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.

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.

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.

What Did We Think Could Be Learned About Earth From Lagrange Point Observations?

NASA Technical Reports Server (NTRS)

Wiscombe, Warren

2011-01-01

The scientific excitement surrounding the NASA Lagrange point mission Triana, now called DSCOVR, tended to be forgotten in the brouhaha over other aspects of the mission. Yet a small band of scientists in 1998 got very excited about the possibilities offered by the Lagrange-point perspective on our planet. As one of the original co-investigators on the Triana mission, I witnessed that scientific excitement firsthand. I will bring to life the early period, circa 1998 to 2000, and share the reasons that we thought the Lagrange-point perspective on Earth would be scientifically revolutionary.

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 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.

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.

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.

Gravity Recovery and Interior Laboratory (GRAIL) Mission: Status at the Initiation of the Science Mapping Phase

NASA Technical Reports Server (NTRS)

Zuber, Maria T.; Smith, David E.; Asmar, Sami W.; Alomon; Konopliv, Alexander S.; Lemoine, Frank G.; Melosh, H. Jay; Neumann, Gregory A.; Phillips. Roger J.; Solomon, Sean C.;

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.

Orbit Determination Accuracy for Comets on Earth-Impacting Trajectories

NASA Technical Reports Server (NTRS)

Kay-Bunnell, Linda

2004-01-01

The results presented show the level of orbit determination accuracy obtainable for long-period comets discovered approximately one year before collision with Earth. Preliminary orbits are determined from simulated observations using Gauss' method. Additional measurements are incorporated to improve the solution through the use of a Kalman filter, and include non-gravitational perturbations due to outgassing. Comparisons between observatories in several different circular heliocentric orbits show that observatories in orbits with radii less than 1 AU result in increased orbit determination accuracy for short tracking durations due to increased parallax per unit time. However, an observatory at 1 AU will perform similarly if the tracking duration is increased, and accuracy is significantly improved if additional observatories are positioned at the Sun-Earth Lagrange points L3, L4, or L5. A single observatory at 1 AU capable of both optical and range measurements yields the highest orbit determination accuracy in the shortest amount of time when compared to other systems of observatories.

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

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.

Minimum Propellant Low-Thrust Maneuvers near the Libration Points

NASA Astrophysics Data System (ADS)

Marinescu, A.; Dumitrache, M.

The impulse technique certainly can bring the vehicle on orbits around the libration points or close to them. The question that aries is, by what means can the vehicle arrive in such cases at the libration points? A first investigation carried out in this paper can give an answer: the use of the technique of low-thrust, which, in addition, can bring the vehicle from the libration points near to or into orbits around these points. This aspect is considered in this present paper where for the applications we have considered the transfer for orbits of the equidistant point L4 and of the collinear point L2, from Earth-moon system. This transfer maneuver can be used to insertion one satellite on libration points orbits. In Earth- moon system the points L 4 and L 5 because an vehicle in on of the equidistant points in quite stable and remains in its vicinity of perturbed, have potential interest for the establishment of transporder satellite for interplanetary tracking. In contrast an vehicle in one of the collinear points is quite instable and it will oscillate along the Earth-moon-axis at increasing amplitude and gradually escape from the libration point. Let use assume that a space vehicle equipped with a low-thrust propulsion is near a libration point L. We consider the planar motion in the restricted frame of the three bodies in the rotating system L, where the Earth-moon distance D=l. The unit of time T is period of the moon's orbit divided by 2 and multiplied by the square root of the quantity one plus the moon/Earth mass ratio, and the unit of mass is the Earth's mass. With these predictions the motion equatios of the vehicle equiped with a low-thrust propulsion installation in the linear approximation near the libration point, have been established. The parameters of the motion at the beginning and the end of these maneuvers are known, the variational problem has been formulated as a Lagrange type problem with fixed extremities. On established the differential equations of the extremals and integrating these differential equations we obtain the desired extremals which characterize the minimum propellant optimal manoeuvres of transfer from libration points to their orbits. By means of Legendre conditions for weak minimum and Weierstrass condition for strong minimum, is demonstrated that variational problem so formulated has sense and is a problem of minimum. The integration of extremal's differential equations system can not lead to analytical solutions easily to obtain and for this we have directed to a numerical integration. The problem is a bilocal one because the motion parameter values are predicted at the beginning and of the maneuver (the manoeuvre duration coincides with the combustion duration) the values of the Lagrange multipliers not being specified at the beginning and end of the manoeuvre. For determination of the velocities at any point on the libration point L4 and L2 has been elaborated the program of calculus on the integration of the motion equations without accelerations due thrust during a revolution period the coordinates and velocities to be equal, with which have been calculated the velocities at the apoapsis A and respectively A'. With these specifications, the final conditions (at the end of the maneuver) could be established, and the determination of optimal transfer parameters in the specified points could be determined. The calculus performed for the transfer from the libration points L4 and L2 to their orbits, shows that the evolution velocities on the orbits are in general small, the velocities on the L2 orbits being greater than the velocities on L 4 orbits having the same semimajor axis. This fact is explicable because the period of evolution on orbits of libration point L4 is greater than the period of orbits of the libration point L2. For the transfer in the apoapsis of both orbits (the points A. and A') on can remarque the fact the accelerations due thrust are greater for orbits around the libration point L2 comparatively with orbits having the same semimajor axis around the libration point L 4 ( maneuver duration = 106 s = 11.574 days for L 4 and = 105 s = 1.157 days for L2 ). Considering orbits around libration points L4 and L2 with semimajor axis between 150-15000 km the components of acceleration due thrust have values between 10-2 -10-5 m/S2 which lays in the range of performances of law thrust propulsion installations (the D, T units have been converted in m, s). *Senior Scientist. Member AIAA **Researche Engineer

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.

Spin-Orbit Coupling and the Conservation of Angular Momentum

ERIC Educational Resources Information Center

Hnizdo, V.

2012-01-01

In nonrelativistic quantum mechanics, the total (i.e. orbital plus spin) angular momentum of a charged particle with spin that moves in a Coulomb plus spin-orbit-coupling potential is conserved. In a classical nonrelativistic treatment of this problem, in which the Lagrange equations determine the orbital motion and the Thomas equation yields the…

Lagrange Point Missions: the Key to Next-Generation Integrated Earth Observations. DSCOVR Innovation

NASA Astrophysics Data System (ADS)

Valero, F. P. J.

2016-12-01

From L-1 DSCOVR is capable of new, unique observations potentially conducive to a deeper scientific understanding of the Earth sciences. At L-1 and L-2 the net gravitational pull of the Earth and Sun equals the centripetal force required to orbit the Sun with the same period as the Earth. Satellites at or near L-1 and L-2 keep the same position relative to the Sun and the Earth. DSCOVR does not orbit the Earth but the Sun in synchronism with Earth, acts like a planetoid (orbits the Sun in the ecliptic plane) while acquiring integrated plus spatially and time resolved scientific data as Earth rotates around its axis. Because of the planet's axial tilt relative to the ecliptic plane, the Polar Regions are visible during local summer from L-1 and local winter from L-2 (Fig. 1). DSCOVR's synoptic and continuous observations solve most of the temporal and spatial limitations associated with low Earth (LEO) and Geostationary (GEO) orbits. Two observatories, one at L-1 (daytime) and one at L-2 (nighttime), would acquire minute-by-minute climate quality data for essentially every point on Earth. The integration of L-1, L-2, LEO, and GEO satellites plus the Moon offers new scientific tools and enriched data sets for Earth sciences. Lagrange points observatories are key to next-generation integrated Earth observations. For example, DSCOVR at L-1 views the Earth plus the Moon (a reference) and simultaneously, at one time or another, all LEO and GEO satellites. The L-1 and L-2 satellites would be the link between the Moon, LEO and GEO satellites while providing the data needed to build an integrated Earth observational system. The above properties are the bases for DSCOVR's innovation and scientific approach that systematically observes climate drivers (radiation, aerosols, ozone, clouds, water vapor, vegetation) from L-1 in a way not possible but synergistic with other satellites. Next step: more capable L-1 plus L-2 satellites. The way of the future.

NASA Human Spaceflight Architecture Team Cis-Lunar Analysis

NASA Technical Reports Server (NTRS)

Lupisella, M.; Bobskill, M. R.

2012-01-01

The Cis-Lunar Destination Team of NASA's Human Spaceflight Architecture Teait1 (HAT) has been perfom1ing analyses of a number of cis-lunar locations to infom1 architecture development, transportation and destination elements definition, and operations. The cis-lunar domain is defined as that area of deep space under the gravitation influence of the earth-moon system, including a set of orbital locations (low earth orbit (LEO]. geosynchronous earth orbit [GEO]. highly elliptical orbits [HEO]); earth-moon libration or "Lagrange·· points (EMLl through EMLS, and in particular, EMLI and EML2), and low lunar orbit (LLO). We developed a set of cis-lunar mission concepts defined by mission duration, pre-deployment, type of mission, and location, to develop mission concepts and the associated activities, capabilities, and architecture implications. To date, we have produced two destination operations J concepts based on present human space exploration architectural considerations. We have recently begun defining mission activities that could be conducted within an EM LI or EM L2 facility.

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.

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.

Overview: Solar Electric Propulsion Concept Designs for SEP Technology Demonstration Mission

NASA Technical Reports Server (NTRS)

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

2014-01-01

JPC presentation of the Concept designs for NASA Solar Electric Propulsion Technology Demonstration mission paper. Multiple Solar Electric Propulsion Technology Demonstration Missions were developed to assess vehicle performance and estimated mission cost. Concepts ranged from a 10,000 kg spacecraft capable of delivering 4000 kg of payload to one of the Earth Moon Lagrange points in support of future human-crewed outposts to a 180 kg spacecraft capable of performing an asteroid rendezvous mission after launched to a geostationary transfer orbit as a secondary payload.

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

On the stability of dust orbits in mean-motion resonances perturbed by from an interstellar wind

NASA Astrophysics Data System (ADS)

Pástor, Pavol

2014-09-01

Circumstellar dust particles can be captured in a mean-motion resonance (MMR) with a planet and simultaneously be affected by non-gravitational effects. It is possible to describe the secular variations of a particle orbit in the MMR analytically using averaged resonant equations. We derive the averaged resonant equations from the equations of motion in near-canonical form. The secular variations of the particle orbit depending on the orientation of the orbit in space are taken into account. The averaged resonant equations can be derived/confirmed also from Lagrange's planetary equations. We apply the derived theory to the case when the non-gravitational effects are the Poynting-Robertson effect, the radial stellar wind, and an interstellar wind. The analytical and numerical results obtained are in excellent agreement. We found that the types of orbits correspond to libration centers of the conservative problem. The averaged resonant equations can lead to a system of equations which holds for stationary points in a subset of resonant variables. Using this system we show analytically that for the considered non-gravitational effects, all stationary points should correspond to orbits which are stationary in interplanetary space after an averaging over a synodic period. In an exact resonance, the stationary orbits are stable. The stability is achieved by a periodic repetition of the evolution during the synodic period. Numerical solutions of this system show that there are no stationary orbits for either the exact or non-exact resonances.

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.

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…

Orbital and escape dynamics in barred galaxies - III. The 3D system: correlations between the basins of escape and the NHIMs

NASA Astrophysics Data System (ADS)

Zotos, Euaggelos E.; Jung, Christof

2018-01-01

The escape dynamics of the stars in a barred galaxy composed of a spherically symmetric central nucleus, a bar, a flat thin disc and a dark matter halo component is investigated by using a realistic three degrees of freedom (3-d.o.f.) dynamical model. Modern colour-coded diagrams are used for distinguishing between bounded and escaping motion. In addition, the smaller alignment index method is deployed for determining the regular, sticky or chaotic nature of bounded orbits. We reveal the basins of escape corresponding to the escape through the two symmetrical escape channels around the Lagrange points L2 and L3 and also we relate them with the corresponding distribution of the escape times of the orbits. Furthermore, we demonstrate how the stable manifolds, around the index-1 saddle points, accurately define the fractal basin boundaries observed in the colour-coded diagrams. The development scenario of the fundamental vertical Lyapunov periodic orbit is thoroughly explored for obtaining a more complete view of the unfolding of the singular behaviour of the dynamics at the cusp values of the parameters. Finally, we examine how the combination of the most important parameters of the bar (such as the semimajor axis and the angular velocity) influences the observed stellar structures (rings and spirals), which are formed by escaping stars guided by the invariant manifolds near the saddle points.

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.

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.

Orbit Determination Support for the Microwave Anisotropy Probe (MAP)

NASA Technical Reports Server (NTRS)

Bauer, Frank (Technical Monitor); Truong, Son H.; Cuevas, Osvaldo O.; Slojkowski, Steven

2003-01-01

NASA's Microwave Anisotropy Probe (MAP) was launched from the Cape Canaveral Air Force Station Complex 17 aboard a Delta II 7425-10 expendable launch vehicle on June 30, 2001. The spacecraft received a nominal direct insertion by the Delta expendable launch vehicle into a 185-km circular orbit with a 28.7deg inclination. MAP was then maneuvered into a sequence of phasing loops designed to set up a lunar swingby (gravity-assisted acceleration) of the spacecraft onto a transfer trajectory to a lissajous orbit about the Earth-Sun L2 Lagrange point, about 1.5 million km from Earth. Because of its complex orbital characteristics, the mission provided a unique challenge for orbit determination (OD) support in many orbital regimes. This paper summarizes the premission trajectory covariance error analysis, as well as actual OD results. The use and impact of the various tracking stations, systems, and measurements will be also discussed. Important lessons learned from the MAP OD support team will be presented. There will be a discussion of the challenges presented to OD support including the effects of delta-Vs at apogee as well as perigee, and the impact of the spacecraft attitude mode on the OD accuracy and covariance analysis.

Atmospheric Chemistry from Space: Present Status and Future Plans

NASA Technical Reports Server (NTRS)

Schoeberl, Mark R.; Einaudi, Franco (Technical Monitor)

2001-01-01

One of the unqualified successes of the earth observation program is NASA's continuing monitoring of the ozone layer from space. This activity began in the early 70's with research instruments and continues to this day with the TOMS instrument series and the Upper Atmosphere Research Satellite. In the near future, NASA will be launching the EOS Aura spacecraft (launch mid-2003) which will continue our study of the chemical processes that produce stratospheric ozone depletion. In addition, Aura will begin the first global study of lower atmospheric air pollution including urban ozone, aerosols, nitrogen oxides and carbon monoxide. Atmospheric air pollution measurements from earth orbit involve the development of very high precision spectrometer technologies that have never been flown in space. Farther into the future, lower atmospheric ozone and aerosols may be monitored by space based lidars in low earth orbit, by sensors in geostationary orbit and by continuous limb observations instrument from the Lagrange point L2.

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.

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

Optimal Electrodynamic Tether Phasing Maneuvers

NASA Technical Reports Server (NTRS)

Bitzer, Matthew S.; Hall, Christopher D.

2007-01-01

We study the minimum-time orbit phasing maneuver problem for a constant-current electrodynamic tether (EDT). The EDT is assumed to be a point mass and the electromagnetic forces acting on the tether are always perpendicular to the local magnetic field. After deriving and non-dimensionalizing the equations of motion, the only input parameters become current and the phase angle. Solution examples, including initial Lagrange costates, time of flight, thrust plots, and thrust angle profiles, are given for a wide range of current magnitudes and phase angles. The two-dimensional cases presented use a non-tilted magnetic dipole model, and the solutions are compared to existing literature. We are able to compare similar trajectories for a constant thrust phasing maneuver and we find that the time of flight is longer for the constant thrust case with similar initial thrust values and phase angles. Full three-dimensional solutions, which use a titled magnetic dipole model, are also analyzed for orbits with small inclinations.

James Webb Space Telescope Observations of Stellar Occultations by Solar System Bodies and Rings

NASA Technical Reports Server (NTRS)

Santos-Sanz, P.; French, R. G.; Pinilla-Alonso, N.; Stansberry, J.; Lin, Z-Y.; Zhang, Z-W.; Vilenius, E.; Mueller, Th.; Ortiz, J. L.; Braga-Ribas, F.;

Astrodynamics. Volume 1 - Orbit determination, space navigation, celestial mechanics.

NASA Technical Reports Server (NTRS)

Herrick, S.

1971-01-01

Essential navigational, physical, and mathematical problems of space exploration are covered. The introductory chapters dealing with conic sections, orientation, and the integration of the two-body problem are followed by an introduction to orbit determination and design. Systems of units and constants, as well as ephemerides, representations, reference systems, and data are then dealt with. A detailed attention is given to rendezvous problems and to differential processes in observational orbit correction, and in rendezvous or guidance correction. Finally, the Laplacian methods for determining preliminary orbits, and the orbit methods of Lagrange, Gauss, and Gibbs are reviewed.

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.

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.

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.

SEL2 servicing: increased science return via on-orbit propellant replenishment

NASA Astrophysics Data System (ADS)

Reed, Benjamin B.; DeWeese, Keith; Kienlen, Michael; Aranyos, Thomas; Pellegrino, Joseph; Bacon, Charles; Qureshi, Atif

2016-07-01

Spacecraft designers are driving observatories to the distant Sun-Earth Lagrange Point 2 (SEL2) to meet ever-increasing science requirements. The mass fraction dedicated to propellant for these observatories to reach and operate at SEL2 will be allocated with the upmost care, as it comes at the expense of optics and instrument masses. As such, these observatories could benefit from on-orbit refueling, allowing greater dry-to-wet mass ratio at launch and/or longer mission life. NASA is developing technologies, capabilities and integrated mission designs for multiple servicing applications in low Earth orbit (LEO), geosynchronous Earth orbit (GEO) and cisluner locations. Restore-L, a mission officially in formulation, will launch a free-flying robotic servicer to refuel a government-owned satellite in LEO by mid 2020. This paper will detail the results of a point design mission study to extend Restore-L servicing technologies from LEO to SEL2. This SEL2 mission would launch an autonomous, robotic servicer spacecraft equipped to extend the life of two space assets through refueling. Two space platforms were chosen to 1) drive the requirements for achieving SEL2 orbit and rendezvous with a spacecraft, and 2) to drive the requirements to translate within SEL2 to conduct a follow-on servicing mission. Two fuels, xenon and hydrazine, were selected to assess a multiple delivery system. This paper will address key mission drivers, such as servicer autonomy (necessitated due to communications latency at L2). Also discussed will be the value of adding cooperative servicing elements to the client observatories to reduce mission risk.

Optimal Sunshade Configurations for Space-Based Geoengineering near the Sun-Earth L1 Point.

PubMed

Sánchez, Joan-Pau; McInnes, Colin R

2015-01-01

Within the context of anthropogenic climate change, but also considering the Earth's natural climate variability, this paper explores the speculative possibility of large-scale active control of the Earth's radiative forcing. In particular, the paper revisits the concept of deploying a large sunshade or occulting disk at a static position near the Sun-Earth L1 Lagrange equilibrium point. Among the solar radiation management methods that have been proposed thus far, space-based concepts are generally seen as the least timely, albeit also as one of the most efficient. Large occulting structures could potentially offset all of the global mean temperature increase due to greenhouse gas emissions. This paper investigates optimal configurations of orbiting occulting disks that not only offset a global temperature increase, but also mitigate regional differences such as latitudinal and seasonal difference of monthly mean temperature. A globally resolved energy balance model is used to provide insights into the coupling between the motion of the occulting disks and the Earth's climate. This allows us to revise previous studies, but also, for the first time, to search for families of orbits that improve the efficiency of occulting disks at offsetting climate change on both global and regional scales. Although natural orbits exist near the L1 equilibrium point, their period does not match that required for geoengineering purposes, thus forced orbits were designed that require small changes to the disk attitude in order to control its motion. Finally, configurations of two occulting disks are presented which provide the same shading area as previously published studies, but achieve reductions of residual latitudinal and seasonal temperature changes.

Optimal Sunshade Configurations for Space-Based Geoengineering near the Sun-Earth L1 Point

PubMed Central

Sánchez, Joan-Pau; McInnes, Colin R.

2015-01-01

Within the context of anthropogenic climate change, but also considering the Earth’s natural climate variability, this paper explores the speculative possibility of large-scale active control of the Earth’s radiative forcing. In particular, the paper revisits the concept of deploying a large sunshade or occulting disk at a static position near the Sun-Earth L1 Lagrange equilibrium point. Among the solar radiation management methods that have been proposed thus far, space-based concepts are generally seen as the least timely, albeit also as one of the most efficient. Large occulting structures could potentially offset all of the global mean temperature increase due to greenhouse gas emissions. This paper investigates optimal configurations of orbiting occulting disks that not only offset a global temperature increase, but also mitigate regional differences such as latitudinal and seasonal difference of monthly mean temperature. A globally resolved energy balance model is used to provide insights into the coupling between the motion of the occulting disks and the Earth’s climate. This allows us to revise previous studies, but also, for the first time, to search for families of orbits that improve the efficiency of occulting disks at offsetting climate change on both global and regional scales. Although natural orbits exist near the L1 equilibrium point, their period does not match that required for geoengineering purposes, thus forced orbits were designed that require small changes to the disk attitude in order to control its motion. Finally, configurations of two occulting disks are presented which provide the same shading area as previously published studies, but achieve reductions of residual latitudinal and seasonal temperature changes. PMID:26309047

Radioisotope Electric Propulsion Missions Utilizing a Common Spacecraft Design

NASA Technical Reports Server (NTRS)

Fiehler, Douglas; Oleson, Steven

2004-01-01

A study was conducted that shows how a single Radioisotope Electric Propulsion (REP) spacecraft design could be used for various missions throughout the solar system. This spacecraft design is based on a REP feasibility design from a study performed by NASA Glenn Research Center and the Johns Hopkins University Applied Physics Laboratory. The study also identifies technologies that need development to enable these missions. The mission baseline for the REP feasibility design study is a Trojan asteroid orbiter. This mission sends an REP spacecraft to Jupiter s leading Lagrange point where it would orbit and examine several Trojan asteroids. The spacecraft design from the REP feasibility study would also be applicable to missions to the Centaurs, and through some change of payload configuration, could accommodate a comet sample-return mission. Missions to small bodies throughout the outer solar system are also within reach of this spacecraft design. This set of missions, utilizing the common REP spacecraft design, is examined and required design modifications for specific missions are outlined.

The dynamics and control of large flexible space structures - 13

NASA Technical Reports Server (NTRS)

Bainum, Peter M.; Li, Feiyue; Xu, Jianke

1990-01-01

The optimal control of three-dimensional large angle maneuvers and vibrations of a Shuttle-mast-reflector system is considered. The nonlinear equations of motion are formulated by using Lagrange's formula, with the mast modeled as a continuous beam subject to three-dimensional deformations. Pontryagin's Maximum Principle is applied to the slewing problem, to derive the necessary conditions for the optimal controls, which are bounded by given saturation levels. The resulting two point boundary value problem is then solved by using the quasilinearization algorithm and the method of particular solutions. The study of the large angle maneuvering of the Shuttle-beam-reflector spacecraft in the plane of a circular earth orbit is extended to consider the effects of the structural offset connection, the axial shortening, and the gravitational torque on the slewing motion. Finally the effect of additional design parameters (such as related to additional payload requirement) on the linear quadratic regulator based design of an orbiting control/structural system is examined.

Trajectory Design for the Microwave Anisotropy Probe (MAP)

NASA Technical Reports Server (NTRS)

Newman, Lauri Kraft; Rohrbaugh, David; Bauer, Frank H. (Technical Monitor)

2001-01-01

The Microwave Anisotropy, Probe (MAP) is a Medium Class Explorers (MIDEX) Mission produced in partnership between Goddard Space Flight Center (GSFC) and Princeton University. The goal of the MAP mission is to produce an accurate fill-sky, map of the cosmic microwave background temperature fluctuations (anisotropy). The mission orbit is a Lissajous orbit about the L(sub 2) Sun-Earth Lagrange point. The trajectory design for MAP is complex, having many requirements that must be met including shadow avoidance, sun angle constraints, Lissqjous size and shape characteristics, and limited Delta-V budget. In order to find a trajectory that met the design requirements for the entire 4-year mission lifetime goal, GSFC Flight Dynamics engineers performed many analyses, the results of which are presented herein. The paper discusses the preliminary trade-offs to establish a baseline trajectory, analysis to establish the nominal daily trajectory, and the launch window determination to widen the opportunity from instantaneous to several minutes for each launch date.

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.

