of systole (the stage when blood pressure is elevated within the heart to pump blood to the body). The geometry was simplified to represent the mitral valve within the heart walls in two dimensions. Only the mitral valve undergoes deformation. A moving arbitrary Lagrange-Euler mesh is used to allow true fluid-structure interaction (FSI). The FSI model requires blood flow to induce valve closure by inducing strains in the region of 10-20%. Model predictions were found to be consistent with existing literature and will undergo further development.

Modelling of Dynamics of a Wheeled Mobile Robot with Mecanum Wheels with the use of Lagrange Equations of the Second Kind

NASA Astrophysics Data System (ADS)

Hendzel, Z.; Rykała, Ł.

2017-02-01

The work presents the dynamic equations of motion of a wheeled mobile robot with mecanum wheels derived with the use of Lagrange equations of the second kind. Mecanum wheels are a new type of wheels used in wheeled mobile robots and they consist of freely rotating rollers attached to the circumference of the wheels. In order to derive dynamic equations of motion of a wheeled mobile robot, the kinetic energy of the system is determined, as well as the generalised forces affecting the system. The resulting mathematical model of a wheeled mobile robot was generated with the use of Maple V software. The results of a solution of inverse and forward problems of dynamics of the discussed object are also published.

Robust adaptive uniform exact tracking control for uncertain Euler-Lagrange system

NASA Astrophysics Data System (ADS)

Yang, Yana; Hua, Changchun; Li, Junpeng; Guan, Xinping

2017-12-01

This paper offers a solution to the robust adaptive uniform exact tracking control for uncertain nonlinear Euler-Lagrange (EL) system. An adaptive finite-time tracking control algorithm is designed by proposing a novel nonsingular integral terminal sliding-mode surface. Moreover, a new adaptive parameter tuning law is also developed by making good use of the system tracking errors and the adaptive parameter estimation errors. Thus, both the trajectory tracking and the parameter estimation can be achieved in a guaranteed time adjusted arbitrarily based on practical demands, simultaneously. Additionally, the control result for the EL system proposed in this paper can be extended to high-order nonlinear systems easily. Finally, a test-bed 2-DOF robot arm is set-up to demonstrate the performance of the new control algorithm.

On a Lagrange-Hamilton formalism describing position and momentum uncertainties

NASA Technical Reports Server (NTRS)

Schuch, Dieter

1993-01-01

According to Heisenberg's uncertainty relation, in quantum mechanics it is not possible to determine, simultaneously, exact values for the position and the momentum of a material system. Calculating the mean value of the Hamiltonian operator with the aid of exact analytic Gaussian wave packet solutions, these uncertainties cause an energy contribution additional to the classical energy of the system. For the harmonic oscillator, e.g., this nonclassical energy represents the ground state energy. It will be shown that this additional energy contribution can be considered as a Hamiltonian function, if it is written in appropriate variables. With the help of the usual Lagrange-Hamilton formalism known from classical particle mechanics, but now considering this new Hamiltonian function, it is possible to obtain the equations of motion for position and momentum uncertainties.

Safe landing area determination for a Moon lander by reachability analysis

NASA Astrophysics Data System (ADS)

Arslantaş, Yunus Emre; Oehlschlägel, Thimo; Sagliano, Marco

2016-11-01

In the last decades developments in space technology paved the way to more challenging missions like asteroid mining, space tourism and human expansion into the Solar System. These missions result in difficult tasks such as guidance schemes for re-entry, landing on celestial bodies and implementation of large angle maneuvers for spacecraft. There is a need for a safety system to increase the robustness and success of these missions. Reachability analysis meets this requirement by obtaining the set of all achievable states for a dynamical system starting from an initial condition with given admissible control inputs of the system. This paper proposes an algorithm for the approximation of nonconvex reachable sets (RS) by using optimal control. Therefore subset of the state space is discretized by equidistant points and for each grid point a distance function is defined. This distance function acts as an objective function for a related optimal control problem (OCP). Each infinite dimensional OCP is transcribed into a finite dimensional Nonlinear Programming Problem (NLP) by using Pseudospectral Methods (PSM). Finally, the NLPs are solved using available tools resulting in approximated reachable sets with information about the states of the dynamical system at these grid points. The algorithm is applied on a generic Moon landing mission. The proposed method computes approximated reachable sets and the attainable safe landing region with information about propellant consumption and time.