Time and Energy, Exploring Trajectory Options Between Nodes in Earth-Moon Space

NASA Technical Reports Server (NTRS)

Martinez, Roland; Condon, Gerald; Williams, Jacob

2012-01-01

The Global Exploration Roadmap (GER) was released by the International Space Exploration Coordination Group (ISECG) in September of 2011. It describes mission scenarios that begin with the International Space Station and utilize it to demonstrate necessary technologies and capabilities prior to deployment of systems into Earth-Moon space. Deployment of these systems is an intermediate step in preparation for more complex deep space missions to near-Earth asteroids and eventually Mars. In one of the scenarios described in the GER, "Asteroid Next", there are activities that occur in Earth-Moon space at one of the Earth-Moon Lagrange (libration) points. In this regard, the authors examine the possible role of an intermediate staging point in an effort to illuminate potential trajectory options for conducting missions in Earth-Moon space of increasing duration, ultimately leading to deep space missions. This paper will describe several options for transits between Low Earth Orbit (LEO) and the libration points, transits between libration points, and transits between the libration points and interplanetary trajectories. The solution space provided will be constrained by selected orbital mechanics design techniques and physical characteristics of hardware to be used in both crewed missions and uncrewed missions. The relationships between time and energy required to transfer hardware between these locations will provide a better understanding of the potential trade-offs mission planners could consider in the development of capabilities, individual missions, and mission series in the context of the ISECG GER.

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.

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.

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.

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

Microwave Anisotrophy Probe Launch and Early Operations

NASA Technical Reports Server (NTRS)

ODonnell, James R., Jr.; Andrews, Stephen F.; Starin, Scott R.; Ward, David K.; Bauer, Frank H. (Technical Monitor)

2002-01-01

The Microwave Anisotropy Probe (MAP), a follow-on to the Differential Microwave Radiometer (DMR) instrument on the Cosmic Background Explorer (COBE), was launched from the Kennedy Space Center at 19:46:46 UTC on June 30, 2001. The powered flight and separation from the Delta II appeared to go as designed, with the launch placing MAP well within sigma launch dispersion and with less than 7 Nms of tip-off momentum. Because of this relatively low momentum, MAP was able to acquire the sun within only 15 minutes with a battery state of charge of 94%. After MAP's successful launch, a six week period of in-orbit checkout and orbit maneuvers followed. The dual purpose of the in-orbit checkout period was to validate the correct performance of all of MAP's systems and, from the attitude control system (ACS) point of view, to calibrate the performance of the spacecraft ACS sensors and actuators to maximize system performance. In addition to the checkout activities performed by the MAP team, the other critical activity taking place during the first six weeks after launch were a series of orbit maneuvers necessary to get the spacecraft from its launch orbit out to its desired orbit about L2, the second Earth-Sun Lagrange point. As MAP continues its standard operations, its ACS design is meeting all of its requirements to successfully complete the mission. This paper will describe the launch and early operations summarized above in greater detail, and show the performance of the attitude control and attitude determination system versus its requirements. Additionally, some of the unexpected events that occurred during this period will be discussed, including two events which dropped the spacecraft into its Safehold Mode and the presence of an "anomalous force" observed during each of the perigee orbit maneuvers that had the potential to cause these critical maneuvers to be prematurely aborted.

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.

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.

Orbital Applications of Electrodynamic Propulsion

DTIC Science & Technology

1993-12-01

Constraint function 4 Greenwich equatorial frame Nt Amp2 .m2/kg 2 Minimize function W Amp2 r-m2 /kg 2 Constrained minimize function h Equinoctial element ...studies will be how a force, besides the two body force, changes the orbital elements . For this, we turn to the force form of Lagrange’s planetary...singularity in e of Equa- tion (10). To do this we introduce two of the equinoctial elements (18:22): h = esinw k = ecosw 11 Note we easily recover e

The effects of Poynting-Robertson drag on solar sails

NASA Astrophysics Data System (ADS)

Abd El-Salam, F. A.

2018-06-01

In the present work, the concept of solar sailing and its developing spacecraft are presented. The effects of Poynting-Robertson drag on solar sails are considered. Some analytical control laws with some mentioned input constraints for optimizing solar sails dynamics in heliocentric orbit using Lagrange's planetary equations are obtained. Optimum force vector in a required direction is maximized by deriving optimal sail cone angle. New control laws that maximize thrust to obtain certain required maximization in some particular orbital element are obtained.

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.

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.;

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.

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.

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.

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.

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.

Getting to L1 the Hard Way: Triana's Launch Options

NASA Technical Reports Server (NTRS)

Houghton, Martin B.; Bauer, Frank H. (Technical Monitor)

2002-01-01

Over the past four years, NASA's Goddard Space Flight Center has built and tested the Triana observatory, which will be the first Earth observing science satellite to take advantage of the unique perspective offered by a Lissajous orbit about the first Earth-Sun Lagrange Point (L1). Triana was originally meant to fly on the U.S. Space Transportation System (a.k.a. the Space Shuttle but complications with the shuttle manifest have forced Triana into a 'wait and see' attitude. The observatory is currently being stored at NASA's Goddard Space Flight Center, where it waits for an appropriate launch opportunity to surface. To that end, several possible alternatives have been considered, including variations on the nominal shuttle deployment scenario, a high inclination Delta-type launch from Vandenberg Air Force Base, a Tsyklon class vehicle launched from Baikonur, Kazakhstan, and a ride on a French Ariane vehicle out of French Guiana into a somewhat arbitrary geostationary transfer orbit (GTO). This paper chronicles and outlines the pros and cons of how each of these opportunities could be used to send Triana on its way to L1.

Getting to L1 the Hard Way: Triana's Launch Options

NASA Technical Reports Server (NTRS)

Houghton, Martin B.; Bauer, Frank H. (Technical Monitor)

2002-01-01

Over the past four years, NASA's Goddard Space Flight Center has built and tested the Triana observatory, which will be the first Earth observing science satellite to take advantage of the unique perspective offered by a Lissajous orbit about the first Earth-Sun Lagrange Point (L1). Triana was originally meant to fly on the U.S. Space Transportation System (a.k.a. the Space Shuttle), but complications with the shuttle manifest have forced Triana into a "wait and see" attitude. The observatory is currently being stored at NASA's Goddard Space Flight Center, where it waits for an appropriate launch opportunity to materialize. To that end, several possible alternatives have been considered, including variations on the nominal shuttle deployment scenario, a high inclination Delta-type launch from Vandenberg Air Force Base, a Tsyklon class vehicle launched from Baikonur, Kazakhstan, and a ride on a French Ariane vehicle out of French Guiana into a somewhat arbitrary geostationary transfer orbit (GTO). This paper chronicles and outlines the pros and cons of how each of these opportunities could be used to send Triana on its way to L1.

Multi-Planetary Systems: Observations and Models of Dynamical Interactions

NASA Technical Reports Server (NTRS)

Lissauer, Jack J.

2018-01-01

More than 600 multi-planet systems are known. The vast majority of these systems have been discovered by NASA's Kepler spacecraft, but dozens were found using the Doppler technique, the first multi-exoplanet system was identified through pulsar timing, and the most massive system has been found using imaging. More than one-third of the 4000+ planet candidates found by NASA's Kepler spacecraft are associated with target stars that have more than one planet candidate, and the large number of such Kepler "multis" tells us that flat multiplanet systems like our Solar System are common. Virtually all of Kepler candidate multis are stable, as tested by numerical integrations that assume a physically motivated mass-radius relationship. Statistical studies performed on these candidate systems reveal a great deal about the architecture of planetary systems, including the typical spacing of orbits and flatness. The characteristics of several of the most interesting confirmed multi-exoplanet systems will also be discussed.HR 8799's four massive planets orbit tens of AU from their host star and travel on nearly circular orbits. PSR B1257+12 has three much smaller planets orbiting close to a neutron star. Both represent extremes and show that planet formation is a robust process that produces a diversity of outcomes. Although both exomoons and Trojan (triangle Lagrange point) planets have been searched for, neither has yet been found.

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

Averaged model to study long-term dynamics of a probe about Mercury

NASA Astrophysics Data System (ADS)

Tresaco, Eva; Carvalho, Jean Paulo S.; Prado, Antonio F. B. A.; Elipe, Antonio; de Moraes, Rodolpho Vilhena

2018-02-01

This paper provides a method for finding initial conditions of frozen orbits for a probe around Mercury. Frozen orbits are those whose orbital elements remain constant on average. Thus, at the same point in each orbit, the satellite always passes at the same altitude. This is very interesting for scientific missions that require close inspection of any celestial body. The orbital dynamics of an artificial satellite about Mercury is governed by the potential attraction of the main body. Besides the Keplerian attraction, we consider the inhomogeneities of the potential of the central body. We include secondary terms of Mercury gravity field from J_2 up to J_6, and the tesseral harmonics \\overline{C}_{22} that is of the same magnitude than zonal J_2. In the case of science missions about Mercury, it is also important to consider third-body perturbation (Sun). Circular restricted three body problem can not be applied to Mercury-Sun system due to its non-negligible orbital eccentricity. Besides the harmonics coefficients of Mercury's gravitational potential, and the Sun gravitational perturbation, our average model also includes Solar acceleration pressure. This simplified model captures the majority of the dynamics of low and high orbits about Mercury. In order to capture the dominant characteristics of the dynamics, short-period terms of the system are removed applying a double-averaging technique. This algorithm is a two-fold process which firstly averages over the period of the satellite, and secondly averages with respect to the period of the third body. This simplified Hamiltonian model is introduced in the Lagrange Planetary equations. Thus, frozen orbits are characterized by a surface depending on three variables: the orbital semimajor axis, eccentricity and inclination. We find frozen orbits for an average altitude of 400 and 1000 km, which are the predicted values for the BepiColombo mission. Finally, the paper delves into the orbital stability of frozen orbits and the temporal evolution of the eccentricity of these orbits.

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.

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

Bound Motion of Bodies and Paticles in the Rotating Systems

NASA Astrophysics Data System (ADS)

Pardy, Miroslav

2007-04-01

The Lagrange theory of particle motion in the noninertial systems is applied to the Foucault pendulum, isosceles triangle pendulum and the general triangle pendulum swinging on the rotating Earth. As an analogue, planet orbiting in the rotating galaxy is considered as the giant galactic gyroscope. The Lorentz equation and the Bargmann-Michel-Telegdi equations are generalized for the rotation system. The knowledge of these equations is inevitable for the construction of LHC where each orbital proton “feels” the Coriolis force caused by the rotation of the Earth.

Compilation on the use of the stroboscopic method in orbital dynamics

NASA Astrophysics Data System (ADS)

Lecohier, G.

In this paper, the application of the stroboscopic method to orbital dynamics is described. As opposed to averaging methods, the stroboscopic solutions of the perturbed Lagrangian system are derived explicitly in the osculating elements which eases greatly their utilization in practical cases. Using this semi-analytical method, the first order solutions of the Lagrange equations including the perturbations by central body gravity field, the third-bodies, the radiation pressure and by the air-drag are derived. In a next step, the accuracy of the first order solution derived for the classical and equinoctial elements is assessed for the long-term prediction of highly eccentric, low altitude, polar and geostationary orbits is estimated.

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.

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.

Petit Grand Tour: Mission Concepts to Outer Planet Satellites Using Non-Conic Low Energy Trajectories

NASA Technical Reports Server (NTRS)

Lo, M. W.

2001-01-01

Our Solar System is connected by a vast Interplanetary Superhighway System (ISSys) providing low energy transport throughout. The Outer Planets with their satellites and rings are smaller replicas of the Solar System with their own ISSys, also providing low energy transport within their own satellite systems. This low energy transport system is generated by all of the Lagrange points of the planets and satellites within the Solar System. Figures show the tubular passage-ways near L1 of Jupiter and the ISSys of Jupiter schematically. These delicate and resilient dynamics may be used to great effect to produce free temporary captures of a spacecraft by a planet or satellite, low energy interplanetary and inter-satellite transfers, as well as precision impact orbits onto the surface of the satellites. Additional information is contained in the original extended abstract.

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.

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.

Development of a Boundary Layer Property Interpolation Tool in Support of Orbiter Return To Flight

NASA Technical Reports Server (NTRS)

Greene, Francis A.; Hamilton, H. Harris

2006-01-01

A new tool was developed to predict the boundary layer quantities required by several physics-based predictive/analytic methods that assess damaged Orbiter tile. This new tool, the Boundary Layer Property Prediction (BLPROP) tool, supplies boundary layer values used in correlations that determine boundary layer transition onset and surface heating-rate augmentation/attenuation factors inside tile gouges (i.e. cavities). BLPROP interpolates through a database of computed solutions and provides boundary layer and wall data (delta, theta, Re(sub theta)/M(sub e), Re(sub theta)/M(sub e), Re(sub theta), P(sub w), and q(sub w)) based on user input surface location and free stream conditions. Surface locations are limited to the Orbiter s windward surface. Constructed using predictions from an inviscid w/boundary-layer method and benchmark viscous CFD, the computed database covers the hypersonic continuum flight regime based on two reference flight trajectories. First-order one-dimensional Lagrange interpolation accounts for Mach number and angle-of-attack variations, whereas non-dimensional normalization accounts for differences between the reference and input Reynolds number. Employing the same computational methods used to construct the database, solutions at other trajectory points taken from previous STS flights were computed: these results validate the BLPROP algorithm. Percentage differences between interpolated and computed values are presented and are used to establish the level of uncertainty of the new tool.

Deployment and Simulation of the Astrod-Gw Formation

NASA Astrophysics Data System (ADS)

Wu, An-Ming; Ni, Wei-Tou

2013-01-01

Constellation or formation flying is a common concept in space Gravitational Wave (GW) mission proposals for the required interferometry implementation. The spacecraft of most of these mission proposals go to deep space and many have Earthlike orbits around the Sun. Astrodynamical Space Test of Relativity using Optical Devices optimized for Gravitation Wave detection (ASTROD-GW), Big Bang Observer (BBO) and DECIGO have spacecraft distributed in Earthlike orbits in formation. The deployment of orbit formation is an important issue for these missions. ASTROD-GW is to focus on the goal of detection of GWs. The mission orbits of the three spacecraft forming a nearly equilateral triangular array are chosen to be near the Sun-Earth Lagrange points L3, L4 and L5. The three spacecraft range interferometrically with one another with arm length about 260 million kilometers with the scientific goals including detection of GWs from Massive Black Holes (MBH) and Extreme-Mass-Ratio Black Hole Inspirals (EMRI), and using these observations to find the evolution of the equation of state of dark energy and to explore the co-evolution of MBH with galaxies. In this paper, we review the formation flying for fundamental physics missions, design the preliminary transfer orbits of the ASTROD-GW spacecraft from the separations of the launch vehicles to the mission orbits, and simulate the arm lengths of the triangular formation. From our study, the optimal delta-Vs and propellant ratios of the transfer orbits could be within about 2.5 km/s and 0.55, respectively. From the simulation of the formation for 10 years, the arm lengths of the formation vary in the range 1.73210 ± 0.00015 AU with the arm length differences varying in the range ±0.00025 AU for formation with 1° inclination to the ecliptic plane. This meets the measurement requirements. Further studies on the optimizations of deployment and orbit configurations for a period of 20 years and with inclinations between 1° to 3° are currently ongoing.

Analytic first derivatives for a spin-adapted open-shell coupled cluster theory: Evaluation of first-order electrical properties

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

Datta, Dipayan, E-mail: datta@uni-mainz.de; Gauss, Jürgen, E-mail: gauss@uni-mainz.de

2014-09-14

An analytic scheme is presented for the evaluation of first derivatives of the energy for a unitary group based spin-adapted coupled cluster (CC) theory, namely, the combinatoric open-shell CC (COSCC) approach within the singles and doubles approximation. The widely used Lagrange multiplier approach is employed for the derivation of an analytical expression for the first derivative of the energy, which in combination with the well-established density-matrix formulation, is used for the computation of first-order electrical properties. Derivations of the spin-adapted lambda equations for determining the Lagrange multipliers and the expressions for the spin-free effective density matrices for the COSCC approachmore » are presented. Orbital-relaxation effects due to the electric-field perturbation are treated via the Z-vector technique. We present calculations of the dipole moments for a number of doublet radicals in their ground states using restricted open-shell Hartree-Fock (ROHF) and quasi-restricted HF (QRHF) orbitals in order to demonstrate the applicability of our analytic scheme for computing energy derivatives. We also report calculations of the chlorine electric-field gradients and nuclear quadrupole-coupling constants for the CCl, CH{sub 2}Cl, ClO{sub 2}, and SiCl radicals.« less

The PLATO camera

NASA Astrophysics Data System (ADS)

Laubier, D.; Bodin, P.; Pasquier, H.; Fredon, S.; Levacher, P.; Vola, P.; Buey, T.; Bernardi, P.

2017-11-01

PLATO (PLAnetary Transits and Oscillation of stars) is a candidate for the M3 Medium-size mission of the ESA Cosmic Vision programme (2015-2025 period). It is aimed at Earth-size and Earth-mass planet detection in the habitable zone of bright stars and their characterisation using the transit method and the asterosismology of their host star. That means observing more than 100 000 stars brighter than magnitude 11, and more than 1 000 000 brighter than magnitude 13, with a long continuous observing time for 20 % of them (2 to 3 years). This yields a need for an unusually long term signal stability. For the brighter stars, the noise requirement is less than 34 ppm.hr-1/2, from a frequency of 40 mHz down to 20 μHz, including all sources of noise like for instance the motion of the star images on the detectors and frequency beatings. Those extremely tight requirements result in a payload consisting of 32 synchronised, high aperture, wide field of view cameras thermally regulated down to -80°C, whose data are combined to increase the signal to noise performances. They are split into 4 different subsets pointing at 4 directions to widen the total field of view; stars in the centre of that field of view are observed by all 32 cameras. 2 extra cameras are used with color filters and provide pointing measurement to the spacecraft Attitude and Orbit Control System (AOCS) loop. The satellite is orbiting the Sun at the L2 Lagrange point. This paper presents the optical, electronic and electrical, thermal and mechanical designs devised to achieve those requirements, and the results from breadboards developed for the optics, the focal plane, the power supply and video electronics.

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.

Candidate Binary Trojan and Hilda Asteroids from Rotational Light Curves

NASA Astrophysics Data System (ADS)

Sonnett, Sarah M.; Mainzer, Amy K.; Grav, Tommy; Masiero, Joseph R.; Bauer, James M.; Kramer, Emily A.

2017-10-01

Jovian Trojans (hereafter, Trojans) are asteroids in stable orbits at Jupiter's L4 and L5 Lagrange points, and Hilda asteroids are inwards of the Trojans in 3:2 mean-motion resonance with Jupiter. Due to their special dynamical properties, observationally constraining the formation location and dynamical histories of Trojans and HIldas offers key input for giant planet migration models. A fundamental parameter in assessing formation location is the bulk density - with low-density objects associated with an ice-rich formation environment in the outer solar system and high-density objects typically linked to the warmer inner solar system. Bulk density can only be directly measured during a close fly-by or by determining the mutual orbits of binary asteroid systems. With the aim of determining densities for a statistically significant sample of Trojans and Hildas, we are undertaking an observational campaign to confirm and characterize candidate binary asteroids published in Sonnett et al. (2015). These objects were flagged as binary candidates because their large NEOWISE brightness variations imply shapes so elongated that they are not likely explained by a singular equilibrium rubble pile and instead may be two elongated, gravitationally bound asteroids. We are obtaining densely sampled rotational light curves of these possible binaries to search for light curve features diagnostic of binarity and to determine the orbital properties of any confirmed binary systems by modeling the light curve. We compare the We present an update on this follow-up campaign and comment on future steps.

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.

Site Selection and Deployment Scenarios for Servicing of Deep-Space Observatories

NASA Technical Reports Server (NTRS)

Willenberg, Harvey J.; Fruhwirth, Michael A.; Potter, Seth D.; Leete, Stephen J.; Moe, Rud V.

2001-01-01

The deep-space environment and relative transportation accessibility of the Weak Stability Boundary (WSB) region connecting the Earth-Moon and Sun-Earth libration points makes the Sun-Earth L2 an attractive operating location for future observatories. A summary is presented of key characteristics of future observatories designed to operate in this region. The ability to service observatories that operate within the region around the Lagrange points may greatly enhance their reliability, lifetime, and scientific return. The range of servicing missions might begin with initial deployment, assembly, test, and checkout. Post-assembly servicing missions might also include maintenance and repair, critical fluids resupply, and instrument upgrades. We define the range of servicing missions that can be performed with extravehicular activity, with teleoperated robots, and with autonomous robots. We then describe deployment scenarios that affect payload design. A trade study is summarized of the benefits and risks of alternative servicing sites, including at the International Space Station, at other low-Earth-orbit locations, at the Earth-Moon L1 location, and on-site at the Sun-Earth L2 location. Required technology trades and development issues for observatory servicing at each site, and with each level of autonomy, are summarized.

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.

Model predictive control of attitude maneuver of a geostationary flexible satellite based on genetic algorithm

NASA Astrophysics Data System (ADS)

TayyebTaher, M.; Esmaeilzadeh, S. Majid

2017-07-01

This article presents an application of Model Predictive Controller (MPC) to the attitude control of a geostationary flexible satellite. SIMO model has been used for the geostationary satellite, using the Lagrange equations. Flexibility is also included in the modelling equations. The state space equations are expressed in order to simplify the controller. Naturally there is no specific tuning rule to find the best parameters of an MPC controller which fits the desired controller. Being an intelligence method for optimizing problem, Genetic Algorithm has been used for optimizing the performance of MPC controller by tuning the controller parameter due to minimum rise time, settling time, overshoot of the target point of the flexible structure and its mode shape amplitudes to make large attitude maneuvers possible. The model included geosynchronous orbit environment and geostationary satellite parameters. The simulation results of the flexible satellite with attitude maneuver shows the efficiency of proposed optimization method in comparison with LQR optimal controller.

Post-Newtonian Circular Restricted 3-Body Problem: Schwarzschild primaries

NASA Astrophysics Data System (ADS)

Dubeibe, F. L.; Lora-Clavijo, F. D.; González, G. A.

2017-07-01

The restricted three-body problem (RTBP) has been extensively studied to investigate the stability of the solar system, extra-solar subsystems, asteroid capture, and the dynamics of two massive black holes orbited by a sun. In the present work, we study the stability of the planar circular restricted three-body problem in the context of post-Newtonian approximations. First of all, we review the results obtained from the post-Newtonian equations of motion calculated in the framework of the Einstein-Infeld-Hoffmann formalism (EIH). Therefore, using the Fodor-Hoenselers-Perjes formalism (FHP), we have performed an expansion of the gravitational potential for two primaries, deriving a new system of equations of motion, which unlike the EIH-approach, preserves the Jacobian integral of motion. Additionally, we have obtained approximate expressions for the Lagrange points in terms of a mass parameter μ, where it is found that the deviations from the classical regime are larger for the FHP than for the EIH equations.

Spectroscopy of the Stellar Wind in the Cygnus X-1 System

NASA Technical Reports Server (NTRS)

Miskovicova, Ivica; Hanke, Manfred; Wilms, Joern; Nowak, Michael A.; Pottschmidt, Katja; Schultz, Norbert

2010-01-01

The X-ray luminosity of black holes is produced through the accretion of material from their companion stars. Depending on the mass of the donor star, accretion of the material falling onto the black hole through the inner Lagrange point of the system or accretion by the strong stellar wind can occur. Cygnus X-1 is a high mass X-ray binary system, where the black hole is powered by accretion of the stellar wind of its supergiant companion star HDE226868. As the companion is close to filling its Roche lobe, the wind is not symmetric, but strongly focused towards the black hole. Chandra-HETGS observations allow for an investigation of this focused stellar wind, which is essential to understand the physics of the accretion flow. We compare observations at the distinct orbital phases of 0.0, 0.2, 0.5 and 0.75. These correspond to different lines of sights towards the source, allowing us to probe the structure and the dynamics of the wind.

Monitoring solar irradiance from L2 with Gaia

NASA Astrophysics Data System (ADS)

Serpell, E.

2017-09-01

Gaia is the European Space Agency's cornerstone astrometry mission to measure the positions of a billion stars in the Milky Way with unprecedented accuracy. Since early 2014 Gaia has been operating in a halo orbit around the second Sun-Earth Lagrange point that provides the stable thermal environment, without Earth eclipses, needed for the payload to function accurately. The spacecraft is equipped with a number of thermally isolated, sun-facing thermistors that provide a continuous measurement of the local equilibrium temperature. As a consequence of the spacecraft design and operational conditions these temperature measurements have been used to infer the solar output over a broad wavelength range. In this paper we present an analysis of temperature measurements made of the Gaia solar panels at frequencies of up to 1 Hz for the first 35 months of routine operations. We show that the Gaia solar panel temperature measurements are capable of precisely determining short term changes to the solar output at a level of better than 0.04% with time constants of a few minutes.

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.

A Gauge-generalized Solution for Non-Keplerian Motion in the Frenet-Serret Frame

NASA Astrophysics Data System (ADS)

Garber, Darren D.

2009-05-01

The customary modeling of perturbed planetary and spacecraft motion as a continuous sequence of unperturbed two-body orbits (instantaneous ellipses) is conveniently assigned a physical interpretation through the Keplerian and Delaunay elements and complemented mathematically by the Lagrange-type equations which describe the evolution of these variables. If however the actual motion is very non-Keplerian (i.e. the perturbed orbit varies greatly from a two-body orbit), then its modeling by a sequence of conics is not necessarily optimal in terms of its mathematical description and its resulting physical interpretation. Since, in principle a curve of any type can be represented as a sequence of points from a family of curves of any other type (Efroimsky 2005), alternate non-conic curves can be utilized to better describe the perturbed non-Keplerian motion of the body both mathematically and with a physically relevant interpretation. Non-Keplerian motion exists in both celestial mechanics and astrodynamics as evident by the complex interactions within star clusters and also as the result of a spacecraft accelerating via ion propulsion, solar sails and electro-dynamic tethers. For these cases, the sequence of simple orbits to describe the motion is not based on conics, but instead a family of spirals. The selection of spirals as the underlying simple motion is supported by the fact that it is unnecessary to describe the motion in terms of instantaneous orbits tangent to the actual trajectory (Efroimsky 2002, Newman & Efroimsky 2003) and at times there is an advantage to deviate from osculation, in order to greatly simplify the resulting mathematics via gauge freedom (Efroimsky & Goldreich 2003, Slabinski 2003, Gurfil 2004). From these two principles, (1) spirals as instantaneous orbits, and (2) controlled deviation from osculation, new planetary equations are derived for new non-osculating elements in the Frenet-Serret frame with the gauge function as a measure of non-osculation.

Relativistic semiempirical-core-potential calculations in Ca+,Sr+ , and Ba+ ions on Lagrange meshes

NASA Astrophysics Data System (ADS)

Filippin, Livio; Schiffmann, Sacha; Dohet-Eraly, Jérémy; Baye, Daniel; Godefroid, Michel

2018-01-01

Relativistic atomic structure calculations are carried out in alkaline-earth-metal ions using a semiempirical-core-potential approach. The systems are partitioned into frozen-core electrons and an active valence electron. The core orbitals are defined by a Dirac-Hartree-Fock calculation using the grasp2k package. The valence electron is described by a Dirac-like Hamiltonian involving a core-polarization potential to simulate the core-valence electron correlation. The associated equation is solved with the Lagrange-mesh method, which is an approximate variational approach having the form of a mesh calculation because of the use of a Gauss quadrature to calculate matrix elements. Properties involving the low-lying metastable D 3 /2 ,5 /2 2 states of Ca+, Sr+, and Ba+ are studied, such as polarizabilities, one- and two-photon decay rates, and lifetimes. Good agreement is found with other theory and observation, which is promising for further applications in alkalilike systems.

Ultraviolet anomalies of the WASP-12 and HD 189733 systems: Trojan satellites as a plasma source

NASA Astrophysics Data System (ADS)

Kislyakova, Kristina; Pilat-Lohinger, Elke; Funk, Barbara; Lammer, Helmut; Fossati, Luca; Eggl, Siegfried; Schwarz, Richard; Boudyada, Mohammed; Erkaev, Nikolai

2017-04-01

We suggest an additional possible plasma source in the WASP-12 and HD189733b systems to explain part of the phenomena observed in ultraviolet (UV) light curves during planetary transits. In the proposed scenario, material originates from the molten surface of Trojan satellites on orbits near the Lagrange points L4 and L5. We show that the temperature at the orbital location of WASP-12b is high enough to melt the surface of rocky Trojans and to form shallow lava oceans on them. At the orbital distance of WASP-12b, this leads to the release of elements such as Mg and Ca, which are expected to surround the system. The predicted Mg and Ca outgassing rates from two Io-sized WASP-12b Trojans are ≈ 2.2 × 1027 s-1 and ≈ 2.2 × 1026 s-1, respectively. Trojan outgassing can lead to the observed lack of emission in MgII h&k and CaII H&K line cores of WASP-12. For HD 189733b, the mechanism is only marginally possible due to the lower temperature. The early ingress of HD 189733b observed in the far-UV (FUV) CII doublet couldn't be explained by this mechanism due to absence of carbon within elements outgassed by molten lava. We investigate the long-term stability region of WASP-12b and HD 189733b in case of planar and inclined motion of these satellites and show that unlike the classical exomoons orbiting the planet, Io-sized Trojans can be stable for the whole systems life time.

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.

An Efficient Algorithm for Perturbed Orbit Integration Combining Analytical Continuation and Modified Chebyshev Picard Iteration

NASA Astrophysics Data System (ADS)

Elgohary, T.; Kim, D.; Turner, J.; Junkins, J.

2014-09-01

Several methods exist for integrating the motion in high order gravity fields. Some recent methods use an approximate starting orbit, and an efficient method is needed for generating warm starts that account for specific low order gravity approximations. By introducing two scalar Lagrange-like invariants and employing Leibniz product rule, the perturbed motion is integrated by a novel recursive formulation. The Lagrange-like invariants allow exact arbitrary order time derivatives. Restricting attention to the perturbations due to the zonal harmonics J2 through J6, we illustrate an idea. The recursively generated vector-valued time derivatives for the trajectory are used to develop a continuation series-based solution for propagating position and velocity. Numerical comparisons indicate performance improvements of ~ 70X over existing explicit Runge-Kutta methods while maintaining mm accuracy for the orbit predictions. The Modified Chebyshev Picard Iteration (MCPI) is an iterative path approximation method to solve nonlinear ordinary differential equations. The MCPI utilizes Picard iteration with orthogonal Chebyshev polynomial basis functions to recursively update the states. The key advantages of the MCPI are as follows: 1) Large segments of a trajectory can be approximated by evaluating the forcing function at multiple nodes along the current approximation during each iteration. 2) It can readily handle general gravity perturbations as well as non-conservative forces. 3) Parallel applications are possible. The Picard sequence converges to the solution over large time intervals when the forces are continuous and differentiable. According to the accuracy of the starting solutions, however, the MCPI may require significant number of iterations and function evaluations compared to other integrators. In this work, we provide an efficient methodology to establish good starting solutions from the continuation series method; this warm start improves the performance of the MCPI significantly and will likely be useful for other applications where efficiently computed approximate orbit solutions are needed.

Gravitational wave detection in space

NASA Astrophysics Data System (ADS)

Ni, Wei-Tou

Gravitational Wave (GW) detection in space is aimed at low frequency band (100nHz-100mHz) and middle frequency band (100mHz-10Hz). The science goals are the detection of GWs from (i) Supermassive Black Holes; (ii) Extreme-Mass-Ratio Black Hole Inspirals; (iii) Intermediate-Mass Black Holes; (iv) Galactic Compact Binaries and (v) Relic GW Background. In this paper, we present an overview on the sensitivity, orbit design, basic orbit configuration, angular resolution, orbit optimization, deployment, time-delay interferometry (TDI) and payload concept of the current proposed GW detectors in space under study. The detector proposals under study have arm length ranging from 1000km to 1.3 × 109km (8.6AU) including (a) Solar orbiting detectors — (ASTROD Astrodynamical Space Test of Relativity using Optical Devices (ASTROD-GW) optimized for GW detection), Big Bang Observer (BBO), DECi-hertz Interferometer GW Observatory (DECIGO), evolved LISA (e-LISA), Laser Interferometer Space Antenna (LISA), other LISA-type detectors such as ALIA, TAIJI etc. (in Earthlike solar orbits), and Super-ASTROD (in Jupiterlike solar orbits); and (b) Earth orbiting detectors — ASTROD-EM/LAGRANGE, GADFLI/GEOGRAWI/g-LISA, OMEGA and TIANQIN.

An Empirical Method for Determining the Lunar Gravity Field. Ph.D. Thesis - George Washington Univ.

NASA Technical Reports Server (NTRS)

Ferrari, A. J.

1971-01-01

A method has been devised to determine the spherical harmonic coefficients of the lunar gravity field. This method consists of a two-step data reduction and estimation process. In the first step, a weighted least-squares empirical orbit determination scheme is applied to Doppler tracking data from lunar orbits to estimate long-period Kepler elements and rates. Each of the Kepler elements is represented by an independent function of time. The long-period perturbing effects of the earth, sun, and solar radiation are explicitly modeled in this scheme. Kepler element variations estimated by this empirical processor are ascribed to the non-central lunar gravitation features. Doppler data are reduced in this manner for as many orbits as are available. In the second step, the Kepler element rates are used as input to a second least-squares processor that estimates lunar gravity coefficients using the long-period Lagrange perturbation equations.

Analytic theory of orbit contraction

NASA Technical Reports Server (NTRS)

Vinh, N. X.; Longuski, J. M.; Busemann, A.; Culp, R. D.

1977-01-01

The motion of a satellite in orbit, subject to atmospheric force and the motion of a reentry vehicle are governed by gravitational and aerodynamic forces. This suggests the derivation of a uniform set of equations applicable to both cases. For the case of satellite motion, by a proper transformation and by the method of averaging, a technique appropriate for long duration flight, the classical nonlinear differential equation describing the contraction of the major axis is derived. A rigorous analytic solution is used to integrate this equation with a high degree of accuracy, using Poincare's method of small parameters and Lagrange's expansion to explicitly express the major axis as a function of the eccentricity. The solution is uniformly valid for moderate and small eccentricities. For highly eccentric orbits, the asymptotic equation is derived directly from the general equation. Numerical solutions were generated to display the accuracy of the analytic theory.

First observations of volcanic eruption clouds from L1 by DSCOVR/EPIC

NASA Astrophysics Data System (ADS)

Carn, S. A.; Krotkov, N. A.; Taylor, S.; Fisher, B. L.; Li, C.; Hughes, E. J.; Bhartia, P. K.; Prata, F.

2016-12-01

Volcanic emissions of sulfur dioxide (SO2) and ash have been measured by ultraviolet (UV) sensors on US and European polar-orbiting satellites since the late 1970s. Although successful, the main limitation of these UV observations from low-Earth orbit has been poor temporal resolution. Timeliness can be crucial when detecting hazardous volcanic eruption clouds that threaten aviation, and most operational geostationary satellites cannot detect SO2, a key tracer of volcanic plumes. In 2015, the launch of the Earth Polychromatic Imaging Camera (EPIC) aboard the Deep Space Climate Observatory (DSCOVR) provided the first opportunity to observe volcanic clouds from the L1 Lagrange point. EPIC is a 10-band spectroradiometer spanning UV to near-IR wavelengths with two UV channels sensitive to SO2, and a ground resolution of 25 km. The unique L1 vantage point provides continuous observations of the sunlit Earth disk, potentially offering multiple daily observations of volcanic SO2 and ash clouds in the EPIC field of view. When coupled with complementary retrievals from polar-orbiting UV and infrared (IR) sensors such as the Ozone Monitoring Instrument (OMI), the Ozone Mapping and Profiler Suite (OMPS), and the Atmospheric Infrared Sounder (AIRS), the increased observation frequency afforded by DSCOVR/EPIC will permit more timely volcanic eruption detection, improved trajectory modeling, and novel analyses of the temporal evolution of volcanic clouds. We demonstrate the sensitivity of EPIC UV radiances to volcanic clouds using examples from the first year of EPIC observations including the December 2015 paroxysmal eruption of Etna volcano (Italy). When combined with OMI and OMPS measurements, the EPIC SO2 data permit hourly tracking of the Etna eruption cloud as it drifts away from the volcano. We also describe ongoing efforts to adapt existing UV backscatter (BUV) algorithms to produce operational EPIC SO2 and Ash Index (AI) products.

Conceptual Design of the TPF-O SC Buses

NASA Technical Reports Server (NTRS)

Purves, Lloyd R.

2007-01-01

The Terrestrial Planet Finder - Occulter (TPF-O) mission has two Spacecraft (SC) buses, one for a space telescope and the other for a formation-flying occulter. SC buses typically supply the utilities (support structures, propulsion, attitude control, power, communications, etc) required by the payloads. Unique requirements for the occulter SC bus are to provide the large delta V required for the slewing maneuvers of the occulter, and comunications for formation flying. The TPF-O telescope SC bus shares some key features of the one for the Hubble Space Telescope (HST): both support space telescopes designed to observe in the visible to near infrared range of wavelengths with comparable primary mirror apertures (2.4 m for HST, 2.4 - 4.0 m for TPF-O). However, TPF-O is expected to have a Wide Field Camera (WFC) with a Field of View (FOV) much larger than that of HST. Ths WFC is also expected to provide fine guidance. TPF-O is designed to operate in an orbit around the Sun-Earth Lagrange 2 (SEL2) point. The longer communications range to SEL2 and the large science FOV require higher performance communications than HST. Maintaining a SEL2 orbit requires TPF-O, unlike HST, to have a propulsion system. The velocity required for reachng SEL2 and the limited capabilities of affordable launch vehicles require both TPF-O elements to have compact, low-mass designs. Finally, it is possible that TPF-O may utilize a modular design derived fiom that of HST to allow servicing in the SEL2 orbit.

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

Resonance Occupation in the Kuiper Belt: Case Examples of the 5:2 and Trojan Resonances

NASA Astrophysics Data System (ADS)

Chiang, E. I.; Jordan, A. B.; Millis, R. L.; Buie, M. W.; Wasserman, L. H.; Elliot, J. L.; Kern, S. D.; Trilling, D. E.; Meech, K. J.; Wagner, R. M.

2003-07-01

As part of our ongoing Deep Ecliptic Survey (DES) of the Kuiper belt, we report on the occupation of the 1:1 (Trojan), 4:3, 3:2, 7:4, 2:1, and 5:2 Neptunian mean motion resonances (MMRs). The previously unrecognized occupation of the 1:1 and 5:2 MMRs is not easily understood within the standard model of resonance sweeping by a migratory Neptune over an initially dynamically cold belt. Among all resonant Kuiper belt objects (KBOs), the three observed members of the 5:2 MMR discovered by DES possess the largest semimajor axes (a~55.4 AU), the highest eccentricities (e~0.4), and substantial orbital inclinations (i~10deg). Objects (38084) 1999HB12 and possibly 2001KC77 can librate with modest amplitudes of ~90° within the 5:2 MMR for at least 1 Gyr. Their trajectories cannot be explained by close encounters with Neptune alone, given the latter's current orbit. The dynamically hot orbits of such 5:2 resonant KBOs, unlike hot orbits of previously known resonant KBOs, may imply that these objects were preheated to large inclination and large eccentricity prior to resonance capture by a migratory Neptune. Our first discovered Neptunian Trojan, 2001QR322, may not owe its existence to Neptune's migration at all. The trajectory of 2001QR322 is remarkably stable; the object can undergo tadpole-type libration about Neptune's leading Lagrange (L4) point for at least 1 Gyr with a libration amplitude of 24°. Trojan capture probably occurred while Neptune accreted the bulk of its mass. For an assumed albedo of 12%-4%, our Trojan is ~130-230 km in diameter. Model-dependent estimates place the total number of Neptune Trojans resembling 2001QR322 at ~20-60. Their existence helps to rule out violent orbital histories for Neptune.

SURVEY SIMULATIONS OF A NEW NEAR-EARTH ASTEROID DETECTION SYSTEM

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

Mainzer, A.; Bauer, J.; Giorgini, J.

We have carried out simulations to predict the performance of a new space-based telescopic survey operating at thermal infrared wavelengths that seeks to discover and characterize a large fraction of the potentially hazardous near-Earth asteroid (NEA) population. Two potential architectures for the survey were considered: one located at the Earth–Sun L1 Lagrange point, and one in a Venus-trailing orbit. A sample cadence was formulated and tested, allowing for the self-follow-up necessary for objects discovered in the daytime sky on Earth. Synthetic populations of NEAs with sizes as small as 140 m in effective spherical diameter were simulated using recent determinationsmore » of their physical and orbital properties. Estimates of the instrumental sensitivity, integration times, and slew speeds were included for both architectures assuming the properties of newly developed large-format 10 μm HgCdTe detector arrays capable of operating at ∼35 K. Our simulation included the creation of a preliminary version of a moving object processing pipeline suitable for operating on the trial cadence. We tested this pipeline on a simulated sky populated with astrophysical sources such as stars and galaxies extrapolated from Spitzer Space Telescope and Wide-field Infrared Explorer data, the catalog of known minor planets (including Main Belt asteroids, comets, Jovian Trojans, planets, etc.), and the synthetic NEA model. Trial orbits were computed for simulated position-time pairs extracted from the synthetic surveys to verify that the tested cadence would result in orbits suitable for recovering objects at a later time. Our results indicate that the Earth–Sun L1 and Venus-trailing surveys achieve similar levels of integral completeness for potentially hazardous asteroids larger than 140 m; placing the telescope in an interior orbit does not yield an improvement in discovery rates. This work serves as a necessary first step for the detailed planning of a next-generation NEA survey.« less

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.

Challenges in photon-starved space astronomy in a harsh radiation environment using CCDs

NASA Astrophysics Data System (ADS)

Hall, David J.; Bush, Nathan; Murray, Neil; Gow, Jason; Clarke, Andrew; Burgon, Ross; Holland, Andrew

2015-09-01

The Charge Coupled Device (CCD) has a long heritage for imaging and spectroscopy in many space astronomy missions. However, the harsh radiation environment experienced in orbit creates defects in the silicon that capture the signal being transferred through the CCD. This radiation damage has a detrimental impact on the detector performance and requires carefully planned mitigation strategies. The ESA Gaia mission uses 106 CCDs, now orbiting around the second Lagrange point as part of the largest focal-plane ever launched. Following readout, signal electrons will be affected by the traps generated in the devices from the radiation environment and this degradation will be corrected for using a charge distortion model. ESA's Euclid mission will contain a focal plane of 36 CCDs in the VIS instrument. Moving further forwards, the World Space Observatory (WSO) UV spectrographs and the WFIRST-AFTA coronagraph intend to look at very faint sources in which mitigating the impact of traps on the transfer of single electron signals will be of great interest. Following the development of novel experimental and analysis techniques, one is now able to study the impact of radiation on the detector to new levels of detail. Through a combination of TCAD simulations, defect studies and device testing, we are now probing the interaction of single electrons with individual radiation-induced traps to analyse the impact of radiation in photon-starved applications.

Closed Loop Software Control of the MIDEX Power System

NASA Technical Reports Server (NTRS)

Castell, Karen; Hernandez-Pellerano, Amri; Wismer, Margaret

1998-01-01

The Microwave Anisotropy Probe (MAP) is a follow-on to the Differential Microwave Radiometer (DMR) instrument on the Cosmic Background Explorer (COBE) spacecraft. The design and analysis of the MAP attitude control system (ACS) have been refined since work previously reported. The full spacecraft and instrument flexible model was developed in NASTRAN, and the resulting flexible modes were plotted and reduced with the Modal Significance Analysis Package (MSAP). The reduced-order model was used to perform the linear stability analysis for each control mode, the results of which are presented in this paper. Although MAP is going to a relatively disturbance-free Lissajous orbit around the Earth-Sun L2 Lagrange point, a detailed disturbance-torque analysis is required because there are only a small number of opportunities for momentum unloading each year. Environmental torques, including solar pressure at L2, and aerodynamic and gravity gradient during phasing-loop orbits, were calculated and simulated. A simple model of fuel slosh was derived to model its effect on the motion of the spacecraft. In addition, a thruster mode linear impulse controller was developed to meet the accuracy requirements of the phasing loop burns. A dynamic attitude error limiter was added to improve the performance of the ACS during large attitude slews. The result of this analysis is a stable ACS subsystem that meets all of the mission's requirements.

Stable low-altitude orbits around Ganymede considering a disturbing body in a circular orbit

NASA Astrophysics Data System (ADS)

Cardoso dos Santos, J.; Carvalho, J. P. S.; Vilhena de Moraes, R.

2014-10-01

Some missions are being planned to visit Ganymede like the Europa Jupiter System Mission that is a cooperation between NASA and ESA to insert the spacecraft JGO (Jupiter Ganymede Orbiter) into Ganymedes orbit. This comprehension of the dynamics of these orbits around this planetary satellite is essential for the success of this type of mission. Thus, this work aims to perform a search for low-altitude orbits around Ganymede. An emphasis is given in polar orbits and it can be useful in the planning of space missions to be conducted around, with respect to the stability of orbits of artificial satellites. The study considers orbits of artificial satellites around Ganymede under the influence of the third-body (Jupiter's gravitational attraction) and the polygenic perturbations like those due to non-uniform distribution of mass (J_2 and J_3) of the main body. A simplified dynamic model for these perturbations is used. The Lagrange planetary equations are used to describe the orbital motion of the artificial satellite. The equations of motion are developed in closed form to avoid expansions in eccentricity and inclination. The results show the argument of pericenter circulating. However, low-altitude (100 and 150 km) polar orbits are stable. Another orbital elements behaved variating with small amplitudes. Thus, such orbits are convenient to be applied to future space missions to Ganymede. Acknowledgments: FAPESP (processes n° 2011/05671-5, 2012/12539-9 and 2012/21023-6).

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.

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.

Maneuver simulations of flexible spacecraft by solving TPBVP

NASA Technical Reports Server (NTRS)

Bainum, Peter M.; Li, Feiyue

1991-01-01

The optimal control of large angle rapid maneuvers and vibrations of a Shuttle mast reflector system is considered. The nonlinear equations of motion are formulated by using Lagrange's formula, with the mast modeled as a continuous beam. The nonlinear terms in the equations come from the coupling between the angular velocities, the modal coordinates, and the modal rates. Pontryagin's Maximum Principle is applied to the slewing problem, to derive the necessary conditions for the optimal controls, which are bounded by given saturation levels. The resulting two point boundary value problem (TPBVP) is then solved by using the quasilinearization algorithm and the method of particular solutions. In the numerical simulations, the structural parameters and the control limits from the Spacecraft Control Lab Experiment (SCOLE) are used. In the 2-D case, only the motion in the plane of an Earth orbit or the single axis slewing motion is discussed. In the 3-D slewing, the mast is modeled as a continuous beam subjected to 3-D deformations. The numerical results for both the linearized system and the nonlinear system are presented to compare the differences in their time response.

NASA's Space Launch System: A Flagship for Exploration Beyond Earth's Orbit

NASA Technical Reports Server (NTRS)

May, Todd A.; Creech, Stephen D.

2012-01-01

The National Aeronautics and Space Administration s (NASA s) Space Launch System (SLS) Program, managed at the Marshall Space Flight Center, is making measurable progress toward delivering a new capability for human and scientific exploration. To arrive at the current plan, government and industry experts carefully analyzed hundreds of architecture options and selected the one clear solution to stringent requirements for safety, affordability, and sustainability over the decades that the rocket will be in operation. Slated for its maiden voyage in 2017, the SLS will provide a platform for further cooperation in space based on the International Space Station model. This briefing will focus on specific progress that has been made by the SLS team in its first year, as well as provide a framework for evolving the vehicle for far-reaching missions to destinations such as near-Earth asteroids, Lagrange Points, and Mars. As this briefing will show, the SLS will serve as an infrastructure asset for robotic and human scouts of all nations by harnessing business and technological innovations to deliver sustainable solutions for space exploration.

Cloud Detection with the Earth Polychromatic Imaging Camera (EPIC)

NASA Technical Reports Server (NTRS)

Meyer, Kerry; Marshak, Alexander; Lyapustin, Alexei; Torres, Omar; Wang, Yugie

2011-01-01

The Earth Polychromatic Imaging Camera (EPIC) on board the Deep Space Climate Observatory (DSCOVR) would provide a unique opportunity for Earth and atmospheric research due not only to its Lagrange point sun-synchronous orbit, but also to the potential for synergistic use of spectral channels in both the UV and visible spectrum. As a prerequisite for most applications, the ability to detect the presence of clouds in a given field of view, known as cloud masking, is of utmost importance. It serves to determine both the potential for cloud contamination in clear-sky applications (e.g., land surface products and aerosol retrievals) and clear-sky contamination in cloud applications (e.g., cloud height and property retrievals). To this end, a preliminary cloud mask algorithm has been developed for EPIC that applies thresholds to reflected UV and visible radiances, as well as to reflected radiance ratios. This algorithm has been tested with simulated EPIC radiances over both land and ocean scenes, with satisfactory results. These test results, as well as algorithm sensitivity to potential instrument uncertainties, will be presented.