Extrasolar Planets: Towards Comparative Planetology beyond the Solar System

NASA Astrophysics Data System (ADS)

Khan, A. H.

2012-09-01

Today Scenario planet logy is a very important concept because now days the scientific research finding new and new planets and our work's range becoming too long. In the previous study shows about 10-12 years the research of planet logy now has changed . Few years ago we was talking about Sun planet, Earth planet , Moon ,Mars Jupiter & Venus etc. included but now the time has totally changed the recent studies showed that mono lakes California find the arsenic food use by micro organism that show that our study is very tiny as compare to planet long areas .We have very well known that arsenic is the toxic agent's and the toxic agent's present in the lakes and micro organism developing and life going on it's a unbelievable point for us but nature always play a magical games. In few years ago Aliens was the story no one believe the Aliens origin but now the aliens showed catch by our space craft and shuttle and every one believe that Aliens origin but at the moment's I would like to mention one point's that we have too more work required because our planet logy has a vast field. Most of the time our scientific mission shows that this planet found liquid oxygen ,this planet found hydrogen .I would like to clear that point's that all planet logy depend in to the chemical and these chemical gave the indication of the life but we are not abele to developed the adaptation according to the micro organism . Planet logy compare before study shows that Sun it's a combination of the various gases combination surrounded in a round form and now the central Sun Planets ,moons ,comets and asteroids In other word we can say that Or Sun has a wide range of the physical and Chemical properties in the after the development we can say that all chemical and physical property engaged with a certain environment and form a various contains like asteroids, moon, Comets etc. Few studies shows that other planet life affected to the out living planet .We can assure with the example the life of earth affected by Sun ,Moon because these planet life conjugated relation with the planet life's. Can we realistically expect to identify all the pieces of this celestial puzzle and thereby decipher the full mosaic of our planetary origins? The answer, we think, is yes. Each planet contributes knowledge that widens our appreciation for planetary environment much as diverse stars add to our understanding of the stellar life cycle.

Planet logy : Towards Comparative Planet logy beyond the Solar Earth System

NASA Astrophysics Data System (ADS)

Khan, A. H.

2011-10-01

Today Scenario planet logy is a very important concept because now days the scientific research finding new and new planets and our work's range becoming too long. In the previous study shows about 10-12 years the research of planet logy now has changed . Few years ago we was talking about Sun planet, Earth planet , Moon ,Mars Jupiter & Venus etc. included but now the time has totally changed the recent studies showed that mono lakes California find the arsenic food use by micro organism that show that our study is very tiny as compare to planet long areas .We have very well known that arsenic is the toxic agent's and the toxic agent's present in the lakes and micro organism developing and life going on it's a unbelievable point for us but nature always play a magical games. In few years ago Aliens was the story no one believe the Aliens origin but now the aliens showed catch by our space craft and shuttle and every one believe that Aliens origin but at the moment's I would like to mention one point's that we have too more work required because our planet logy has a vast field. Most of the time our scientific mission shows that this planet found liquid oxygen ,this planet found hydrogen .I would like to clear that point's that all planet logy depend in to the chemical and these chemical gave the indication of the life but we are not abele to developed the adaptation according to the micro organism . Planet logy compare before study shows that Sun it's a combination of the various gases combination surrounded in a round form and now the central Sun Planets ,moons ,comets and asteroids In other word we can say that Or Sun has a wide range of the physical and Chemical properties in the after the development we can say that all chemical and physical property engaged with a certain environment and form a various contains like asteroids, moon, Comets etc. Few studies shows that other planet life affected to the out living planet .We can assure with the example the life of earth affected by Sun ,Moon because these planet life conjugated relation with the planet life's. Can we realistically expect to identify all the pieces of this celestial puzzle and thereby decipher the full mosaic of our planetary origins? The answer, we think, is yes. Each planet contributes knowledge that widens our appreciation for planetary environment much as diverse stars add to our understanding of the stellar life cycle.

Options for a lunar base surface architecture

NASA Technical Reports Server (NTRS)

Roberts, Barney B.