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.

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.

Space Technology 7 Disturbance Reduction System - precision control flight Validation

NASA Technical Reports Server (NTRS)

Carmain, Andrew J.; Dunn, Charles; Folkner, William; Hruby, Vlad; Spence, Doug; O'Donnell, James; Markley, Landis; Maghami, Peiman; Hsu, Oscar; Demmons, N.;

LISA Pathfinder: First steps to observing gravitational waves from space

NASA Astrophysics Data System (ADS)

McNamara, Paul; LISA Pathfinder Collaboration

2017-01-01

With the first direct detection of gravitational waves a little over a year ago, the gravitational window to the Universe has been opened. The gravitational wave spectrum spans many orders of magnitude in frequency, with several of the most interesting astronomical sources emitting gravitational waves at frequencies only observable from space The European Space Agency (ESA) has been active in the field of space-borne gravitational wave detection for many years, and in 2013 selected the Gravitational Universe as the science theme for the third large class mission in the Cosmic Vision science programme. In addition, ESA took the step of developing the LISA Pathfinder mission to demonstrate the critical technologies required for a future mission. The goal of the LISA Pathfinder mission is to place a test body in free fall such that any external forces (acceleration) are reduced to levels lower than those expected from the passage of a gravitational wave LISA Pathfinder was launched on the 3rd December 2015 from the European Spaceport in Kourou, French Guiana. After a series of 6 apogee raising manoeuvres, the satellite left earth orbit, and travelled to its final science orbit around the first Sun-Earth Lagrange point (L1). Following a relatively short commissioning phase, science operations began on 1st March 2016. In the following 3 months over 100 experiments and over 1500hours of noise measurements have been performed, demonstrating that the observation of gravitational waves from space can be realised.

MAP stability, design, and analysis

NASA Technical Reports Server (NTRS)

Ericsson-Jackson, A. J.; Andrews, S. F.; O'Donnell, J. R., Jr.; Markley, F. L.

1998-01-01

The Microwave Anisotropy Probe (MAP) is a follow-on to the Differential Microwave Radiometer (DMR) instrument on the Cosmic Background Explorer (COBE) spacecraft. The design and analysis of the MAP attitude control system (ACS) have been refined since work previously reported. The full spacecraft and instrument flexible model was developed in NASTRAN, and the resulting flexible modes were plotted and reduced with the Modal Significance Analysis Package (MSAP). The reduced-order model was used to perform the linear stability analysis for each control mode, the results of which are presented in this paper. Although MAP is going to a relatively disturbance-free Lissajous orbit around the Earth-Sun L(2) Lagrange point, a detailed disturbance-torque analysis is required because there are only a small number of opportunities for momentum unloading each year. Environmental torques, including solar pressure at L(2), aerodynamic and gravity gradient during phasing-loop orbits, were calculated and simulated. Thruster plume impingement torques that could affect the performance of the thruster modes were estimated and simulated, and a simple model of fuel slosh was derived to model its effect on the motion of the spacecraft. In addition, a thruster mode linear impulse controller was developed to meet the accuracy requirements of the phasing loop burns. A dynamic attitude error limiter was added to improve the performance of the ACS during large attitude slews. The result of this analysis is a stable ACS subsystem that meets all of the mission's requirements.

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.

Remote sensing optical instrumentation for enhanced space weather monitoring from the L1 and L5 Lagrange points

NASA Astrophysics Data System (ADS)

Kraft, S.; Puschmann, K. G.; Luntama, J. P.

2017-09-01

As part of the Space Situational Awareness Programme (SSA), ESA has initiated the assessment of two missions currently foreseen to be implemented to enable enhanced space weather monitoring. These missions utilize the positioning of satellites at the Lagrangian L1 and L5 points. These Phase 0 or Pre-Phase A mission studies are about to be completed and will thereby have soon passed the Mission Definition Review. Phase A studies are planned to start in 2017. The space weather monitoring system currently considers four remote sensing optical instruments and several in-situ instruments to analyse the Sun and the solar wind conditions, in order to provide early warnings of increased solar activity and to identify and mitigate potential threats to society and ground, airborne and space based infrastructure. The suggested optical instruments take heritage from ESA and NASA science missions like SOHO, STEREO and Solar Orbiter, but the instruments are foreseen to be optimized for operational space weather monitoring purposes with high reliability and robustness demands. The instruments are required to provide high quality measurements particularly during severe space weather events. The program intends to utilize the results of the on-going ESA instrument prototyping and technology development activities, and to initiate pre-developments of the operational space weather instruments to ensure the required maturity before the mission implementation.

DSCOVR/EPIC observations of SO2 reveal dynamics of young volcanic eruption clouds

NASA Astrophysics Data System (ADS)

Carn, S. A.; Krotkov, N. A.; Taylor, S.; Fisher, B. L.; Li, C.; Bhartia, P. K.; Prata, F. J.

2017-12-01

Volcanic emissions of sulfur dioxide (SO2) and ash have been measured by ultraviolet (UV) and infrared (IR) sensors on US and European polar-orbiting satellites since the late 1970s. Although successful, the main limitation of these observations from low Earth orbit (LEO) is poor temporal resolution (once per day at low latitudes). Furthermore, most currently operational geostationary satellites cannot detect SO2, a key tracer of volcanic plumes, limiting our ability to elucidate processes in fresh, rapidly evolving volcanic eruption clouds. In 2015, the launch of the Earth Polychromatic Imaging Camera (EPIC) aboard the Deep Space Climate Observatory (DSCOVR) provided the first opportunity to observe volcanic clouds from the L1 Lagrange point. EPIC is a 10-band spectroradiometer spanning UV to near-IR wavelengths with two UV channels sensitive to SO2, and a ground resolution of 25 km. The unique L1 vantage point provides continuous observations of the sunlit Earth disk, from sunrise to sunset, offering multiple daily observations of volcanic SO2 and ash clouds in the EPIC field of view. When coupled with complementary retrievals from polar-orbiting UV and IR sensors such as the Ozone Monitoring Instrument (OMI), the Ozone Mapping and Profiler Suite (OMPS), and the Atmospheric Infrared Sounder (AIRS), we demonstrate how the increased observation frequency afforded by DSCOVR/EPIC permits more timely volcanic eruption detection and novel analyses of the temporal evolution of volcanic clouds. Although EPIC has detected several mid- to high-latitude volcanic eruptions since launch, we focus on recent eruptions of Bogoslof volcano (Aleutian Islands, AK, USA). A series of EPIC exposures from May 28-29, 2017, uniquely captures the evolution of SO2 mass in a young Bogoslof eruption cloud, showing separation of SO2- and ice-rich regions of the cloud. We show how analyses of these sequences of EPIC SO2 data can elucidate poorly understood processes in transient eruption clouds, such as the relative roles of H2S oxidation and ice scavenging in modifying volcanic SO2 emissions. Detection of these relatively small events also proves EPIC's ability to provide timely detection of volcanic clouds in the upper troposphere and lower stratosphere.

Hybrid threshold adaptable quantum secret sharing scheme with reverse Huffman-Fibonacci-tree coding.

PubMed

Lai, Hong; Zhang, Jun; Luo, Ming-Xing; Pan, Lei; Pieprzyk, Josef; Xiao, Fuyuan; Orgun, Mehmet A

2016-08-12

With prevalent attacks in communication, sharing a secret between communicating parties is an ongoing challenge. Moreover, it is important to integrate quantum solutions with classical secret sharing schemes with low computational cost for the real world use. This paper proposes a novel hybrid threshold adaptable quantum secret sharing scheme, using an m-bonacci orbital angular momentum (OAM) pump, Lagrange interpolation polynomials, and reverse Huffman-Fibonacci-tree coding. To be exact, we employ entangled states prepared by m-bonacci sequences to detect eavesdropping. Meanwhile, we encode m-bonacci sequences in Lagrange interpolation polynomials to generate the shares of a secret with reverse Huffman-Fibonacci-tree coding. The advantages of the proposed scheme is that it can detect eavesdropping without joint quantum operations, and permits secret sharing for an arbitrary but no less than threshold-value number of classical participants with much lower bandwidth. Also, in comparison with existing quantum secret sharing schemes, it still works when there are dynamic changes, such as the unavailability of some quantum channel, the arrival of new participants and the departure of participants. Finally, we provide security analysis of the new hybrid quantum secret sharing scheme and discuss its useful features for modern applications.

Hybrid threshold adaptable quantum secret sharing scheme with reverse Huffman-Fibonacci-tree coding

PubMed Central

Lai, Hong; Zhang, Jun; Luo, Ming-Xing; Pan, Lei; Pieprzyk, Josef; Xiao, Fuyuan; Orgun, Mehmet A.

2016-01-01

With prevalent attacks in communication, sharing a secret between communicating parties is an ongoing challenge. Moreover, it is important to integrate quantum solutions with classical secret sharing schemes with low computational cost for the real world use. This paper proposes a novel hybrid threshold adaptable quantum secret sharing scheme, using an m-bonacci orbital angular momentum (OAM) pump, Lagrange interpolation polynomials, and reverse Huffman-Fibonacci-tree coding. To be exact, we employ entangled states prepared by m-bonacci sequences to detect eavesdropping. Meanwhile, we encode m-bonacci sequences in Lagrange interpolation polynomials to generate the shares of a secret with reverse Huffman-Fibonacci-tree coding. The advantages of the proposed scheme is that it can detect eavesdropping without joint quantum operations, and permits secret sharing for an arbitrary but no less than threshold-value number of classical participants with much lower bandwidth. Also, in comparison with existing quantum secret sharing schemes, it still works when there are dynamic changes, such as the unavailability of some quantum channel, the arrival of new participants and the departure of participants. Finally, we provide security analysis of the new hybrid quantum secret sharing scheme and discuss its useful features for modern applications. PMID:27515908

Computational Methods for Frictional Contact With Applications to the Space Shuttle Orbiter Nose-Gear Tire

NASA Technical Reports Server (NTRS)

Tanner, John A.

1996-01-01

A computational procedure is presented for the solution of frictional contact problems for aircraft tires. A Space Shuttle nose-gear tire is modeled using a two-dimensional laminated anisotropic shell theory which includes the effects of variations in material and geometric parameters, transverse-shear deformation, and geometric nonlinearities. Contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the stress resultants, the generalized displacements, and the Lagrange multipliers associated with both contact and friction conditions. The contact-friction algorithm is based on a modified Coulomb friction law. A modified two-field, mixed-variational principle is used to obtain elemental arrays. This modification consists of augmenting the functional of that principle by two terms: the Lagrange multiplier vector associated with normal and tangential node contact-load intensities and a regularization term that is quadratic in the Lagrange multiplier vector. These capabilities and computational features are incorporated into an in-house computer code. Experimental measurements were taken to define the response of the Space Shuttle nose-gear tire to inflation-pressure loads and to inflation-pressure loads combined with normal static loads against a rigid flat plate. These experimental results describe the meridional growth of the tire cross section caused by inflation loading, the static load-deflection characteristics of the tire, the geometry of the tire footprint under static loading conditions, and the normal and tangential load-intensity distributions in the tire footprint for the various static vertical loading conditions. Numerical results were obtained for the Space Shuttle nose-gear tire subjected to inflation pressure loads and combined inflation pressure and contact loads against a rigid flat plate. The experimental measurements and the numerical results are compared.

Computational methods for frictional contact with applications to the Space Shuttle orbiter nose-gear tire: Comparisons of experimental measurements and analytical predictions

NASA Technical Reports Server (NTRS)

Tanner, John A.

1996-01-01

A computational procedure is presented for the solution of frictional contact problems for aircraft tires. A Space Shuttle nose-gear tire is modeled using a two-dimensional laminated anisotropic shell theory which includes the effects of variations in material and geometric parameters, transverse-shear deformation, and geometric nonlinearities. Contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the stress resultants, the generalized displacements, and the Lagrange multipliers associated with both contact and friction conditions. The contact-friction algorithm is based on a modified Coulomb friction law. A modified two-field, mixed-variational principle is used to obtain elemental arrays. This modification consists of augmenting the functional of that principle by two terms: the Lagrange multiplier vector associated with normal and tangential node contact-load intensities and a regularization term that is quadratic in the Lagrange multiplier vector. These capabilities and computational features are incorporated into an in-house computer code. Experimental measurements were taken to define the response of the Space Shuttle nose-gear tire to inflation-pressure loads and to inflation-pressure loads combined with normal static loads against a rigid flat plate. These experimental results describe the meridional growth of the tire cross section caused by inflation loading, the static load-deflection characteristics of the tire, the geometry of the tire footprint under static loading conditions, and the normal and tangential load-intensity distributions in the tire footprint for the various static vertical-loading conditions. Numerical results were obtained for the Space Shuttle nose-gear tire subjected to inflation pressure loads and combined inflation pressure and contact loads against a rigid flat plate. The experimental measurements and the numerical results are compared.

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.

Effects of structural flexibility of wings in flapping flight of butterfly.

PubMed

Senda, Kei; Obara, Takuya; Kitamura, Masahiko; Yokoyama, Naoto; Hirai, Norio; Iima, Makoto

2012-06-01

The objective of this paper is to clarify the effects of structural flexibility of wings of a butterfly in flapping flight. For this purpose, a dynamics model of a butterfly is derived by Lagrange's method, where the butterfly is considered as a rigid multi-body system. The panel method is employed to simulate the flow field and the aerodynamic forces acting on the wings. The mathematical model is validated by the agreement of the numerical result with the experimentally measured data. Then, periodic orbits of flapping-of-wings flights are parametrically searched in order to fly the butterfly models. Almost periodic orbits are found, but they are unstable. Deformation of the wings is modeled in two ways. One is bending and its effect on the aerodynamic forces is discussed. The other is passive wing torsion caused by structural flexibility. Numerical simulations demonstrate that flexible torsion reduces the flight instability.

One Year on Earth – Seen From 1 Million Miles

NASA Image and Video Library

2017-12-08

On July 20, 2015, NASA released to the world the first image of the sunlit side of Earth captured by the space agency's EPIC camera on NOAA's DSCOVR satellite. The camera has now recorded a full year of life on Earth from its orbit at Lagrange point 1, approximately 1 million miles from Earth, where it is balanced between the gravity of our home planet and the sun. EPIC takes a new picture every two hours, revealing how the planet would look to human eyes, capturing the ever-changing motion of clouds and weather systems and the fixed features of Earth such as deserts, forests and the distinct blues of different seas. EPIC will allow scientists to monitor ozone and aerosol levels in Earth’s atmosphere, cloud height, vegetation properties and the ultraviolet reflectivity of Earth. The primary objective of DSCOVR, a partnership between NASA, the National Oceanic and Atmospheric Administration (NOAA) and the U.S. Air Force, is to maintain the nation’s real-time solar wind monitoring capabilities, which are critical to the accuracy and lead time of space weather alerts and forecasts from NOAA. For more information about DSCOVR, visit: go.nasa.gov/29Pqm15

The Near-Earth Object Camera: A Next-Generation Minor Planet Survey

NASA Astrophysics Data System (ADS)

Mainzer, Amy K.; Wright, Edward L.; Bauer, James; Grav, Tommy; Cutri, Roc M.; Masiero, Joseph; Nugent, Carolyn R.

2015-11-01

The Near-Earth Object Camera (NEOCam) is a next-generation asteroid and comet survey designed to discover, characterize, and track large numbers of minor planets using a 50 cm infrared telescope located at the Sun-Earth L1 Lagrange point. Proposed to NASA's Discovery program, NEOCam is designed to carry out a comprehensive inventory of the small bodies in the inner regions of our solar system. It address three themes: 1) quantify the potential hazard that near-Earth objects may pose to Earth; 2) study the origins and evolution of our solar system as revealed by its small body populations; and 3) identify the best destinations for future robotic and human exploration. With a dual channel infrared imager that observes at 4-5 and 6-10 micron bands simultaneously through the use of a beamsplitter, NEOCam enables measurements of asteroid diameters and thermal inertia. NEOCam complements existing and planned visible light surveys in terms of orbital element phase space and wavelengths, since albedos can be determined for objects with both visible and infrared flux measurements. NEOCam was awarded technology development funding in 2011 to mature the necessary megapixel infrared detectors.

James Webb Space Telescope: Large Deployable Cryogenic Telescope in Space

NASA Technical Reports Server (NTRS)

Lightsey, Paul A.; Atkinson, Charles; Clampin, Mark; Feinberg, Lee D.

2012-01-01

The James Webb Space Telescope (JWST) is an infrared space telescope designed to explore four major science themes: first light and reionization, the assembly of galaxies, the birth of stars and protoplanetary systems, and planetary systems and origins of life. JWST is a segmented architecture telescope with an aperture of 6.6 m. It will operate at cryogenic temperature (40 K), achieved via passive cooling, in an orbit about the Earth-Sun second Lagrange point (L2). Passive cooling is facilitated by means of a large sunshield that provides thermal isolation and protection from direct illumination from the Sun. The large size of the telescope and spacecraft systems require that they are stowed for launch in a configuration that fits the Ariane 5 fairing, and then deployed after launch. Routine wavefront sensing and control measurements are used to achieve phasing of the segmented primary mirror and initial alignment of the telescope. A suite of instruments will provide the capability to observe over a spectral range from 0.6- to 27-micron wavelengths with imaging and spectroscopic configurations. An overview is presented of the architecture and selected optical design features of JWST are described

The Near-Earth Object Camera

NASA Astrophysics Data System (ADS)

Mainzer, Amy K.; NEOCam Science Team

2017-10-01

The Near-Earth Object Camera (NEOCam) is a NASA mission in formulation designed to find, track, and provide basic physical characterization of asteroids and comets that make close approaches to Earth. Its goal is to reduce the risk of impacts from undetected near-Earth objects (NEOs) capable of causing global and regional disasters. NEOCam consists of a 50 cm telescope operating at two channels dominated by NEO thermal emission, 4.2-5.0um and 6-10um, in order to better constrain the objects' temperatures and diameters. Orbiting the Sun-Earth L1 Lagrange point, the mission would find hundreds of thousands of NEOs and would make significant progress toward the Congressional objective of discovering more than 90% of NEOs larger than 140 m during its five-year lifetime. The mission uses novel 2048x2048 HgCdTe detectors that extend the wavelength cutoff beyond 10um at an operating temperature of 40K (Dorn et al. 2016). Both the optical system and the detectors are cooled passively using radiators and thermal shields to enable long mission life and to avoid the complexity of cryocoolers or cryogens. NEOCam is currently in an extended Phase A.

Estimation of Canopy Sunlit Fraction of Leaf Area from Ground-Based Measurements

NASA Astrophysics Data System (ADS)

Yang, B.; Knyazikhin, Y.; Yan, K.; Chen, C.; Park, T.; CHOI, S.; Mottus, M.; Rautiainen, M.; Stenberg, P.; Myneni, R.; Yan, L.

2015-12-01

The sunlit fraction of leaf area (SFLA) defined as the fraction of the total hemisurface leaf area illuminated by the direct solar beam is a key structural variable in many global models of climate, hydrology, biogeochemistry and ecology. SFLAI is expected to be a standard product from the Earth Polychromatic Imaging Camera (EPIC) on board the joint NOAA, NASA and US Air Force Deep Space Climate Observatory (DSCOVR) mission, which was successfully launched from Cape Canaveral, Florida on February 11, 2015. The DSCOVR EPIC sensor orbiting the Sun-Earth Lagrange L1 point provides multispectral measurements of the radiation reflected by Earth in retro-illumination directions. This poster discusses a methodology for estimating the SFLA using LAI-2000 Canopy Analyzer, which is expected to underlie the strategy for validation of the DSCOVR EPIC land surface products. LAI-2000 data collected over 18 coniferous and broadleaf sites in Hyytiälä, Central Finland, were used to estimate the SFLA. Field data on canopy geometry were used to simulate selected sites. Their SFLAI was calculated using a Monte Carlo (MC) technique. LAI-2000 estimates of SFLA showed a very good agreement with MC results, suggesting validity of the proposed approach.

Science with the James Webb Space Telescope

NASA Technical Reports Server (NTRS)

Gardner, Jonathan P.

2012-01-01

The James Webb Space Telescope is the scientific successor to the Hubble and Spitzer Space Telescopes. It will be a large (6.6m) cold (50K) telescope launched into orbit around the second Earth-Sun lagrange point. It is a partnership of NASA with the European and Canadian Space Agencies. The science goals for JWST include the formation of the first stars and galaxies in the early universe; the chemical, morphological and dynamical buildup of galaxies and the formation of stars and planetary systems. Recently, the goals have expanded to include studies of dark energy, dark matter, active galactic nuclei, exoplanets and Solar System objects. Webb will have four instruments: The Near-Infrared Camera, the Near-Infrared multi-object Spectrograph, and the Near-Infrared Imager and Slitiess Spectrograph will cover the wavelength range 0.6 to 5 microns, while the Mid-Infrared Instrument will do both imaging and spectroscopy from 5 to 28.5 microns. The observatory is confirmed for launch in 2018; the design is complete and it is in its construction phase. Recent progress includes the completion of the mirrors, the delivery of the first flight instrument(s) and the start of the integration and test phase.

The James Webb Space Telescope

NASA Technical Reports Server (NTRS)

Gardner, Jonathan P.

2012-01-01

The James Webb Space Telescope is the scientific successor to the Hubble and Spitzer Space Telescopes. It will be a large (6.6m) cold (SDK) telescope launched into orbit around the second Earth-Sun Lagrange point. It is a partnership of NASA with the European and Canadian Space Agencies. The science goals for JWST include the formation of the first stars and galaxies in the early universe; the chemical, morphological and dynamical buildup of galaxies and the formation of stars and planetary systems. Recently, the goals have expanded to include studies of dark energy, dark matter, active galactic nuclei, exoplanets and Solar System objects. Webb will have four instruments: The Near-Infrared Camera, the Near-Infrared multi-object Spectrograph, and the Near-Infrared Imager and Slitless Spectrograph will cover the wavelength range 0.6 to S microns, while the Mid-Infrared Instrument will do both imaging and spectroscopy from 5 to 28.5 microns. The observatory is confirmed for launch in 2018; the design is complete and it is in its construction phase. Recent progress includes the completion of the mirrors, the delivery of the first flight instruments and the start of the integration and test phase.

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.

A Flexible Path for Human and Robotic Space Exploration

NASA Technical Reports Server (NTRS)

Korsmeyer, David J.; Landis, Robert; Merrill, Raymond Gabriel; Mazanek, Daniel D.; Falck, Robert D.; Adams, Robert B.

2010-01-01

During the summer of 2009, a flexible path scenario for human and robotic space exploration was developed that enables frequent, measured, and publicly notable human exploration of space beyond low-Earth orbit (LEO). The formulation of this scenario was in support of the Exploration Beyond LEO subcommittee of the Review of U.S. Human Space Flight Plans Committee that was commissioned by President Obama. Exploration mission sequences that allow humans to visit a wide number of inner solar system destinations were investigated. The scope of destinations included the Earth-Moon and Earth-Sun Lagrange points, near-Earth objects (NEOs), the Moon, and Mars and its moons. The missions examined assumed the use of Constellation Program elements along with existing launch vehicles and proposed augmentations. Additionally, robotic missions were envisioned as complements to human exploration through precursor missions, as crew emplaced scientific investigations, and as sample gathering assistants to the human crews. The focus of the flexible path approach was to gain ever-increasing operational experience through human exploration missions ranging from a few weeks to several years in duration, beginning in deep space beyond LEO and evolving to landings on the Moon and eventually Mars.

'EPIC' View of Africa and Europe from a Million Miles Away

NASA Image and Video Library

2015-07-29

Africa is front and center in this image of Earth taken by a NASA camera on the Deep Space Climate Observatory (DSCOVR) satellite. The image, taken July 6 from a vantage point one million miles from Earth, was one of the first taken by NASA’s Earth Polychromatic Imaging Camera (EPIC). Central Europe is toward the top of the image with the Sahara Desert to the south, showing the Nile River flowing to the Mediterranean Sea through Egypt. The photographic-quality color image was generated by combining three separate images of the entire Earth taken a few minutes apart. The camera takes a series of 10 images using different narrowband filters -- from ultraviolet to near infrared -- to produce a variety of science products. The red, green and blue channel images are used in these Earth images. The DSCOVR mission is a partnership between NASA, the National Oceanic and Atmospheric Administration (NOAA) and the U.S. Air Force, with the primary objective to maintain the nation’s real-time solar wind monitoring capabilities, which are critical to the accuracy and lead time of space weather alerts and forecasts from NOAA. DSCOVR was launched in February to its planned orbit at the first Lagrange point or L1, about one million miles from Earth toward the sun. It’s from that unique vantage point that the EPIC instrument is acquiring images of the entire sunlit face of Earth. Data from EPIC will be used to measure ozone and aerosol levels in Earth’s atmosphere, cloud height, vegetation properties and a variety of other features. Image Credit: NASA

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.

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.

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.

Dynamical Evolution of Planetesimals in the Outer Solar System. II. The Saturn/Uranus and Uranus/Neptune Zones

NASA Astrophysics Data System (ADS)

Grazier, Kevin R.; Newman, William I.; Varadi, Ferenc; Kaula, William M.; Hyman, James M.

1999-08-01

We report on numerical simulations exploring the dynamical stability of planetesimals in the gaps between the outer Solar System planets. We search for stable niches in the Saturn/Uranus and Uranus/Neptune zones by employing 10,000 massless particles-many more than previous studies in these two zones-using high-order optimized multistep integration schemes coupled with roundoff error minimizing methods. An additional feature of this study, differing from its predecessors, is the fact that our initial distributions contain particles on orbits which are both inclined and noncircular. These initial distributions were also Gaussian distributed such that the Gaussian peaks were at the midpoint between the neighboring perturbers. The simulations showed an initial transient phase where the bulk of the primordial planetesimal swarm was removed from the Solar System within 105 years. This is about 10 times longer than we observed in our previous Jupiter/Saturn studies. Next, there was a gravitational relaxation phase where the particles underwent a random walk in momentum space and were exponentially eliminated by random encounters with the planets. Unlike our previous Jupiter/Saturn simulation, the particles did not fully relax into a third Lagrangian niche phase where long-lived particles are at Lagrange points or stable niches. This is either because the Lagrangian niche phase never occurs or because these simulations did not have enough particles for this third phase to manifest. In these simulations, there was a general trend for the particles to migrate outward and eventually to be cleared out by the outermost planet in the zone. We confirmed that particles with higher eccentricities had shorter lifetimes and that the resonances between the jovian planets "pumped up" the eccentricities of the planetesimals with low-inclination orbits more than those with higher inclinations. We estimated the expected lifetime of particles using kinetic theory and even though the time scale of the Uranus/Neptune simulation was 380 times longer than our previous Jupiter/Saturn simulation, the planetesimals in the Uranus/Neptune zone were cleared out more quickly than those in the Saturn/Uranus zone because of the positions of resonances with the jovian planets. These resonances had an even greater effect than random gravitational stirring in the winnowing process and confirm that all the jovian planets are necessary in long simulations. Even though we observed several long-lived zones near 12.5, 14.4, 16, 24.5, and 26 AU, only two particles remained at the end of the 109-year integration: one near the 2 : 3 Saturn resonance, and the other near the Neptune 1 : 1 resonance. This suggests that niches for planetesimal material in the jovian planets are rare and may exist either only in extremely narrow bands or in the neighborhoods of the triangular Lagrange points of the outer planets.

Multiple positive normalized solutions for nonlinear Schrödinger systems

NASA Astrophysics Data System (ADS)

Gou, Tianxiang; Jeanjean, Louis

2018-05-01

We consider the existence of multiple positive solutions to the nonlinear Schrödinger systems set on , under the constraint Here are prescribed, , and the frequencies are unknown and will appear as Lagrange multipliers. Two cases are studied, the first when , the second when In both cases, assuming that is sufficiently small, we prove the existence of two positive solutions. The first one is a local minimizer for which we establish the compactness of the minimizing sequences and also discuss the orbital stability of the associated standing waves. The second solution is obtained through a constrained mountain pass and a constrained linking respectively.

Binary stellar mergers with marginally bound ejecta: excretion discs, inflated envelopes, outflows, and their luminous transients

NASA Astrophysics Data System (ADS)

Pejcha, Ondřej; Metzger, Brian D.; Tomida, Kengo

2016-09-01

We study mass-loss from the outer Lagrange point (L2) in binary stellar mergers and their luminous transients by means of radiative hydrodynamical simulations. Previously, we showed that for binary mass ratios 0.06 ≲ q ≲ 0.8, synchronous L2 mass-loss results in a radiatively inefficient, dust-forming unbound equatorial outflow. A similar outflow exists irrespective of q if the ratio of the sound speed to the orbital speed at the injection point is sufficiently large, ε ≡ cT/vorb ≳ 0.15. By contrast, for cold L2 mass-loss (ε ≲ 0.15) from binaries with q ≲ 0.06 or q ≳ 0.8, the equatorial outflow instead remains marginally bound and falls back to the binary over tens to hundreds of binary orbits, where it experiences additional tidal torquing and shocking. As the bound gas becomes virialized with the binary, the luminosity of the system increases slowly at approximately constant photosphere radius, causing the temperature to rise. Subsequent evolution depends on the efficiency of radiative cooling. If the bound atmosphere is able to cool efficiently, as quantified by radiative diffusion time being shorter than the advection time (tdiff/tadv ≪ 1), then the virialized gas collapses to an excretion disc, while for tdiff/tadv ≳ 1 an isotropic wind is formed. Between these two extremes, an inflated envelope transports the heat generated near the binary to the surface by meridional flows. In all cases, the radiated luminosity reaches a fraction ˜10-2 to 10-1 of dot{M}v_orb^2/2, where dot{M} is the mass outflow rate. We discuss the implications of our results for transients in the luminosity gap between classical novae and supernovae, such as V1309 Sco and V838 Mon.

International Space Station Centrifuge Rotor Models A Comparison of the Euler-Lagrange and the Bond Graph Modeling Approach

NASA Technical Reports Server (NTRS)

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

2006-01-01

The assembly and operation of the International Space Station (ISS) require extensive testing and engineering analysis to verify that the Space Station system of systems would work together without any adverse interactions. Since the dynamic behavior of an entire Space Station cannot be tested on earth, math models of the Space Station structures and mechanical systems have to be built and integrated in computer simulations and analysis tools to analyze and predict what will happen in space. The ISS Centrifuge Rotor (CR) is one of many mechanical systems that need to be modeled and analyzed to verify the ISS integrated system performance on-orbit. This study investigates using Bond Graph modeling techniques as quick and simplified ways to generate models of the ISS Centrifuge Rotor. This paper outlines the steps used to generate simple and more complex models of the CR using Bond Graph Computer Aided Modeling Program with Graphical Input (CAMP-G). Comparisons of the Bond Graph CR models with those derived from Euler-Lagrange equations in MATLAB and those developed using multibody dynamic simulation at the National Aeronautics and Space Administration (NASA) Johnson Space Center (JSC) are presented to demonstrate the usefulness of the Bond Graph modeling approach for aeronautics and space applications.

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

Stability of orbits around planetary satellites considering a disturbing body in an elliptical orbit: Applications to Europa and Ganymede

NASA Astrophysics Data System (ADS)

Cardoso dos Santos, Josué; Carvalho, Jean Paulo; Vilhena de Moraes, Rodolpho

Europa and Ganymede are two of the four Jupiter’s moons which compose the Galilean satellite. These ones are planetary satellites of greater interest at the present moment among the scientific community. There are some missions being planned to visit them and and the Jovian system. One of them is the cooperation between NASA and ESA for the Europa Jupiter System Mission (EJSM). In this mission are planned the insertion of the spacecrafts JEO (Jupiter Europa Orbiter) and JGO (Jupiter Ganymede Orbiter) into Europa and Ganymede’s orbit. Thus, there is a great necessity for having a better comprehension of the dynamics of the orbits around this planetary satellite. This comprehension is essential for the success of this type of mission. In this context, this work aims to perform a search for low-altitude orbits around these planetary satellites. An emphasis is given in polar orbits. These orbits can be useful in the planning of aerospace activities to be conducted around this planetary satellite, with respect to the stability of orbits of artificial satellites. The study considers orbits of an artificial satellite around Europa and Ganymede under the influence of the third-body perturbation (the gravitational attraction of Jupiter) and the polygenic perturbations. These last ones occur due to forces such as the non-uniform distribution of mass (J2 and J3) of the main (central) body. A simplified dynamic model for polygenic perturbations is used. A new model for the third-body disturbance is presented considering it in an elliptical orbit. The Lagrange planetary equations, which compose a system of nonlinear differential equations, are used to describe the orbital motion of the artificial satellite around Ganymede. The equations showed here are developed in closed form to avoid expansions in inclination and eccentricity.

Trojan Tour and Rendezvous (TTR): A New Frontiers Mission to Conduct the First Detailed Reconnaissance of the Jupiter Trojan Asteroids

NASA Astrophysics Data System (ADS)

Bell, James F.; Olkin, Cathy; Castillo-Rogez, Julie

2015-11-01

Among the most potentially diagnostic but least explored populations of small bodies are the Jupiter Trojan asteroids, which orbit at ~5 AU in the L4 and L5 Lagrange points of Jupiter. The Trojans provide a unique perspective on solar system history, because their locations and physical, compositional, and mineralogic properties preserve evidence for important gravitational interactions among the giant planets. The locations and orbital properties of more than 6200 Jupiter Trojans are now known, but that is likely only a small fraction of a population of up to ~1e6 Trojans >1 km in size. The Trojans are hypothesized to be either former KBOs scattered into the inner solar system by early giant planet migration and then trapped in L4 and L5, or bodies formed near 5 AU in a more quiescent early solar system.Important Planetary Decadal Survey questions that can be addressed by studying the Trojans include: (a) How did the giant planets and their satellite systems accrete, and is there evidence that they migrated to new orbital positions? (b) What is the relationship between large and small KBOs? Is the small population derived by impact disruption of the large one? (c) What kinds of surface evolution, radiation chemistry, and surface-atmosphere interactions occur on distant icy primitive bodies? And (d) What are the sources of asteroid groups (Trojans and Centaurs) that remain to be explored by spacecraft?Here we describe the Trojan Tour and Rendezvous (TTR) New Frontiers mission concept, which is designed to answer these Decadal questions and to test hypotheses for early giant planet migration and solar system evolution. Via close flybys of many of these objects, and orbital characterization of at least one large Trojan, TTR will enable the initial up-close exploration of this population. Our primary mission goals are to characterize the overall surface geology, geochemistry and mineralogy of these worlds; to characterize their internal structure and dynamical properties; to investigate the nature, sources and history of activity on these bodies; and to explore the diversity of the broader Trojan asteroid population.

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.

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.

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.

Breaking the current density threshold in spin-orbit-torque magnetic random access memory

NASA Astrophysics Data System (ADS)

Zhang, Yin; Yuan, H. Y.; Wang, X. S.; Wang, X. R.

2018-04-01

Spin-orbit-torque magnetic random access memory (SOT-MRAM) is a promising technology for the next generation of data storage devices. The main bottleneck of this technology is the high reversal current density threshold. This outstanding problem is now solved by a new strategy in which the magnitude of the driven current density is fixed while the current direction varies with time. The theoretical limit of minimal reversal current density is only a fraction (the Gilbert damping coefficient) of the threshold current density of the conventional strategy. The Euler-Lagrange equation for the fastest magnetization reversal path and the optimal current pulse is derived for an arbitrary magnetic cell and arbitrary spin-orbit torque. The theoretical limit of minimal reversal current density and current density for a GHz switching rate of the new reversal strategy for CoFeB/Ta SOT-MRAMs are, respectively, of the order of 105 A/cm 2 and 106 A/cm 2 far below 107 A/cm 2 and 108 A/cm 2 in the conventional strategy. Furthermore, no external magnetic field is needed for a deterministic reversal in the new strategy.

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.

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.

SOHO, an early start, a long lifetime

NASA Astrophysics Data System (ADS)

1996-01-01

SOHO currently cruises through space towards its station near the so-called first Lagrange point 1.5 million km towards the Sun where it will be in uninterrupted daylight and where the gravitational pull of the Sun and the Earth are balanced. The spacecraft is now expected to arrive at its station on 14 March 1996, two weeks earlier than originally planned. Coincidentally, this is the tenth anniversary of another space milestone, the encounter of ESA's Giotto probe with Comet Halley! An optimised orbit-shaping manoeuvre on 4 January, further refined SOHO's trajectory. Enough fuel remains on board to maintain SOHO's position in space for at least twenty instead of the planned six years. All systems of the 1850 kg spacecraft designed and built by European industry have been checked after launch and are in excellent shape. Their nominal performance has allowed an early and uninterrupted start of the commissioning of the scientific payload. SOHO's 12 scientific instruments* are currently being tested. Scientists are studying the first images and calibrating their instruments for the scheduled start of operations in late March. The craft's particle detectors investigating "in situ" the solar wind streaming around SOHO at its vantage point near Lagrange point 1, have been operational for some time and SOHO's first image of the Sun was taken on 19 December 1995. "All those who have worked tirelessly on the SOHO payload, spacecraft and ground-segment are to be congratulated on their excellent work and for having developed the most remarkable tool to help us understand the Sun and its environment, the heliosphere" said Roger Bonnet, ESA's Director of Science. According to present plans one month of early science is scheduled to begin around end of March and scientists hope to present their initial findings to the wide public by early May. SOHO is a project of international cooperation between ESA and NASA. The mission is led and coordinated by ESA who also procured the spacecraft; NASA provided the launch and operates the satellite. The European scientists who designed nine of the observatory's instruments and their US colleagues who built a further three are all present at Goddard Space Flight Center, where they jointly plan the optimum scientific use of the satellite. The spacecraft is part of the international Solar-Terrestrial Science Programme, the next member of which is Cluster, a flotilla of four spacecraft that will study how the Sun affects Earth and surrounding space. Cluster is scheduled for launch in May 1996 on the first Ariane 5 rocket. It will be the second mission belonging to the first "Cornerstone" of ESA's long- term scientific programme "Horizon 2000".

Anti-sway control of tethered satellite systems using attitude control of the main satellite

NASA Astrophysics Data System (ADS)

Yousefian, Peyman; Salarieh, Hassan

2015-06-01

In this study a new method is introduced to suppress libration of a tethered satellite system (TSS). It benefits from coupling between satellites and tether libration dynamics. The control concept uses the main satellite attitude maneuvers to suppress librational motion of the tether, and the main satellite's actuators for attitude control are used as the only actuation in the system. The study considers planar motion of a two body TSS system in a circular orbit and it is assumed that the tether's motion will not change it. Governing dynamic equations of motion are derived using the extended Lagrange method. Controllability of the system around the equilibrium state is studied and a linear LQG controller is designed to regulate libration of the system. Tether tension and satellite attitude are assumed as only measurable outputs of the system. The Extended Kalman Filter (EKF) is used to estimate states of the system to be used as feedback to the controller. The designed controller and observer are implemented to the nonlinear plant and simulations demonstrate that the controller lead to reduction of the tether libration propoerly. By the way, because the controller is linear, it is applicable only at low amplitudes in the vicinity of equilibrium point. To reach global stability, a nonlinear controller is demanded.

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.

The Scientific Value and Technical Challenge of Chang'E-4 Landing on the Far-side of the Moon

NASA Astrophysics Data System (ADS)

Li, Fei; Zhang, He; Wu, Xueying; Ma, Jinan; Zhou, Wenyan

2016-07-01

The mission of Chang'E-4 probe is landing on the far-side of the moon for the first time in human history. Compared with the near-side, far-side landing has unique scientific value and more challenging technology implementation. The scientific significance of the exploration of far-side of the moon and the technical difficulties and solution approach of the Chang'E-4 were discussed in this paper. In science, the far-side of the Moon is an ideal scientific platform in that it is shielded from terrestrial radio-frequency interference. The terrane that records the formation of the primordial crust is located largely on the far-side hemisphere, and there is the largest and oldest recognized impact basin in our Solar System, the South Pole-Aitken basin. In technology, the difficulties mainly includes the analysis of the influence of lunar topography of far-side on the landing descent strategy, the study of relay orbit and operating modes for the relay satellite in the Earth-Moon L2(Lagrange point 2), and the requirement analysis of autonomous management due to the relay communication. It will provide the reference for landing exploration of the far-side of the moon.

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.

Building the James Webb Space Telescope

NASA Technical Reports Server (NTRS)

Gardner, Jonathan P.

2012-01-01

The James Webb Space Telescope is the scientific successor to the Hubble and Spitzer Space Telescopes. It will be a large (6.6m) cold (50K) telescope launched into orbit around the second Earth-Sun Lagrange point. It is a partnership of NASA with the European and Canadian Space Agencies. JWST will make progress In almost every area of astronomy, from the first galaxies to form in the early universe to exoplanets and Solar System objects. Webb will have four instruments: The Near-Infrared Camera, the Near-Infrared multi-object Spectrograph, and the Near-Infrared Imager and Slitless Spectrograph will cover the wavelength range 0.6 to 5 microns, while the Mid-Infrared Instrument will do both imaging and spectroscopy from 5 to 28.5 microns. The observatory Is confirmed for launch in 2018; the design is complete and it is in its construction phase. Innovations that make JWST possible include large-area low-noise infrared detectors, cryogenic ASICs, a MEMS micro-shutter array providing multi-object spectroscopy, a non-redundant mask for interferometric coronagraphy and diffraction-limited segmented beryllium mirrors with active wavefront sensing and control. Recent progress includes the completion of the mirrors, the delivery of the first flight instruments and the start of the integration and test phase.

Low Energy Transfer to the Moon

NASA Astrophysics Data System (ADS)

Koon, W. S.; Lo, M. W.; Marsden, J. E.; Ross, S. D.

2001-11-01

New space missions are increasingly more complex; demand for exotic orbits to solve engineering problems has grown beyond the existing astrodynamic infrastructure based on two-body interactions. The delicate heteroclinic dynamics used by the Genesis Mission dramatically illustrate the need for a new paradigm: dynamical system study of three-body problem. Furthermore, this dynamics has much to say about the morphology and transport of materials within the Solar System. The cross-fertilization of ideas between the natural dynamics of the Solar System and applications to engineering has produced new techniques for constructing spacecraft trajectories with interesting characteristics. Specifically, these techniques are used here to produce a lunar capture mission which uses less fuel than a Hohmann transfer. We approximate the Sun-Earth-Moon-Spacecraft four-body problem as two three-body problems. Using the invariant manifold structures of the Lagrange points of the three-body systems, we are able to construct low energy transfer trajectories from the Earth which exhibit ballistic capture at the Moon. The techniques used in the design and construction of this trajectory may be applied in many situations. This is joint work with Martin W. Lo, Jerrold E. Marsden and Shane D. Ross and was partially supported by the National Science Foundation Grant No. KFI/ATM-9873133 under a contract with the Jet Propulsion Laboratory, NASA.

Studying Galaxy Formation with the Hubble, Spitzer and James Webb Space Telescopes

NASA Technical Reports Server (NTRS)

Gardner, Jonathan P.

2007-01-01

The deepest optical to infrared observations of the universe include the Hubble Deep Fields, the Great Observatories Origins Deep Survey and the recent Hubble Ultra-Deep Field. Galaxies are seen in these surveys at redshifts 2x3, less than 1 Gyr after the Big Bang, at the end of a period when light from the galaxies has reionized Hydrogen in the inter-galactic medium. These observations, combined with theoretical understanding, indicate that the first stars and galaxies formed at z>lO, beyond the reach of the Hubble and Spitzer Space Telescopes. To observe the first galaxies, NASA is planning the James Webb Space Telescope (JWST), a large (6.5m), cold (<50K), infrared-optimized observatory to be launched early in the next decade into orbit around the second Earth- Sun Lagrange point. JWST will have four instruments: The Near-Infrared Camera, the Near-Infrared multi-object Spectrograph, and the Tunable Filter Imager will cover the wavelength range 0.6 to 5 microns, while the Mid-Infrared Instrument will do both imaging and spectroscopy from 5 to 28.5 microns. In addition to JWST's ability to study the formation and evolution of galaxies, I will also briefly review its expected contributions to studies of the formation of stars and planetary systems.

Studying Galaxy Formation with the Hubble, Spitzer and James Webb Space Telescopes

NASA Technical Reports Server (NTRS)

Gardner, Jonathan F.; Barbier, L. M.; Barthelmy, S. D.; Cummings, J. R.; Fenimore, E. E.; Gehrels, N.; Hullinger, D. D.; Markwardt, C. B.; Palmer, D. M.; Parsons, A. M.;

Studying Galaxy Formation with the Hubble, Spitzer and James Webb Space Telescopes

NASA Technical Reports Server (NTRS)

Gardner, Jonathan P.

2007-01-01

The deepest optical to infrared observations of the universe include the Hubble Deep Fields, the Great Observatories Origins Deep Survey and the recent Hubble Ultra-Deep Field. Galaxies are seen in these surveys at redshifts z>6, less than 1 Gyr after the Big Bang, at the end of a period when light from the galaxies has reionized Hydrogen in the inter-galactic medium. These observations, combined with theoretical understanding, indicate that the first stars and galaxies formed at z>10, beyond the reach of the Hubble and Spitzer Space Telescopes. To observe the first galaxies, NASA is planning the James Webb Space Telescope (JWST), a large (6.5m), cold (<50K), infrared-optimized observatory to be launched early in the next decade into orbit around the second Earth- Sun Lagrange point. JWST will have four instruments: The Near-Infrared Camera, the Near-Infrared multi-object Spectrograph, and the Tunable Filter Imager will cover the wavelength range 0.6 to 5 microns, while the Mid-Infrared Instrument will do both imaging and spectroscopy from 5 to 28.5 microns. In addition to JWST's ability to study the formation and evolution of galaxies, I will also briefly review its expected contributions to studies of the formation of stars and planetary systems.

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.

A Relationship Between Visible and Near-IR Global Spectral Reflectance based on DSCOVR/EPIC

NASA Astrophysics Data System (ADS)

Wen, G.; Marshak, A.; Song, W.; Knyazikhin, Y.

2017-12-01

The launch of Deep Space Climate Observatory (DSCOVR) to the Earth's first Lagrange point (L1) allows us to see a new perspective of the Earth. The Earth Polychromatic Imaging Camera (EPIC) on the DSCOVR measures the back scattered radiation of the entire sunlit side of the Earth at 10 narrow band wavelengths ranging from ultraviolet to visible and near-infrared. We analyzed EPIC global averaged reflectance data. We found that the global averaged visible reflectance has a unique non-linear relationship with near infrared (NIR) reflectance. This non-linear relationship was not observed by any other satellite observations due to a limited spatial and temporal coverage of either low earth orbit (LEO) or geostationary satellite. The non-linear relationship is associated with the changing in the coverages of ocean, cloud, land, and vegetation as the Earth rotates. We used Terra and Aqua MODIS daily global radiance data to simulate EPIC observations. Since MODIS samples the Earth in a limited swath (2330km cross track) at a specific local time (10:30 am for Terra, 1:30 pm for Aqua) with approximately 15 orbits per day, the global average reflectance at a given time may be approximated by averaging the reflectance in the MODIS nearest-time swaths in the sunlit hemisphere. We found that MODIS simulated global visible and NIR spectral reflectance captured the major feature of the EPIC observed non-linear relationship with some errors. The difference between the two is mainly due to the sampling limitation of polar satellite. This suggests that that EPIC observations can be used to reconstruct MODIS global average reflectance time series for studying Earth system change in the past decade.

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.

Effect of mass variation on dynamics of tethered system in orbital maneuvering

NASA Astrophysics Data System (ADS)

Sun, Liang; Zhao, Guowei; Huang, Hai

2018-05-01

In orbital maneuvering, the mass variation due to fuel consumption has an obvious impact on the dynamics of tethered system, which cannot be neglected. The contributions of the work are mainly shown in two aspects: 1) the improvement of the model; 2) the analysis of dynamics characteristics. As the mass is variable, and the derivative of the mass is directly considered in the traditional Lagrange equation, the expression of generalized force is complicated. To solve this problem, the coagulated derivative is adopted in the paper; besides, the attitude dynamics equations derived in this paper take into account the effect of mass variation and the drift of orbital trajectory at the same time. The bifurcation phenomenon, the pendular motion angular frequency, and amplitudes of tether vibration revealed in this paper can provide a reference for the parameters and controller design in practical engineering. In the article, a dumbbell model is adopted to analyze the dynamics of tethered system, in which the mass variation of base satellite is fully considered. Considering the practical application, the case of orbital transfer under a transversal thrust is mainly studied. Besides, compared with the analytical solutions of librational angles, the effects of mass variation on stability and librational characteristic are studied. Finally, in order to make an analysis of the effect on vibrational characteristic, a lumped model is introduced, which reveals a strong coupling of librational and vibrational characteristics.

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).

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.

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

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).