1992-01-01

The Planet Surface Systems Office at the NASA Johnson Space Center has participated in an analysis of the Space Exploration Initiative architectures described in the Synthesis Group report. This effort involves a Systems Engineering and Integration effort to define point designs for evolving lunar and Mars bases that support substantial science, exploration, and resource production objectives. The analysis addresses systems-level designs; element requirements and conceptual designs; assessments of precursor and technology needs; and overall programmatics and schedules. This paper focuses on the results of the study of the Space Resource Utilization Architecture. This architecture develops the capability to extract useful materials from the indigenous resources of the Moon and Mars. On the Moon, a substantial infrastructure is emplaced which can support a crew of up to twelve. Two major process lines are developed: one produces oxygen, ceramics, and metals; the other produces hydrogen, helium, and other volatiles. The Moon is also used for a simulation of a Mars mission. Significant science capabilities are established in conjunction with resource development. Exploration includes remote global surveys and piloted sorties of local and regional areas. Science accommodations include planetary science, astronomy, and biomedical research. Greenhouses are established to provide a substantial amount of food needs.

Very large Arecibo-type telescopes

NASA Technical Reports Server (NTRS)

Drake, Frank D.

1988-01-01

The Arecibo-type radio telescope, based on a fixed spherical reflector, is a very effective design for a large radio telescope on the Moon. In such telescopes, major structural members are provided by the ground on which they are built, and thus are provided at no cost in materials or transportation. The strong compression members, the tall towers which support the suspended platform, are an expensive part of the Arecibo telescope. The need for such towers can be eliminated if a suitable valley or crater can be found wherein the rim of the depression can be used as the support point for the cables which support the suspended platform. With an Arecibo-type radio telescope on the Moon, there are no changing gravity loads because of the design and no changing wind loads because of the location; therefore, the only source of time variation in the telescope geometry is thermal changes. Calculations show that with conventional materials, such as steel, it should be possible to construct an Arecibo-type telescope with a reflector diameter of some 30 km on the Moon, and with a reflector diameter of some 60 to 90 km if materials of high specific strength are used.

Report of the Working Group on Space/Lunar Tradeoffs

NASA Technical Reports Server (NTRS)

1992-01-01

The group discussed the advantages and disadvantages of five locations for an optical/infrared array: low-Earth orbit (LEO), Sun-synchronous Earth-orbit, geosynchronous orbit (GEO), Lagrangian points (L4 and L5), and the lunar surface. The factors affecting an array and our assessments of them are given and briefly discussed. In the discussions, two axioms are assumed: (1) Human expansion into space and to the Moon will occur; and (2) The Space Station will be constructed and operational. The major conclusion reached is that baselines of moderate size (greater than 300 m) are best done on the Moon and that large baselines (greater than 10 km) can be done only on the Moon. Three areas needing additional research were identified as follows. (1) Studies are needed on methods to steer long-baseline systems in orbit. This involves learning how to control free-flyers. It is not clear how the difficulty of control varies with orbital elevation. (2) More work is needed on the internal metrology of array systems, both orbital and lunar-surface systems.(3) We need to understand the radiation effects on detectors and electronics and learn how to mitigate them.

Decelerated invasion and waning-moon patterns in public goods games with delayed distribution.

PubMed

Szolnoki, Attila; Perc, Matjaž

2013-05-01

We study the evolution of cooperation in the spatial public goods game, focusing on the effects that are brought about by the delayed distribution of goods that accumulate in groups due to the continuous investments of cooperators. We find that intermediate delays enhance network reciprocity because of a decelerated invasion of defectors, who are unable to reap the same high short-term benefits as they do in the absence of delayed distribution. Long delays, however, introduce a risk because the large accumulated wealth might fall into the wrong hands. Indeed, as soon as the curvature of a cooperative cluster turns negative, the engulfed defectors can collect the heritage of many generations of cooperators and by doing so start a waning-moon pattern that nullifies the benefits of decelerated invasion. Accidental meeting points of growing cooperative clusters may also act as triggers for the waning-moon effect, thus linking the success of cooperators with their propensity to fail in a rather bizarre way. Our results highlight that "investing in the future" is a good idea only if that future is sufficiently near and not likely to be burdened by inflation.

Refractory materials from lunar resources

NASA Technical Reports Server (NTRS)

Fabes, B. D.; Poisl, W. H.