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

Bifurcation and chaos analysis of a nonlinear electromechanical coupling relative rotation system

NASA Astrophysics Data System (ADS)

Liu, Shuang; Zhao, Shuang-Shuang; Sun, Bao-Ping; Zhang, Wen-Ming

2014-09-01

Hopf bifurcation and chaos of a nonlinear electromechanical coupling relative rotation system are studied in this paper. Considering the energy in air-gap field of AC motor, the dynamical equation of nonlinear electromechanical coupling relative rotation system is deduced by using the dissipation Lagrange equation. Choosing the electromagnetic stiffness as a bifurcation parameter, the necessary and sufficient conditions of Hopf bifurcation are given, and the bifurcation characteristics are studied. The mechanism and conditions of system parameters for chaotic motions are investigated rigorously based on the Silnikov method, and the homoclinic orbit is found by using the undetermined coefficient method. Therefore, Smale horseshoe chaos occurs when electromagnetic stiffness changes. Numerical simulations are also given, which confirm the analytical results.

White Dwarf WD-1145+17 "Zombie Star" Consumes Asteroid

NASA Astrophysics Data System (ADS)

Kaye, Thomas G.; Gary, Bruce L.; Rappaport, Saul A.; Foote, Jerry, Benni, Paul

2016-05-01

It has long been suspected that white dwarfs accrete asteroid debris as evidenced by heavy metals in many white dwarf spectra. WD1145 was initially detected in Kepler data as an exoplanet candidate with a repeating 1.3% dip over the course of the Jul-Sep 2014 observing season. Follow-up ground based observations were conducted with professional telescopes during March through May of 2015, and these showed that the Kepler dip must likely consist of deeper and shorter dips which come and go with an uncertain pattern. It was hypothesized that the observations were due to an asteroid in a 4.5 hour orbit. In anticipation of its return to nighttime visibility, major observatories scheduled time starting in 2016 Feb. A pro/am collaboration was formed in late 2015 for amateur observations prior to the 2016 Feb professional observations in order to determine an ephemeris for fade activity for the purpose of scheduling relatively short observations with professional telescopes. The amateur observations began in 2015 Nov, sooner than requested, and they showed that the fade activity level had exploded, becoming 20 times the level measured by Kepler. As many as 13 different fades per 4.5-hour orbit were measured, and these varied in depth from night to night. The amateur project turned into a full assault on the star with as many as 4 amateur telescopes observing on the same night. Continuous monitoring mysteriously showed that the clouds drifted in phase with respect to the dominant period i.e., they have a shorter period than measured by Kepler; this would imply that the orbiting dust clouds were located inside the orbit of the parent planetesimal. The best model indicated that the parent planetesimal was releasing fragments from inside its Hill sphere at the L1 Lagrange point, causing them to fall into an inner orbit. New astrophysics was described for the first time when the team used the diameter of the planetesimal orbit, and the diameter of the drift fragment orbit, to calculate the diameter of the Hill sphere from which the mass of the still unseen planetesimal could be inferred. Additionally, retroactive plotting of the drifting fade events backward in time hinted at a convergence date sometime in 2015 Aug, suggesting that this is when fragments broke away from the planetesimal's L1 end and began the dramatic rise in fade activity; this tentative scenario requires more observational confirmation. Since 2015 Dec the fade activity subsided to 5 times the level Kepler observed, occurring just before the scheduled professional observations. These amateur observations remain the most comprehensive to date.

Periodic orbits around areostationary points in the Martian gravity field

NASA Astrophysics Data System (ADS)

Liu, Xiao-Dong; Baoyin, Hexi; Ma, Xing-Rui

2012-05-01

This study investigates the problem of areostationary orbits around Mars in three-dimensional space. Areostationary orbits are expected to be used to establish a future telecommunication network for the exploration of Mars. However, no artificial satellites have been placed in these orbits thus far. The characteristics of the Martian gravity field are presented, and areostationary points and their linear stability are calculated. By taking linearized solutions in the planar case as the initial guesses and utilizing the Levenberg-Marquardt method, families of periodic orbits around areostationary points are shown to exist. Short-period orbits and long-period orbits are found around linearly stable areostationary points, but only short-period orbits are found around unstable areostationary points. Vertical periodic orbits around both linearly stable and unstable areostationary points are also examined. Satellites in these periodic orbits could depart from areostationary points by a few degrees in longitude, which would facilitate observation of the Martian topography. Based on the eigenvalues of the monodromy matrix, the evolution of the stability index of periodic orbits is determined. Finally, heteroclinic orbits connecting the two unstable areostationary points are found, providing the possibility for orbital transfer with minimal energy consumption.

Space Technology 7 : Micropropulsion and Mass Distribution

NASA Technical Reports Server (NTRS)

Carnaub, A.; Dunn, C.; Ziemer, J,; Hruby, V.; Spence, D.; Demmons, N.; Roy, T.; McCormick, R.; Gasaska, C.; Young, J.;

Addressing the statistical mechanics of planet orbits in the solar system

NASA Astrophysics Data System (ADS)

Mogavero, Federico

2017-10-01

The chaotic nature of planet dynamics in the solar system suggests the relevance of a statistical approach to planetary orbits. In such a statistical description, the time-dependent position and velocity of the planets are replaced by the probability density function (PDF) of their orbital elements. It is natural to set up this kind of approach in the framework of statistical mechanics. In the present paper, I focus on the collisionless excitation of eccentricities and inclinations via gravitational interactions in a planetary system. The future planet trajectories in the solar system constitute the prototype of this kind of dynamics. I thus address the statistical mechanics of the solar system planet orbits and try to reproduce the PDFs numerically constructed by Laskar (2008, Icarus, 196, 1). I show that the microcanonical ensemble of the Laplace-Lagrange theory accurately reproduces the statistics of the giant planet orbits. To model the inner planets I then investigate the ansatz of equiprobability in the phase space constrained by the secular integrals of motion. The eccentricity and inclination PDFs of Earth and Venus are reproduced with no free parameters. Within the limitations of a stationary model, the predictions also show a reasonable agreement with Mars PDFs and that of Mercury inclination. The eccentricity of Mercury demands in contrast a deeper analysis. I finally revisit the random walk approach of Laskar to the time dependence of the inner planet PDFs. Such a statistical theory could be combined with direct numerical simulations of planet trajectories in the context of planet formation, which is likely to be a chaotic process.

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.

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.

Trojan Tour and Rendezvous (TTR): A New Frontiers Mission to Explore the Origin and Evolution of the Early Solar System

NASA Astrophysics Data System (ADS)

Bell, J. F., III; Olkin, C.; Castillo, J. C.

2015-12-01

The orbital properties, compositions, and physical properties of the diverse populations of small outer solar system bodies provide a forensic map of how our solar system formed and evolved. Perhaps the most potentially diagnostic, but least explored, of those populations are the Jupiter Trojan asteroids, which orbit at ~5 AU in the L4 and L5 Lagrange points of Jupiter. More than 6200 Jupiter Trojans are presently known, but these are predicted to be only a small fraction of the 500,000 to 1 million Trojans >1 km in size. The Trojans are hypothesized to be either former Kuiper Belt Objects (KBOs) that were scattered into the inner solar system by early giant planet migration and then trapped in the 1:1 Jupiter mean motion resonance, or bodies formed near 5 AU in a much more quiescent early solar system, and then trapped at L4 and L5. The 2011 Planetary Science Decadal Survey identified important questions about the origin and evolution of the solar system that can be addressed by studying of the Trojan asteroids, including: (a) How did the giant planets and their satellite systems accrete, and is there evidence that they migrated to new orbital positions? (b) What is the relationship between large and small KBOs? Is the small population derived by impact disruption of the large one? (c) What kinds of surface evolution, radiation chemistry, and surface-atmosphere interactions occur on distant icy primitive bodies? And (d) What are the sources of asteroid groups (Trojans and Centaurs) that remain to be explored by spacecraft? The Trojan Tour and Rendezvous (TTR) is a New Frontiers-class mission designed to answer these questions, and to test hypotheses for early giant planet migration and solar system evolution. Via close flybys of a large number of these objects,, and orbital characterization of at least one large Trojan, TTR will enable the first-time exploration of this population. Our primary mission goals are to characterize the overall surface geology, geochemistry and mineralogy of these worlds; to characterize their internal structure and dynamical properties; to investigate the nature, sources and history of activity on these bodies; and to explore the diversity of the broader Trojan asteroid population.

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

Water production in comets C/2011 L4 (PanSTARRS) and C/2012 F6 (Lemmon) from observations with Soho/Swan

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

Combi, M. R.; Aptekar, G.; Bertaux, J.-L.

2014-06-01

Comets C/2011 L4 (PanSTARRS) and C/2012 F6 (Lemmon) were observed throughout their 2012-2013 apparitions with the Solar Wind Anisotropies (SWAN) all-sky hydrogen Lyα camera on board the Solar and Heliosphere Observatory (SOHO) satellite. SOHO has been in a halo orbit around the L1 Earth-Sun Lagrange point since early 1996 and has been observing the interplanetary medium and comets beginning with C/1996 B2 (Hyakutake). The global water production from these comets was determined from an analysis of the SWAN Lyα camera observations. Comet C/2011 L4 (PanSTARRS), which reached its perihelion distance of 0.302 AU on 2013 March 10.17, was observed onmore » 50 days between 2013 January 29 and April 30. Comet C/2012 F6 (Lemmon), which reached its perihelion distance of 0.731 AU on 2013 March 24.51, was observed on 109 days between 2012 November 29 and 2013 June 31. The maximum water production rates were ∼1 × 10{sup 30} molecules s{sup –1} for both comets. The activities of both comets were asymmetric about perihelion. C/2011 L4 (PanSTARRS) was more active before perihelion than after, but C/2012 F6 (Lemmon) was more active after perihelion than before.« less

The research and development program for the SNAP dark energy experiment

NASA Astrophysics Data System (ADS)

Levi, Michael E.

2007-03-01

The SNAP mission includes two surveys to study dark energy. In the deep survey, we detect more than 2000 matched Type Ia supernovae within a 7.5 deg2 field, with redshifts covering the range z=0.1 1.7. This uniform and high-quality set of “standard candles” will provide the most precise mapping of the expansion of the universe through the magnitude-redshift relation (Hubble diagram) ever constructed. The SNAP wide survey maps 1000 deg2/year in nine passbands to 28th magnitude. A weak-lensing study of the wide survey data traces the growth of structure and provides completely independent constraints on dark energy parameters. SNAP utilizes a 2 m class rigid light-weight telescope with a three-mirror anastigmatic design for a large, diffraction-limited field of view. The telescope feeds an instrumented ˜0.7 deg2 focal plane with ˜600 million pixels sensitive to wavelengths from 400 to 1700 nm. Full-depletion, high-purity silicon CCDs detect visible wavelengths, and 1700 nm cutoff HgCdTe detector arrays detect the near-IR. Passive cooling of the focal plane, fixed solar panels, fixed filters, and fixed antenna for telemetry simplify the mission. Room temperature operation of the telescope facilitates preflight testing. The satellite is placed in orbit about the second Earth Sun Lagrange point (L2).

STATISTICAL CHARACTERISTICS OF ELEMENTAL ABUNDANCE RATIOS: OBSERVATIONS FROM THE ACE SPACECRAFT

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

Zhao, L.-L.; Zhang, H.

We statistically analyze the elemental galactic cosmic ray (GCR) composition measurements of elements 5 ≤ Z ≤ 28 within the energy range 30–500 MeV/nucleon from the CRIS instrument on board the ACE spacecraft in orbit about the L1 Lagrange point during the period from 1997 to 2014. Similarly to the last unusual solar minimum, the elevated elemental intensities of all heavy nuclei during the current weak solar maximum in 2014 are ∼40% higher than that of the previous solar maximum in 2002, which has been attributed to the weak modulation associated with low solar activity levels during the ongoing weakestmore » solar maximum since the dawn of space age. In addition, the abundance ratios of heavy nuclei with respect to elemental oxygen are generally independent of kinetic energy per nucleon in the energy region 60–200 MeV/nuc, in good agreement with previous experiments. Furthermore, the abundance ratios of most relatively abundant species, except carbon, exhibit considerable solar-cycle variation, which are obviously positively correlated with the sunspot numbers with about one-year time lag. We also find that the percentage variation of abundance ratios for most elements are approximately identical. These preliminary results provide valuable insights into the characteristics of elemental heavy nuclei composition and place new and significant constraints on future GCR heavy nuclei propagation and modulation models.« less

Studying Galaxy Formation with the Hubble, Spitzer and James Webb Space Telescopes

NASA Technical Reports Server (NTRS)

Gardner, Jonathan P.

2009-01-01

The deepest optical to infrared observations of the universe include the Hubble Deep Fields, the Great Observatories Origins Deep Survey and the recent Hubble Ultra-Deep Field. Galaxies are seen in these surveys at redshifts z greater than 6, less than 1 Gyr after the Big Bang, at the end of a period when light from the galaxies has reionized Hydrogen in the inter-galactic medium. These observations, combined with theoretical understanding, indicate that the first stars and galaxies formed at z greater than 10, beyond the reach of the Hubble and Spitzer Space Telescopes. To observe the first galaxies, NASA is planning the James Webb Space Telescope (JWST), a large (6.5m), cold (less than 50K), infrared-optimized observatory to be launched early in the next decade into orbit around the second Earth-Sun Lagrange point. JWST will have four instruments: The Near-Infrared Camera, the Near-Infrared multi-object Spectrograph, and the Tunable Filter Imager will cover the wavelength range 0.6 to 5 microns, while the Mid-Infrared Instrument will do both imaging and spectroscopy from 5 to 28.5 microns. In addition to JWST's ability to study the formation and evolution of galaxies, I will also briefly review its expected contributions to studies of the formation of stars and planetary systems, and discuss recent progress in constructing the observatory.

A Lunar L2-Farside Exploration and Science Mission Concept with the ORion Multi-Purpose Crew Vehicle and a Teleoperated Lander/Rover

NASA Technical Reports Server (NTRS)

Burns, Jack O.; Kring, David; Norris, Scott; Hopkins, Josh; Lazio, Joseph; Kasper, Justin

2012-01-01

A novel concept is presented in this paper for a human mission to the lunar L2 (Lagrange) point that would be a proving ground for future exploration missions to deep space while also overseeing scientifically important investigations. In an L2 halo orbit above the lunar farside, the astronauts would travel 15% farther from Earth than did the Apollo astronauts and spend almost three times longer in deep space. Such missions would validate the Orion MPCV's life support systems, would demonstrate the high-speed re-entry capability needed for return from deep space, and would measure astronauts' radiation dose from cosmic rays and solar flares to verify that Orion would provide sufficient protection, as it is designed to do. On this proposed mission, the astronauts would teleoperate landers and rovers on the unexplored lunar farside, which would obtain samples from the geologically interesting farside and deploy a low radio frequency telescope. Sampling the South Pole-Aitkin basin (one of the oldest impact basins in the solar system) is a key science objective of the 2011 Planetary Science Decadal Survey. Observations of the Universe's first stars/galaxies at low radio frequencies are a priority of the 2010 Astronomy & Astrophysics Decadal Survey. Such telerobotic oversight would also demonstrate capability for human and robotic cooperation on future, more complex deep space missions.

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

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).

In-orbit performance of the LISA Pathfinder drag-free and attitude control system

NASA Astrophysics Data System (ADS)

Schleicher, A.; Ziegler, T.; Schubert, R.; Brandt, N.; Bergner, P.; Johann, U.; Fichter, W.; Grzymisch, J.

2018-04-01

LISA Pathfinder is a technology demonstrator mission that was funded by the European Space Agency and that was launched on December 3, 2015. LISA Pathfinder has been conducting experiments to demonstrate key technologies for the gravitational wave observatory LISA in its operational orbit at the L1 Lagrange point of the Earth-Sun system until final switch off on July 18, 2017. These key technologies include the inertial sensors, the optical metrology system, a set of µ-propulsion cold gas thrusters and in particular the high performance drag-free and attitude control system (DFACS) that controls the spacecraft in 15 degrees of freedom during its science phase. The main goal of the DFACS is to shield the two test masses inside the inertial sensors from all external disturbances to achieve a residual differential acceleration between the two test masses of less than 3 × 10-14 m/s2/√Hz over the frequency bandwidth of 1-30 mHz. This paper focuses on two important aspects of the DFACS that has been in use on LISA Pathfinder: the DFACS Accelerometer mode and the main DFACS Science mode. The Accelerometer mode is used to capture the test masses after release into free flight from the mechanical grabbing mechanism. The main DFACS Science Mode is used for the actual drag-free science operation. The DFACS control system has very strong interfaces with the LISA Technology Package payload which is a key aspect to master the design, development, and analysis of the DFACS. Linear as well as non-linear control methods are applied. The paper provides pre-flight predictions for the performance of both control modes and compares these predictions to the performance that is currently achieved in-orbit. Some results are also discussed for the mode transitions up to science mode, but the focus of the paper is on the Accelerometer mode performance and on the performance of the Science mode in steady state. Based on the achieved results, some lessons learnt are formulated to extend the results to the drag-free control system to be designed for future space-based gravity wave observatories like LISA.

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.

Mission to the Trojan asteroids: Lessons learned during a JPL Planetary Science Summer School mission design exercise

NASA Astrophysics Data System (ADS)

Diniega, Serina; Sayanagi, Kunio M.; Balcerski, Jeffrey; Carande, Bryce; Diaz-Silva, Ricardo A.; Fraeman, Abigail A.; Guzewich, Scott D.; Hudson, Jennifer; Nahm, Amanda L.; Potter-McIntyre, Sally; Route, Matthew; Urban, Kevin D.; Vasisht, Soumya; Benneke, Bjoern; Gil, Stephanie; Livi, Roberto; Williams, Brian; Budney, Charles J.; Lowes, Leslie L.

2013-02-01

The 2013 Planetary Science Decadal Survey identified a detailed investigation of the Trojan asteroids occupying Jupiter's L4 and L5 Lagrange points as a priority for future NASA missions. Observing these asteroids and measuring their physical characteristics and composition would aid in identification of their source and provide answers about their likely impact history and evolution, thus yielding information about the makeup and dynamics of the early Solar System. We present a conceptual design for a mission to the Jovian Trojan asteroids: the Trojan ASteroid Tour, Exploration, and Rendezvous (TASTER) mission, that is consistent with the NASA New Frontiers candidate mission recommended by the Decadal Survey and the final result of the 2011 NASA-JPL Planetary Science Summer School. Our proposed mission includes visits to two Trojans in the L4 population: a 500 km altitude fly-by of 1999 XS143, followed by a rendezvous with and detailed observations of 911 Agamemnon at orbital altitudes of 1000-100 km over a 12 month nominal science data capture period. Our proposed instrument payload - wide- and narrow-angle cameras, a visual and infrared mapping spectrometer, and a neutron/gamma ray spectrometer - would provide unprecedented high-resolution, regional-to-global datasets for the target bodies, yielding fundamental information about the early history and evolution of the Solar System. Although our mission design was completed as part of an academic exercise, this study serves as a useful starting point for future Trojan mission design studies. In particular, we identify and discuss key issues that can make large differences in the complex trade-offs required when designing a mission to the Trojan asteroids.

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.

'EPIC' View of Africa and Europe from a Million Miles Away

NASA Image and Video Library

2015-07-29

Africa is front and center in this image of Earth taken by a NASA camera on the Deep Space Climate Observatory (DSCOVR) satellite. The image, taken July 6 from a vantage point one million miles from Earth, was one of the first taken by NASA’s Earth Polychromatic Imaging Camera (EPIC). Central Europe is toward the top of the image with the Sahara Desert to the south, showing the Nile River flowing to the Mediterranean Sea through Egypt. The photographic-quality color image was generated by combining three separate images of the entire Earth taken a few minutes apart. The camera takes a series of 10 images using different narrowband filters -- from ultraviolet to near infrared -- to produce a variety of science products. The red, green and blue channel images are used in these Earth images. The DSCOVR mission is a partnership between NASA, the National Oceanic and Atmospheric Administration (NOAA) and the U.S. Air Force, with the primary objective to maintain the nation’s real-time solar wind monitoring capabilities, which are critical to the accuracy and lead time of space weather alerts and forecasts from NOAA. DSCOVR was launched in February to its planned orbit at the first Lagrange point or L1, about one million miles from Earth toward the sun. It’s from that unique vantage point that the EPIC instrument is acquiring images of the entire sunlit face of Earth. Data from EPIC will be used to measure ozone and aerosol levels in Earth’s atmosphere, cloud height, vegetation properties and a variety of other features. Image Credit: NASA 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

The Longitudinal Properties of a Solar Energetic Particle Event Investigated Using Modern Solar Imaging

NASA Technical Reports Server (NTRS)

Rouillard, A. P.; Sheeley, N.R. Jr.; Tylka, A.; Vourlidas, A.; Ng, C. K.; Rakowski, C.; Cohen, C. M. S.; Mewaldt, R. A.; Mason, G. M.; Reames, D.;

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.

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.

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

The Complex History of Trojan Asteroids

NASA Astrophysics Data System (ADS)

Emery, J. P.; Marzari, F.; Morbidelli, A.; French, L. M.; Grav, T.

The Trojan asteroids, orbiting the Sun in Jupiter's stable Lagrange points, provide a unique perspective on the history of our solar system. As a large population of small bodies, they record important gravitational interactions in the dynamical evolution of the solar system. As primitive bodies, their compositions and physical properties provide windows into the conditions in the solar nebula in the region in which they formed. In the past decade, significant advances have been made in understanding their physical properties, and there has been a revolution in thinking about the origin of Trojans. The ice and organics generally presumed to be a significant part of Trojan composition have yet to be detected directly, although the low density of the binary system Patroclus (and possibly low density of the binary/moonlet system Hektor) is consistent with an interior ice component. By contrast, fine-grained silicates that appear to be similar to cometary silicates in composition have been detected, and a color bimodality may indicate distinct compositional groups among the Trojans. Whereas Trojans had traditionally been thought to have formed near 5 AU, a new paradigm has developed in which the Trojans formed in the proto-Kuiper belt, and were scattered inward and captured in the Trojan swarms as a result of resonant interactions of the giant planets. Whereas the orbital and population distributions of current Trojans are consistent with this origin scenario, there are significant differences between current physical properties of Trojans and those of Kuiper belt objects. These differences may be indicative of surface modification due to the inward migration of objects that became the Trojans, but understanding of appropriate modification mechanisms is poor and would benefit from additional laboratory studies. Many open questions about this intriguing population remain, and the future promises significant strides in our understanding of Trojans. The time is ripe for a spacecraft mission to the Trojans, to transform these objects into geologic worlds that can be studied in detail to unravel their complex history.

Backup Attitude Control Algorithms for the MAP Spacecraft

NASA Technical Reports Server (NTRS)

ODonnell, James R., Jr.; Andrews, Stephen F.; Ericsson-Jackson, Aprille J.; Flatley, Thomas W.; Ward, David K.; Bay, P. Michael

1999-01-01

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, studying the early origins of the universe, in a Lissajous orbit around the Earth-Sun L(sub 2) Lagrange point. Due to limited mass, power, and financial resources, a traditional reliability concept involving fully redundant components was not feasible. This paper will discuss the redundancy philosophy used on MAP, describe the hardware redundancy selected (and why), and present backup modes and algorithms that were designed in lieu of additional attitude control hardware redundancy to improve the odds of mission success. Three of these modes have been implemented in the spacecraft flight software. The first onboard mode allows the MAP Kalman filter to be used with digital sun sensor (DSS) derived rates, in case of the failure of one of MAP's two two-axis inertial reference units. Similarly, the second onboard mode allows a star tracker only mode, using attitude and derived rate from one or both of MAP's star trackers for onboard attitude determination and control. The last backup mode onboard allows a sun-line angle offset to be commanded that will allow solar radiation pressure to be used for momentum management and orbit stationkeeping. In addition to the backup modes implemented on the spacecraft, two backup algorithms have been developed in the event of less likely contingencies. One of these is an algorithm for implementing an alternative scan pattern to MAP's nominal dual-spin science mode using only one or two reaction wheels and thrusters. Finally, an algorithm has been developed that uses thruster one shots while in science mode for momentum management. This algorithm has been developed in case system momentum builds up faster than anticipated, to allow adequate momentum management while minimizing interruptions to science. In this paper, each mode and algorithm will be discussed, and simulation results presented.

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.

Canonical quantization of constrained systems and coadjoint orbits of Diff(S sup 1 )

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

Scherer, W.M.