1991-01-01

Refractories - materials which are able to withstand extremely high temperatures - are sure to be an important part of any processing facility or human outpost which is built on Mars. Containers for processing lunar oxygen will need high temperature components. Fabrication of structural material from lunar resources need both containment vessels to hold high temperature melts and molds in which to form the final shapes. Certainly, it would be desirable to fabricate such vessels and molds on the Moon, rather than carrying them up from the Earth. At first glance, this might appear to be a trivial task, since the Moon's surface consists of a variety of refractory compositions. To turn the regolith into a useful fire brick or mold, however, will require water or other binders and additives which are likely to be in extremely short supply on the Moon. The steps needed to make fire bricks and molds for lunar-derived structural materials are examined, pointing out the critical steps and resources which will be needed. While these processes and applications may seem somewhat mundane, it is emphasized that it is precisely these rudimentary processes which must be mastered before discussing making aerobrakes, and other fancier refractories from lunar resources.

High-resolution local gravity model of the south pole of the Moon from GRAIL extended mission data

PubMed Central

Goossens, Sander; Sabaka, Terence J; Nicholas, Joseph B; Lemoine, Frank G; Rowlands, David D; Mazarico, Erwan; Neumann, Gregory A; Smith, David E; Zuber, Maria T

2014-01-01

We estimated a high-resolution local gravity field model over the south pole of the Moon using data from the Gravity Recovery and Interior Laboratory's extended mission. Our solution consists of adjustments with respect to a global model expressed in spherical harmonics. The adjustments are expressed as gridded gravity anomalies with a resolution of 1/6° by 1/6° (equivalent to that of a degree and order 1080 model in spherical harmonics), covering a cap over the south pole with a radius of 40°. The gravity anomalies have been estimated from a short-arc analysis using only Ka-band range-rate (KBRR) data over the area of interest. We apply a neighbor-smoothing constraint to our solution. Our local model removes striping present in the global model; it reduces the misfit to the KBRR data and improves correlations with topography to higher degrees than current global models. Key Points We present a high-resolution gravity model of the south pole of the Moon Improved correlations with topography to higher degrees than global models Improved fits to the data and reduced striping that is present in global models PMID:26074637

Dynamics of Orbits near 3:1 Resonance in the Earth-Moon System

NASA Technical Reports Server (NTRS)

Dichmann, Donald J.; Lebois, Ryan; Carrico, John P., Jr.

2013-01-01

The Interstellar Boundary Explorer (IBEX) spacecraft is currently in a highly elliptical orbit around Earth with a period near 3:1 resonance with the Moon. Its orbit is oriented so that apogee does not approach the Moon. Simulations show this orbit to be remarkably stable over the next twenty years. This article examines the dynamics of such orbits in the Circular Restricted 3-Body Problem (CR3BP). We look at three types of periodic orbits, each exhibiting a type of symmetry of the CR3BP. For each of the orbit types, we assess the local stability using Floquet analysis. Although not all of the periodic solutions are stable in the mathematical sense, any divergence is so slow as to produce practical stability over several decades. We use Poincare maps with twenty-year propagations to assess the nonlinear stability of the orbits, where the perturbation magnitudes are related to the orbit uncertainty for the IBEX mission. Finally we show that these orbits belong to a family of orbits connected in a bifurcation diagram that exhibits exchange of stability. The analysis of these families of period orbits provides a valuable starting point for a mission orbit trade study.

Application of matched asymptotic expansions to lunar and interplanetary trajectories. Volume 2: Derivations of second-order asymptotic boundary value solutions

NASA Technical Reports Server (NTRS)

Lancaster, J. E.

1973-01-01

Previously published asymptotic solutions for lunar and interplanetery trajectories have been modified and combined to formulate a general analytical solution to the problem of N-bodies. The earlier first-order solutions, derived by the method of matched asymptotic expansions, have been extended to second order for the purpose of obtaining increased accuracy. The complete derivation of the second-order solution, including the application of a regorous matching principle, is given. It is shown that the outer and inner expansions can be matched in a region of order mu to the alpha power, where 2/5 alpha 1/2, and mu (the moon/earth or planet/sun mass ratio) is much less than one. The second-order asymptotic solution has been used as a basis for formulating a number of analytical two-point boundary value solutions. These include earth-to-moon, one- and two-impulse moon-to-Earth, and interplanetary solutions. Each is presented as an explicit analytical solution which does not require iterative steps to satisfy the boundary conditions. The complete derivation of each solution is shown, as well as instructions for numerical evaluation. For Vol. 1, see N73-27738.