It is shown that Dirac's treatment of constrained Hamiltonian systems and Schwinger's action principle quantization lead to identical commutations relations. An explicit relation between the Lagrange multipliers in the action principle approach and the additional terms in the Dirac bracket is derived. The equivalence of the two methods is demonstrated in the case of the non-linear sigma model. Dirac's method is extended to superspace and this extension is applied to the chiral superfield. The Dirac brackets of the massive interacting chiral superfluid are derived and shown to give the correct commutation relations for the component fields. The Hamiltonian of themore » theory is given and the Hamiltonian equations of motion are computed. They agree with the component field results. An infinite sequence of differential operators which are covariant under the coadjoint action of Diff(S{sup 1}) and analogues to Hill's operator is constructed. They map conformal fields of negative integer and half-integer weight to their dual space. Some properties of these operators are derived and possible applications are discussed. The Korteweg-de Vries equation is formulated as a coadjoint orbit of Diff(S{sup 1}).« less

A finite-temperature Hartree-Fock code for shell-model Hamiltonians

NASA Astrophysics Data System (ADS)

Bertsch, G. F.; Mehlhaff, J. M.

2016-10-01

The codes HFgradZ.py and HFgradT.py find axially symmetric minima of a Hartree-Fock energy functional for a Hamiltonian supplied in a shell model basis. The functional to be minimized is the Hartree-Fock energy for zero-temperature properties or the Hartree-Fock grand potential for finite-temperature properties (thermal energy, entropy). The minimization may be subjected to additional constraints besides axial symmetry and nucleon numbers. A single-particle operator can be used to constrain the minimization by adding it to the single-particle Hamiltonian with a Lagrange multiplier. One can also constrain its expectation value in the zero-temperature code. Also the orbital filling can be constrained in the zero-temperature code, fixing the number of nucleons having given Kπ quantum numbers. This is particularly useful to resolve near-degeneracies among distinct minima.

Geodesics In A Spinning String Spacetime

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

Culetu, Hristu

2006-11-28

The geodesics equations for a rotating observer in a spinning string geometry are investigated using the Euler - Lagrange equations. For test particles with vanishing angular momentum, the radial equation of motion does not depend on the angular velocity {omega} but on the angular momentum of the string. A massless particle moves tachyonic but iteed tends asymptotically to unit velocity after a time of the order of few Planck time b. The spacetime has a horizon at r = 0, irrespective of the value of {omega} but its angular velocity is given by {omega} - 1/b. The Sagnac time delaymore » is computed proving to depend both on {omega} and the radius of the circular orbit. The velocity of an ingoing massive test particle approaches zero very close to the spinning string, as if it were rejected by it.« less

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…

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.

`Skinny Milky Way please', says Sagittarius

NASA Astrophysics Data System (ADS)

Gibbons, S. L. J.; Belokurov, V.; Evans, N. W.

2014-12-01

Motivated by recent observations of the Sagittarius stream, we devise a rapid algorithm to generate faithful representations of the centroids of stellar tidal streams formed in a disruption of a progenitor of an arbitrary mass in an arbitrary potential. Our method works by releasing swarms of test particles at the Lagrange points around the satellite and subsequently evolving them in a combined potential of the host and the progenitor. We stress that the action of the progenitor's gravity is crucial to making streams that look almost indistinguishable from the N-body realizations, as indeed ours do. The method is tested on mock stream data in three different Milky Way potentials with increasing complexity, and is shown to deliver unbiased inference on the Galactic mass distribution out to large radii. When applied to the observations of the Sagittarius stream, our model gives a natural explanation of the stream's apocentric distances and the differential orbital precession. We, therefore, provide a new independent measurement of the Galactic mass distribution beyond 50 kpc. The Sagittarius stream model favours a light Milky Way with the mass 4.1 ± 0.4 × 1011 M⊙ at 100 kpc, which can be extrapolated to 5.6 ± 1.2 × 1011 M⊙ at 200 kpc. Such a low mass for the Milky Way Galaxy is in good agreement with estimates from the kinematics of halo stars and from the satellite galaxies (once Leo I is removed from the sample). It entirely removes the `Too Big To Fail Problem'.

The James Webb Telescope Instrument Suite Layout: Optical System Engineering Considerations for a Large, Deployable Space Telescope

NASA Technical Reports Server (NTRS)

Bos, Brent; Davila, Pam; Jurotich, Matthew; Hobbs, Gurnie; Lightsey, Paul; Contreras, Jim; Whitman, Tony

2003-01-01

The James Webb Space Telescope (JWST) is a space-based, infrared observatory designed to study the early stages of galaxy formation in the Universe. The telescope will be launched into an elliptical orbit about the second Lagrange point and passively cooled to 30-50 K to enable astronomical observations from 0.6 to 28 microns. A group from the NASA Goddard Space Flight Center and the Northrop Grumman Space Technology prime contractor team has developed an optical and mechanical layout for the science instruments within the JWST field of view that satisfies the telescope s high-level performance requirements. Four instruments required accommodation within the telescope's field of view: a Near-Infrared Camera (NIRCam) provided by the University of Arizona; a Near-Mared Spectrometer (NIRSpec) provided by the European Space Agency; a Mid-Infrared Instrument (MIRI) provided by the Jet Propulsion Laboratory and a European consortium; and a Fine Guidance Sensor (FGS) with a tunable filter module provided by the Canadian Space Agency. The size and position of each instrument's field of view allocation were developed through an iterative, concurrent engineering process involving the key observatory stakeholders. While some of the system design considerations were those typically encountered during the development of an infrared observatory, others were unique to the deployable and controllable nature of JWST. This paper describes the optical and mechanical issues considered during the field of view layout development, as well as the supporting modeling and analysis activities.

Science with the James Webb Space Telescope

NASA Technical Reports Server (NTRS)

Gardner, Jonathan P.

2011-01-01

The scientific capabilities of the James Webb Space Telescope (JWST) fall into four themes. The End of the Dark Ages: First Light and Reionization theme seeks to identify the first luminous sources to form and to determine the ionization history of the universe. The Assembly of Galaxies theme seeks to determine how galaxies and the dark matter, gas, stars, metals, morphological structures, and active nuclei within them evolved from the epoch of reionization to the present. The Birth of Stars and Protoplanetary Systems theme seeks to unravel the birth and early evolution of stars, from infall onto dust-enshrouded protostars, to the genesis of planetary systems. The Planetary Systems and the Origins of Life theme seeks to determine the physical and chemical properties of planetary systems around nearby stars and of our own, and investigate the potential for life in those systems. To enable these for science themes, JWST will be a large (6.6m) cold (50K) telescope in orbit around the second Earth-Sun Lagrange point. It is the successor to the Hubble and Spitzer Space Telescopes, and is a partnership of NASA, ESA and CSA. JWST will have four instruments: The Near-Infrared Camera, the Near-Infrared multi-object Spectrograph, and the Tunable Filter Imager will cover the wavelength range 0.6 to 5 microns, while the Mid-Infrared Instrument will do both imaging and spectroscopy from 5 to 28.5 microns. I will conclude the talk with a description of recent technical progress in the construction of the observatory.

A Three-Body Simulation of Kepler-91: A Potential Trojan System

NASA Astrophysics Data System (ADS)

D'Angelo, Bryan Daniel

This paper presents a three-body simulation of Kepler-91 (KIC 8219268) using parameters generated by the EXONEST software package. EXONEST uses Bayesian model testing and Bayesian parameter estimation to model photometric variations and three-body motion. A close examination of the Kepler-91 light curve reveals what appears to be a third dimming event that occurs 60° out of phase with the primary transit of the conrmed planet Kepler-91b, which makes a Trojan planet in the L4 or L5 Lagrange point an enticing explanation. EXONEST is also used to model the radial velocity of Kepler-91 based on the three-body motion. The three-body analysis by EXONEST predicts a Jovian planet with mass 2:54 +/- 0:27MJ and radius 2:37 +/- 0:25RJ , and Trojan planet with mass 0:44 +/- 0:26MJ and radius 0:86 +/- 0:14R J that orbits an average of 60:39 +/- 3:74° out of phase with the Jovian, with a maximum separation angle of 68:4 +/- 43:74° and minimum separation angle of 52:33 +/- 3:74°. Both planets are predicted to have an inclination angle of 67:76 +/- 2:26° and eccentricity 0:073 +/- 0:004. The three-body motion predicts Kepler-91 to have a radial velocity semi-amplitude of 66:75 +/- 38:22 m/s and reduced mass times the sine of the inclination angle (mu sin i) of 0:732 +/- 0:385MJ.

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.

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.

Geotechnical Tests on Asteroid Simulant Orgueil

NASA Technical Reports Server (NTRS)

Garcia, Alexander D'marco

2017-01-01

In the last 100 years, the global population has more than quadrupled to over seven billion people. At the same time, the demand for food and standard of living has been increasing which has amplified the global water use by nearly eight times from approximately 500 to 4000 cu km per yr from 1900 to 2010. With the increasing concern to sustain the growing population on Earth it is necessary to seek other approaches to ensure that our planet will have resources for generations to come. In recent years, the advancement of space travel and technology has allowed the idea of mining asteroids with resources closer to becoming a reality. During the duration of the internship at NASA Kennedy Space Center, several geotechnical tests were conducted on BP-1 lunar simulant and asteroid simulant Orgueil. The tests that were conducted on BP-1 was to practice utilizing the equipment that will be used on the asteroid simulant and the data from those tests will be omitted from report. Understanding the soil mechanics of asteroid simulant Orgueil will help provide basis for future technological advances and prepare scientists for the conditions they may encounter when mining asteroids becomes reality in the distant future. Distinct tests were conducted to determine grain size distribution, unconsolidated density, and maximum density. Once the basic properties are known, the asteroid simulant will be altered to different levels of compaction using a vibrator table to see how compaction affects the density. After different intervals of vibration compaction, a miniature vane shear test will be conducted. Laboratory vane shear testing is a reliable tool to investigate strength anisotropy in the vertical and horizontal directions of a very soft to stiff saturated fine-grained clayey soil. This test will provide us with a rapid determination of the shear strength on the undisturbed compacted regolith. The results of these tests will shed light on how much torque is necessary to drill through the surface of an asteroid. Most of the known asteroids are believed to be left over material during the formation of the solar system that never accreted to form planets. Asteroids can be found in several groups such as Trojan Asteroids, Near Earth Asteroids (NEAs) and the main asteroid belt. The Trojan Asteroids orbit the 4th and 5th Lagrange points of major planets in the Solar System while the NEA's have orbits that are close to and sometimes intersect with Earths orbit and the Main Asteroid Belt which is found between the orbit of Mars and Jupiter. Gravitational perturbations can alter the orbit of asteroids in the Main Asteroid Belt causing them to move closer to earth causing them to become in the NEA class.

A Consideration of HALO Type Orbit Designation and Maintaining for KUAFU-A and WSO/UV Missions

NASA Astrophysics Data System (ADS)

Nianchuan, J.; Xian, S.; Jianguo, Y.; Guangli, W.; Jingsong, P.

In the new era of deep space exploration more and more explorations at special places or points in solar system are carried out and planned There are five equilibrium points in the Sun-Earth system and the orbits around these points have good dynamic attribute Due to this reason The areas vicinity equilibrium points have many advantages for space exploration In recent 20 years the NASA and ESA have successfully launched several spacecrafts orbiting the Sun-Earth collinear equilibrium points Following the developing steps of space and deep space exploration in China Chinese scientists and engineers are considering and suggesting two equilibrium points explorations One is named KUAFU-A mission whose craft will orbit L1 point and the scientific target is studying the evolution of space weather of solar-terrestrial area The other is WSO UV mission whose craft will orbit L2 point and the scientific target is studying the structure and evolution of galaxies This report is mainly about HALO type orbit designation and maintaining for these two missions Following points are included 1 Briefly reviewing the explorations at the equilibrium points launched by NASA and ESA 2 Simply introducing the exploration KUAFU-A and WSO UV 3 Discussing the designation and maintaining of HALO type orbits in some detail for KUAFU-A and WSO UV

Modeling low-thrust transfers between periodic orbits about five libration points: Manifolds and hierarchical design

NASA Astrophysics Data System (ADS)

Zeng, Hao; Zhang, Jingrui

2018-04-01

The low-thrust version of the fuel-optimal transfers between periodic orbits with different energies in the vicinity of five libration points is exploited deeply in the Circular Restricted Three-Body Problem. Indirect optimization technique incorporated with constraint gradients is employed to further improve the computational efficiency and accuracy of the algorithm. The required optimal thrust magnitude and direction can be determined to create the bridging trajectory that connects the invariant manifolds. A hierarchical design strategy dividing the constraint set is proposed to seek the optimal solution when the problem cannot be solved directly. Meanwhile, the solution procedure and the value ranges of used variables are summarized. To highlight the effectivity of the transfer scheme and aim at different types of libration point orbits, transfer trajectories between some sample orbits, including Lyapunov orbits, planar orbits, halo orbits, axial orbits, vertical orbits and butterfly orbits for collinear and triangular libration points, are investigated with various time of flight. Numerical results show that the fuel consumption varies from a few kilograms to tens of kilograms, related to the locations and the types of mission orbits as well as the corresponding invariant manifold structures, and indicates that the low-thrust transfers may be a beneficial option for the extended science missions around different libration points.

Resonance and Capture of Jupiter Comets

NASA Astrophysics Data System (ADS)

Koon, W. S.; Lo, M. W.; Marsden, J. E.; Ross, S. D.

A number of Jupiter family comets such as Oterma and Gehrels 3 make a rapid transition from heliocentric orbits outside the orbit of Jupiter to heliocentric orbits inside the orbit of Jupiter and vice versa. During this transition, the comet can be captured temporarily by Jupiter for one to several orbits around Jupiter. The interior heliocentric orbit is typically close to the 3:2 resonance while the exterior heliocentric orbit is near the 2:3 resonance. An important feature of the dynamics of these comets is that during the transition, the orbit passes close to the libration points L_1 and L_2, two of the equilibrium points for the restricted three-body problem for the Sun-Jupiter system. Studying the libration point invariant manifold structures for L_1 and L_2 is a starting point for understanding the capture and resonance transition of these comets. For example, the recently discovered heteroclinic connection between pairs of unstable periodic orbits (one around the L_1 and the other around L_2) implies a complicated dynamics for comets in a certain energy range. Furthermore, the stable and unstable invariant manifold `tubes' associated to libration point periodic orbits, of which the heteroclinic connections are a part, are phase space conduits transporting material to and from Jupiter and between the interior and exterior of Jupiter's orbit.

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.

Frozen Orbits-Near Constant or Beneficially Varying Orbital Parameters.

DTIC Science & Technology

1986-05-15

89 6.3 Equatorial Near-Circular Orbits ............................... 92 6.4 Stable and Unstable Equilibrium Points ...Angle Libration Period......................................... 78 5-2 Lunar Gravitational Effect on Near-Circular Orbits .................... 80 5-3...6-1 Period of Oscillation about the Stable Equilibrium Point ............... 102 FIGURES Figure 2.1 Orbital Parameters

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.

Quasi-Tangency Points on the Orbits of a Small Body and a Planet at the Low-Velocity Encounter

NASA Astrophysics Data System (ADS)

Emel'yanenko, N. Yu.

2018-03-01

We propose a method for selecting a low-velocity encounter of a small body with a planet from the evolution of the orbital elements. Polar orbital coordinates of the quasi-tangency point on the orbit of a small body are determined. Rectangular heliocentric coordinates of the quasi-tangency point on the orbit of a planet are determined. An algorithm to search for low-velocity encounters in the evolution of the orbital elements of small bodies is described. The low-velocity encounter of comet 39P/Oterma with Jupiter is considered as an example.

NASA's Space Launch System: A Flagship for Exploration Beyond Earth's Orbit

NASA Technical Reports Server (NTRS)

May, Todd

2012-01-01

The National Aeronautics and Space Administration s (NASA) Space Launch System (SLS) Program, managed at the Marshall Space Flight Center, is making progress toward delivering a new capability for exploration beyond Earth orbit in an austere economic climate. This fact drives the SLS team to find innovative solutions to the challenges of designing, developing, fielding, and operating the largest rocket in history. To arrive at the current SLS plan, government and industry experts carefully analyzed hundreds of architecture options and arrived at the one clear solution to stringent requirements for safety, affordability, and sustainability over the decades that the rocket will be in operation. This paper will explore ways to fit this major development within the funding guidelines by using existing engine assets and hardware now in testing to meet a first launch by 2017. It will explain the SLS Program s long-range plan to keep the budget within bounds, yet evolve the 70 metric ton (t) initial lift capability to 130-t lift capability after the first two flights. To achieve the evolved configuration, advanced technologies must offer appropriate return on investment to be selected through a competitive process. For context, the SLS will be larger than the Saturn V that took 12 men on 6 trips for a total of 11 days on the lunar surface over 4 decades ago. Astronauts train for long-duration voyages on the International Space Station, but have not had transportation to go beyond Earth orbit in modern times, until now. NASA is refining its mission manifest, guided by U.S. Space Policy and the Global Exploration Roadmap. Launching the Orion Multi-Purpose Cargo Vehicle s first autonomous certification flight in 2017, followed by a crewed flight in 2021, the SLS will offer a robust way to transport international crews and the air, water, food, and equipment they need for extended trips to asteroids, Lagrange Points, and Mars. In addition, the SLS will accommodate high-priority science experiments. SLS affordability initiatives include streamlining interfaces, applying risk-based insight into contracted work, centralizing systems engineering and integration, and nurturing a learning culture that continually benchmarks its performance against successful ventures. As this paper will explain, the SLS is making measurable progress toward becoming a global infrastructure asset for robotic and human scouts of all nations by harnessing business and technological innovations to deliver sustainable solutions for space exploration.

NASA's Space Launch System: A Flagship for Exploration Beyond Earth's Orbit

NASA Technical Reports Server (NTRS)

May, Todd A.

2012-01-01

The National Aeronautics and Space Administration's (NASA) Space Launch System (SLS) Program, managed at the Marshall Space Flight Center, is making progress toward delivering a new capability for exploration beyond Earth orbit in an austere economic climate. This fact drives the SLS team to find innovative solutions to the challenges of designing, developing, fielding, and operating the largest rocket in history. To arrive at the current SLS plan, government and industry experts carefully analyzed hundreds of architecture options and arrived at the one clear solution to stringent requirements for safety, affordability, and sustainability over the decades that the rocket will be in operation. This paper will explore ways to fit this major development within the funding guidelines by using existing engine assets and hardware now in testing to meet a first launch by 2017. It will explain the SLS Program s long-range plan to keep the budget within bounds, yet evolve the 70 metric ton (t) initial lift capability to 130-t lift capability after the first two flights. To achieve the evolved configuration, advanced technologies must offer appropriate return on investment to be selected through a competitive process. For context, the SLS will be larger than the Saturn V that took 12 men on 6 trips for a total of 11 days on the lunar surface over 4 decades ago. Astronauts train for long-duration voyages on the International Space Station, but have not had transportation to go beyond Earth orbit in modern times, until now. NASA is refining its mission manifest, guided by U.S. Space Policy and the Global Exploration Roadmap. Launching the Orion Multi-Purpose Crew Vehicle s (MPCV s) first autonomous certification flight in 2017, followed by a crewed flight in 2021, the SLS will offer a robust way to transport international crews and the air, water, food, and equipment they need for extended trips to asteroids, Lagrange Points, and Mars. In addition, the SLS will accommodate high-priority science experiments. SLS affordability initiatives include streamlining interfaces, applying risk-based insight into contracted work, centralizing systems engineering and integration, and nurturing a learning culture that continually benchmarks its performance against successful ventures. As this paper will explain, the SLS is making measurable progress toward becoming a global infrastructure asset for robotic and human scouts of all nations by harnessing business and technological innovations to deliver sustainable solutions for space exploration.

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.

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.

Development and application of a unified balancing approach with multiple constraints

NASA Technical Reports Server (NTRS)

Zorzi, E. S.; Lee, C. C.; Giordano, J. C.

1985-01-01

The development of a general analytic approach to constrained balancing that is consistent with past influence coefficient methods is described. The approach uses Lagrange multipliers to impose orbit and/or weight constraints; these constraints are combined with the least squares minimization process to provide a set of coupled equations that result in a single solution form for determining correction weights. Proper selection of constraints results in the capability to: (1) balance higher speeds without disturbing previously balanced modes, thru the use of modal trial weight sets; (2) balance off-critical speeds; and (3) balance decoupled modes by use of a single balance plane. If no constraints are imposed, this solution form reduces to the general weighted least squares influence coefficient method. A test facility used to examine the use of the general constrained balancing procedure and application of modal trial weight ratios is also described.

Hamiltonian Systems and Optimal Control in Computational Anatomy: 100 Years Since D'Arcy Thompson.

PubMed

Miller, Michael I; Trouvé, Alain; Younes, Laurent

2015-01-01

The Computational Anatomy project is the morphome-scale study of shape and form, which we model as an orbit under diffeomorphic group action. Metric comparison calculates the geodesic length of the diffeomorphic flow connecting one form to another. Geodesic connection provides a positioning system for coordinatizing the forms and positioning their associated functional information. This article reviews progress since the Euler-Lagrange characterization of the geodesics a decade ago. Geodesic positioning is posed as a series of problems in Hamiltonian control, which emphasize the key reduction from the Eulerian momentum with dimension of the flow of the group, to the parametric coordinates appropriate to the dimension of the submanifolds being positioned. The Hamiltonian viewpoint provides important extensions of the core setting to new, object-informed positioning systems. Several submanifold mapping problems are discussed as they apply to metamorphosis, multiple shape spaces, and longitudinal time series studies of growth and atrophy via shape splines.

Regularization destriping of remote sensing imagery

NASA Astrophysics Data System (ADS)

Basnayake, Ranil; Bollt, Erik; Tufillaro, Nicholas; Sun, Jie; Gierach, Michelle

2017-07-01

We illustrate the utility of variational destriping for ocean color images from both multispectral and hyperspectral sensors. In particular, we examine data from a filter spectrometer, the Visible Infrared Imaging Radiometer Suite (VIIRS) on the Suomi National Polar Partnership (NPP) orbiter, and an airborne grating spectrometer, the Jet Population Laboratory's (JPL) hyperspectral Portable Remote Imaging Spectrometer (PRISM) sensor. We solve the destriping problem using a variational regularization method by giving weights spatially to preserve the other features of the image during the destriping process. The target functional penalizes the neighborhood of stripes (strictly, directionally uniform features) while promoting data fidelity, and the functional is minimized by solving the Euler-Lagrange equations with an explicit finite-difference scheme. We show the accuracy of our method from a benchmark data set which represents the sea surface temperature off the coast of Oregon, USA. Technical details, such as how to impose continuity across data gaps using inpainting, are also described.

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.

Homoclinic orbits and critical points of barrier functions

NASA Astrophysics Data System (ADS)

Cannarsa, Piermarco; Cheng, Wei

2015-06-01

We interpret the close link between the critical points of Mather's barrier functions and minimal homoclinic orbits with respect to the Aubry sets on {{T}}n . We also prove a critical point theorem for barrier functions and the existence of such homoclinic orbits on {{T}}2 as an application.

The end-of-life disposal of satellites in libration-point orbits using solar radiation pressure

NASA Astrophysics Data System (ADS)

Soldini, Stefania; Colombo, Camilla; Walker, Scott

2016-04-01

This paper proposes an end-of-life propellant-free disposal strategy for libration-point orbits which uses solar radiation pressure to restrict the evolution of the spacecraft motion. The spacecraft is initially disposed into the unstable manifold leaving the libration-point orbit, before a reflective sun-pointing surface is deployed to enhance the effect of solar radiation pressure. Therefore, the consequent increase in energy prevents the spacecraft's return to Earth. Three European Space Agency missions are selected as test case scenarios: Herschel, SOHO and Gaia. Guidelines for the end-of-life disposal of future libration-point orbit missions are proposed and a preliminary study on the effect of the Earth's orbital eccentricity on the disposal strategy is shown for the Gaia mission.

Time-free transfers between libration-point orbits in the elliptic restricted problem

NASA Astrophysics Data System (ADS)

Howell, K. C.; Hiday-Johnston, L. A.

This work is part of a larger research effort directed toward the formulation of a strategy to design optimal time-free impulsive transfers between three-dimensional libration-point orbits in the vicinity of the interior LI libration point of the Sun-Earth/Moon barycenter system. Inferior transfers that move a spacecraft from a large halo orbit to a smaller halo orbit are considered here. Primer vector theory is applied to non-optimal impulsive trajectories in the elliptic restricted three-body problem in order to establish whether the implementation of a coast in the initial orbit, a coast in the final orbit, or dual coasts accomplishes a reduction in fuel expenditure. The addition of interior impulses is also considered. Results indicate that a substantial savings in fuel can be achieved by the allowance for coastal periods on the specified libration-point orbits. The resulting time-free inferior transfers are compared to time-free superior transfers between halo orbits of equal z-amplitude separation.

Time-free transfers between libration-point orbits in the elliptic restricted problem

NASA Astrophysics Data System (ADS)

Howell, K. C.; Hiday, L. A.

1992-08-01

This work is directed toward the formulation of a strategy to design optimal time-free impulsive transfers between 3D libration-point orbits in the vicinity of the interior L1 libration point of the sun-earth/moon barycenter system. Inferior transfers that move a spacecraft from a large halo orbit to a smaller halo orbit are considered here. Primer vector theory is applied to nonoptimal impulsive trajectories in the elliptic restricted three-body problem in order to establish whether the implementation of a coast in the initial orbit, a coast in the final orbit, or dual coasts accomplishes a reduction in fuel expenditure. The addition of interior impulses is also considered. Results indicate that a substantial savings in fuel can be achieved by the allowance for coastal periods on the specified libration-point orbits. The resulting time-free inferior transfers are compared to time-free superior transfers between halo orbits of equal z-amplitude separation.

Post-capture vibration suppression of spacecraft via a bio-inspired isolation system

NASA Astrophysics Data System (ADS)

Dai, Honghua; Jing, Xingjian; Wang, Yu; Yue, Xiaokui; Yuan, Jianping

2018-05-01

Inspired by the smooth motions of a running kangaroo, a bio-inspired quadrilateral shape (BIQS) structure is proposed to suppress the vibrations of a free-floating spacecraft subject to periodic or impulsive forces, which may be encountered during on-orbit servicing missions. In particular, the BIQS structure is installed between the satellite platform and the capture mechanism. The dynamical model of the BIQS isolation system, i.e. a BIQS structure connecting the platform and the capture mechanism at each side, is established by Lagrange's equations to simulate the post-capture dynamical responses. The BIQS system suffering an impulsive force is dealt with by means of a modified version of Lagrange's equations. Furthermore, the classical harmonic balance method is used to solve the nonlinear dynamical system subject to periodic forces, while for the case under impulsive forces the numerical integration method is adopted. Due to the weightless environment in space, the present BIQS system is essentially an under-constrained dynamical system with one of its natural frequencies being identical to zero. The effects of system parameters, such as the number of layers in BIQS, stiffness, assembly angle, rod length, damping coefficient, masses of satellite platform and capture mechanism, on the isolation performance of the present system are thoroughly investigated. In addition, comparisons between the isolation performances of the presently proposed BIQS isolator and the conventional spring-mass-damper (SMD) isolator are conducted to demonstrate the advantages of the present isolator. Numerical simulations show that the BIQS system has a much better performance than the SMD system under either periodic or impulsive forces. Overall, the present BIQS isolator offers a highly efficient passive way for vibration suppressions of free-floating spacecraft.

Connecting orbits and invariant manifolds in the spatial restricted three-body problem

NASA Astrophysics Data System (ADS)

Gómez, G.; Koon, W. S.; Lo, M. W.; Marsden, J. E.; Masdemont, J.; Ross, S. D.

2004-09-01

The invariant manifold structures of the collinear libration points for the restricted three-body problem provide the framework for understanding transport phenomena from a geometrical point of view. In particular, the stable and unstable invariant manifold tubes associated with libration point orbits are the phase space conduits transporting material between primary bodies for separate three-body systems. These tubes can be used to construct new spacecraft trajectories, such as a 'Petit Grand Tour' of the moons of Jupiter. Previous work focused on the planar circular restricted three-body problem. This work extends the results to the three-dimensional case. Besides providing a full description of different kinds of libration motions in a large vicinity of these points, this paper numerically demonstrates the existence of heteroclinic connections between pairs of libration orbits, one around the libration point L1 and the other around L2. Since these connections are asymptotic orbits, no manoeuvre is needed to perform the transfer from one libration point orbit to the other. A knowledge of these orbits can be very useful in the design of missions such as the Genesis Discovery Mission, and may provide the backbone for other interesting orbits in the future.

Heteroclinic, Homoclinic Connections Between the Sun-Earth Triangular Points and Quasi-Satellite Orbits for Solar Observations

NASA Technical Reports Server (NTRS)

Llanos, Pedro J.; Hintz, Gerald R.; Lo, Martin W.; Miller, James K.

2013-01-01

Investigation of new orbit geometries exhibits a very attractive behavior for a spacecraft to monitor space weather coming from the Sun. Several orbit transfer mechanisms are analyzed as potential alternatives to monitor solar activity such as a sub-solar orbit or quasi-satellite orbit and short and long heteroclinic and homoclinic connections between the triangular points L(sub 4) and L(sub 5) and the collinear point L(sub 3) of the Circular Restricted Three-Body Problem (CRTBP) in the Sun-Earth system.

Materials trade study for lunar/gateway missions.

PubMed

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

2003-01-01

The National Aeronautics and Space Administration (NASA) administrator has identified protection from radiation hazards as one of the two biggest problems of the agency with respect to human deep space missions. The intensity and strength of cosmic radiation in deep space makes this a 'must solve' problem for space missions. The Moon and two Earth-Moon Lagrange points near Moon are being proposed as hubs for deep space missions. The focus of this study is to identify approaches to protecting astronauts and habitats from adverse effects from space radiation both for single missions and multiple missions for career astronauts to these destinations. As the great cost of added radiation shielding is a potential limiting factor in deep space missions, reduction of mass, without compromising safety, is of paramount importance. The choice of material and selection of the crew profile play major roles in design and mission operations. Material trade studies in shield design over multi-segmented missions involving multiple work and living areas in the transport and duty phase of space mission's to two Earth-Moon co-linear Lagrange points (L1) between Earth and the Moon and (L2) on back side of the moon as seen from Earth, and to the Moon have been studied. It is found that, for single missions, current state-of-the-art knowledge of material provides adequate shielding. On the other hand, the choice of shield material is absolutely critical for career astronauts and revolutionary materials need to be developed for these missions. This study also provides a guide to the effectiveness of multifunctional materials in preparation for more detailed geometry studies in progress. c2003 COSPAR. Published by Elsevier Ltd. All rights reserved.

Three dimensional dynamics of a flexible Motorised Momentum Exchange Tether

NASA Astrophysics Data System (ADS)

Ismail, N. A.; Cartmell, M. P.

2016-03-01

This paper presents a new flexural model for the three dimensional dynamics of the Motorised Momentum Exchange Tether (MMET) concept. This study has uncovered the relationships between planar and nonplanar motions, and the effect of the coupling between these two parameters on pragmatic circular and elliptical orbits. The tether sub-spans are modelled as stiffened strings governed by partial differential equations of motion, with specific boundary conditions. The tether sub-spans are flexible and elastic, thereby allowing three dimensional displacements. The boundary conditions lead to a specific frequency equation and the eigenvalues from this provide the natural frequencies of the orbiting flexible motorised tether when static, accelerating in monotonic spin, and at terminal angular velocity. A rotation transformation matrix has been utilised to get the position vectors of the system's components in an assumed inertial frame. Spatio-temporal coordinates are transformed to modal coordinates before applying Lagrange's equations, and pre-selected linear modes are included to generate the equations of motion. The equations of motion contain inertial nonlinearities which are essentially of cubic order, and these show the potential for intricate intermodal coupling effects. A simulation of planar and non-planar motions has been undertaken and the differences in the modal responses, for both motions, and between the rigid body and flexible models are highlighted and discussed.

Mission design for a halo orbiter of the earth

NASA Technical Reports Server (NTRS)

Farquhar, R. W.; Muhonen, D. P.; Richardson, D. L.

1976-01-01

The International Sun-Earth Explorer (ISEE) scientific satellite to be stationed in 1978 in the vicinity of the sun-earth interior libration point to continuously monitor the space between the sun and the earth, including the distant geomagnetic tail is described. Orbit selection considerations for the ISEE-C are discussed along with stationkeeping requirements and fuel-optimal trajectories. Due to the alignment of the interior libration point with the sun as viewed from the earth, it will be necessary to place the satellite into a 'halo orbit' around the libration point, in order to eliminate solar interference with down-link telemetry. Parametric data for transfer trajectories between an earth parking orbit (altitude about 185 km) and a libration-point orbit are presented. It is shown that the insertion magnitude required for placing a satellite into an acceptable halo orbit is rather modest.

Orbit Determination (OD) Error Analysis Results for the Triana Sun-Earth L1 Libration Point Mission and for the Fourier Kelvin Stellar Interferometer (FKSI) Sun-Earth L2 Libration Point Mission Concept

NASA Technical Reports Server (NTRS)

Marr, Greg C.

2003-01-01

The Triana spacecraft was designed to be launched by the Space Shuttle. The nominal Triana mission orbit will be a Sun-Earth L1 libration point orbit. Using the NASA Goddard Space Flight Center's Orbit Determination Error Analysis System (ODEAS), orbit determination (OD) error analysis results are presented for all phases of the Triana mission from the first correction maneuver through approximately launch plus 6 months. Results are also presented for the science data collection phase of the Fourier Kelvin Stellar Interferometer Sun-Earth L2 libration point mission concept with momentum unloading thrust perturbations during the tracking arc. The Triana analysis includes extensive analysis of an initial short arc orbit determination solution and results using both Deep Space Network (DSN) and commercial Universal Space Network (USN) statistics. These results could be utilized in support of future Sun-Earth libration point missions.

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.

Concept of Operations for Deploying a Lander on the Secondary Body of Binary Asteroid 1996 FG3

NASA Astrophysics Data System (ADS)

Tardivel, Simon; Michel, P.; Scheeres, D.

2012-10-01

The European Space Agency is currently performing an assessment study of the MarcoPolo-R space mission, in the framework of the M3 class competition of its Cosmic Vision Program. MarcoPolo-R is a sample return mission to a primitive asteroid, whose baseline target is the binary asteroid 1996FG3. The baseline mission, including the sample, is focused on the primary of the binary system. To date, little has yet been considered for the investigation of the secondary, apart from remote observations from the spacecraft. However, MarcoPolo-R may carry an optional lander, and if such a lander could be accommodated it may be relevant to use it for a more detailed investigation of the secondary. This poster presents a strategy for deploying a lander using an unpowered trajectory towards the secondary. This ballistic deployment allows for the design of a light lander with minimum platform overhead and maximum payload. The deployment operations are shown to be very simple and require minimum preparation. The main spacecraft is set on an orbit that reaches a specific point near the binary system L2 Lagrange Point facing the far side of the secondary, about 220 meters from the secondary surface, with a relative speed of about 10cm/s. The lander is then jettisoned using a spring-release mechanism that sets it on an impact trajectory that robustly intersects with the secondary surface. On impact, the lander only needs to dissipate a small amount of kinetic energy in order to ensure that it is energetically and dynamically trapped on the surface. Considering errors on spacecraft GNC and on the spring-release mechanism, and very large uncertainties on the gravity field of the asteroids, the strategy presented here yields a successful landing in more than 99.9% of cases, while ensuring the absolute safety of the spacecraft before, during and after deployment operations.

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.

Unusual Water Production Activity of Comet C/2012 S1 (ISON): Outbursts and Continuous Fragmentation

NASA Astrophysics Data System (ADS)

Combi, M. R.; Fougere, N.; Mäkinen, J. T. T.; Bertaux, J.-L.; Quémerais, E.; Ferron, S.

2014-06-01

The Solar Wind ANisotropies (SWAN) all-sky hydrogen Lyα camera on the SOlar and Heliospheric Observer (SOHO) satellite observed the hydrogen coma of comet C/2012 S1 (ISON) for most of the last month of its activity from 2013 October 24 to November 24, ending just 4 days before perihelion and its final disruption. The water production rate of the comet was determined from these observations. SOHO has been operating in a halo orbit around the Earth-Sun L1 Lagrange point since its launch in late 1995. Most water vapor produced by comets is ultimately photodissociated into two H atoms and one O atom producing a huge hydrogen coma that is routinely observed in the daily SWAN images in comets of sufficient brightness. Water production rates were calculated from 22 images over most of the last month of the pre-perihelion apparition. The water production rate increased very slowly on average from October 24.9 until November 12.9, staying between 1.8 and 3.4 × 1028 s-1, after which it increased dramatically, reaching 1.6 to 2 × 1030 s-1 from November 21.6 to 23.6. It was not detected after perihelion on December 3.7 when it should have been visible. We examine the active surface area necessary to explain the water production rate and its variation and are able to place constraints on the physical size of the original nucleus necessary to account for the large amount of activity from November 12.9 and until just before perihelion.

A Novel Approach to Exploring the Mars Polar Caps

NASA Technical Reports Server (NTRS)

Brophy, John R.; Carsey, Frank D.; Rodgers, David H.; Soderblom, L. A.; Wilcox, Brian H.

2000-01-01

The Martian polar caps contain some of the most important scientific sites on the planet. There is much interest in exploring them with a view to understanding their role in the Mars climate system. By gaining access to the stratigraphy of the polar terrain, it is probable that one can access the climate history of the planet. Additionally, investigations aimed at localizing subsurface water--liquid or solid--are not only of great scientific interest but are also germane to the long-term interests of the manned space flight program. A major difficulty with polar exploration is access. Current techniques using chemical propulsion, Holman transfers, and direct-entry landers with aeroshells have limited capability to access the polar terrain. For the near term the authors propose a new approach to solving this transportation issue by using Solar Electric Propulsion (SEP), recently flight demonstrated on NASA's DS1 Mission to an asteroid and a comet. For a longer-term approach there are additional ways in which access to Mars, as well as other planets, can be significantly improved. These include the use of Chaos orbit theory to enable transportation between LaGrange points in the solar system, gossamer structures enabling very low-mass mobility, and advanced ascent vehicles. In this paper the authors describe how a 1000-kG payload can be transported to the surface of Mars and a polar sample obtained and returned to Earth in less than five years using SEP. A vision of how this approach can be integrated into a long-term Mars exploration strategy building toward the future is also discussed.

The James Webb Space Telescope

NASA Technical Reports Server (NTRS)

Gardner, Jonathan P.

2011-01-01

The James Webb Space Telescope is the scientific successor to the Hubble and Spitzer Space Telescopes, and is currently the largest scientific project under construction in the United States. It will be a large (6.6m) cold (50K) telescope launched in about 5 years into orbit around the second Earth-Sun Lagrange point. It is a partnership of NASA with the European and Canadian Space Agencies. Science with the James Webb Space Telescope falls into four themes. The End of the Dark Ages: First Light and Reionization theme seeks to identify the first luminous sources to form and to determine the ionization history of the universe. The Assembly of Galaxies theme seeks to determine how galaxies and the dark matter, gas, stars, metals, morphological structures, and black holes within them evolved from the epoch of reionization to the present. The Birth of Stars and Proto planetary Systems theme seeks to unravel the birth and early evolution of stars, from infall onto dust-enshrouded protostars, to the genesis of planetary systems. The Planetary Systems and the Origins of Life theme seeks to determine the physical and chemical properties of planetary systems around nearby stars and of our own, and investigate the potential for life in those systems. Webb will have four instruments: The Near-Infrared Camera, the Near-Infrared multi-object Spectrograph, and the Tunable Filter Imager will cover the wavelength range 0.6 to 5 microns, while the Mid-Infrared Instrument will do both imaging and spectroscopy from 5 to 28.5 microns. I will conclude the talk with a description of recent technical progress in the construction of the observatory.

The James Webb Space Telescope

NASA Technical Reports Server (NTRS)

Gardner, Jonathan P.

2011-01-01

The James Webb Space Telescope is the scientific successor to the Hubble and Spitzer Space Telescopes, and is currently the largest scientific project under construction in the United States. It will be a large (6.6m) cold (50K) telescope launched into orbit around the second Earth-Sun Lagrange point. It is a partnership of NASA with the European and Canadian Space Agencies. Science with the James Webb Space Telescope falls into four themes. The End of the Dark Ages: First Light and Reionization theme seeks to identify the first luminous sources to form and to determine the ionization history of the universe. The Assembly of Galaxies theme seeks to determine how galaxies and the dark matter, gas, stars, metals, morphological structures, and black holes within them evolved from the epoch of reionization to the present. The Birth of Stars and Protoplanetary Systems theme seeks to unravel the birth and early evolution of stars, from infall onto dust-enshrouded protostars, to the genesis of planetary systems. The Planetary Systems and the Origins of Life theme seeks to determine the physical and chemical properties of planetary systems around nearby stars and of our own, and investigate the potential for life in those systems. Webb will have four instruments: The Near-Infrared Camera, the Near-Infrared multi-object Spectrograph, and the Tunable Filter Imager will cover the wavelength range 0.6 to 5 microns, while the Mid-Infrared Instrument will do both imaging and spectroscopy from 5 to 28.5 microns. I will conclude the talk with a description of recent technical progress in the construction of the observatory.

The James Webb Space Telescope

NASA Technical Reports Server (NTRS)

Gardner, Jonathan P.

2011-01-01

The James Webb Space Telescope is the scientific successor to the Hubble and Spitzer Space Telescopes, and is currently the largest scientific project under construction in the United States. It will be a large (6.6m) cold (50K) telescope launched in about 5 years into orbit around the second Earth-Sun Lagrange point. It is a partnership of NASA with the European and Canadian Space Agencies. Science with the James Webb Space Telescope falls into four themes. The End of the Dark Ages: First Light and Reionization theme seeks to identify the first luminous sources to form and to determine the ionization history of the universe. The Assembly of Galaxies theme seeks to determine how galaxies and the dark matter, gas, stars, metals, morphological structures, and black holes within them evolved from the epoch of reionization to the present. The Birth of Stars and Protoplanetary Systems theme seeks to unravel the birth and early evolution of stars, from infall onto dust-enshrouded protostars, to the genesis of planetary systems. The Planetary Systems and the Origins of Life theme seeks to determine the physical and chemical properties of planetary systems around nearby stars and of our own, and investigate the potential for life in those systems. Webb will have four instruments: The Near-Infrared Camera, the Near-Infrared multi-object Spectrograph, and the Tunable Filter Imager will cover the wavelength range 0.6 to 5 microns, while the Mid-Infrared Instrument will do both imaging and spectroscopy from 5 to 28.5 microns. I will conclude the talk with a description of recent technical progress in the construction of the observatory.

A Novel Approach to Exploring the Mars Polar Caps

NASA Astrophysics Data System (ADS)

Brophy, John R.; Carsey, Frank D.; Rodgers, David H.; Soderblom, L. A.; Wilcox, Brian H.

2000-08-01

The Martian polar caps contain some of the most important scientific sites on the planet. There is much interest in exploring them with a view to understanding their role in the Mars climate system. By gaining access to the stratigraphy of the polar terrain, it is probable that one can access the climate history of the planet. Additionally, investigations aimed at localizing subsurface water--liquid or solid--are not only of great scientific interest but are also germane to the long-term interests of the manned space flight program. A major difficulty with polar exploration is access. Current techniques using chemical propulsion, Holman transfers, and direct-entry landers with aeroshells have limited capability to access the polar terrain. For the near term the authors propose a new approach to solving this transportation issue by using Solar Electric Propulsion (SEP), recently flight demonstrated on NASA's DS1 Mission to an asteroid and a comet. For a longer-term approach there are additional ways in which access to Mars, as well as other planets, can be significantly improved. These include the use of Chaos orbit theory to enable transportation between LaGrange points in the solar system, gossamer structures enabling very low-mass mobility, and advanced ascent vehicles. In this paper the authors describe how a 1000-kG payload can be transported to the surface of Mars and a polar sample obtained and returned to Earth in less than five years using SEP. A vision of how this approach can be integrated into a long-term Mars exploration strategy building toward the future is also discussed.

DAMPING OF THE MILKY WAY BAR BY MANIFOLD-DRIVEN SPIRALS

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

Łokas, Ewa L.

2016-10-10

We describe a new phenomenon of “bar damping” that may have played an important role in shaping the Milky Way bar and bulge as well as its spiral structure. We use a collisionless N -body simulation of a Milky Way–like galaxy initially composed of a dark matter halo and an exponential disk with a Toomre parameter slightly above unity. In this configuration, dominated by the disk in the center, a bar forms relatively quickly, after 1 Gyr of evolution. This is immediately followed by the formation of two manifold-driven spiral arms and the outflow of stars that modifies the potentialmore » in the vicinity of the bar, apparently shifting the position of the L {sub 1}/ L {sub 2} Lagrange points. This modification leads to the shortening of the bar and the creation of a next generation of manifold-driven spiral arms at a smaller radius. The process repeats itself a few times over the next 0.5 Gyr resulting in further substantial weakening and shortening of the bar. The time when the damping comes to an end coincides with the first buckling episode in the bar that rebuilds the orbital structure so that no more new spiral arms are formed. The morphology of the bar and the spiral structure at this time show remarkable similarity to the present properties of the Milky Way. Later on, the bar starts to grow rather steadily again, weakened only by subsequent buckling episodes occurring at more distant parts of the disk.« less

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.

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.

Two-craft Coulomb formation study about circular orbits and libration points

NASA Astrophysics Data System (ADS)

Inampudi, Ravi Kishore

This dissertation investigates the dynamics and control of a two-craft Coulomb formation in circular orbits and at libration points; it addresses relative equilibria, stability and optimal reconfigurations of such formations. The relative equilibria of a two-craft tether formation connected by line-of-sight elastic forces moving in circular orbits and at libration points are investigated. In circular Earth orbits and Earth-Moon libration points, the radial, along-track, and orbit normal great circle equilibria conditions are found. An example of modeling the tether force using Coulomb force is discussed. Furthermore, the non-great-circle equilibria conditions for a two-spacecraft tether structure in circular Earth orbit and at collinear libration points are developed. Then the linearized dynamics and stability analysis of a 2-craft Coulomb formation at Earth-Moon libration points are studied. For orbit-radial equilibrium, Coulomb forces control the relative distance between the two satellites. The gravity gradient torques on the formation due to the two planets help stabilize the formation. Similar analysis is performed for along-track and orbit-normal relative equilibrium configurations. Where necessary, the craft use a hybrid thrusting-electrostatic actuation system. The two-craft dynamics at the libration points provide a general framework with circular Earth orbit dynamics forming a special case. In the presence of differential solar drag perturbations, a Lyapunov feedback controller is designed to stabilize a radial equilibrium, two-craft Coulomb formation at collinear libration points. The second part of the thesis investigates optimal reconfigurations of two-craft Coulomb formations in circular Earth orbits by applying nonlinear optimal control techniques. The objective of these reconfigurations is to maneuver the two-craft formation between two charged equilibria configurations. The reconfiguration of spacecraft is posed as an optimization problem using the calculus of variations approach. The optimality criteria are minimum time, minimum acceleration of the separation distance, minimum Coulomb and electric propulsion fuel usage, and minimum electrical power consumption. The continuous time problem is discretized using a pseudospectral method, and the resulting finite dimensional problem is solved using a sequential quadratic programming algorithm. The software package, DIDO, implements this approach. This second part illustrates how pseudospectral methods significantly simplify the solution-finding process.

Void Points, Rosettes, and a Brief History of Planetary Astronomy

NASA Astrophysics Data System (ADS)

Kosso, Peter

2013-12-01

Almost all models of planetary orbits, from Aristotle through Newton, include void points, empty points in space that have an essential role in defining the orbit. By highlighting the role of these void points, as well as the rosette pattern of the orbit that often results, I bring out different features in the history of planetary astronomy and place a different emphasis on its revolutionary changes, different from those rendered in terms of epicycles or the location of the earth.

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.

Chandra X-Ray Observatory Pointing Control System Performance During Transfer Orbit and Initial On-Orbit Operations

NASA Technical Reports Server (NTRS)

Quast, Peter; Tung, Frank; West, Mark; Wider, John

2000-01-01

The Chandra X-ray Observatory (CXO, formerly AXAF) is the third of the four NASA great observatories. It was launched from Kennedy Space Flight Center on 23 July 1999 aboard the Space Shuttle Columbia and was successfully inserted in a 330 x 72,000 km orbit by the Inertial Upper Stage (IUS). Through a series of five Integral Propulsion System burns, CXO was placed in a 10,000 x 139,000 km orbit. After initial on-orbit checkout, Chandra's first light images were unveiled to the public on 26 August, 1999. The CXO Pointing Control and Aspect Determination (PCAD) subsystem is designed to perform attitude control and determination functions in support of transfer orbit operations and on-orbit science mission. After a brief description of the PCAD subsystem, the paper highlights the PCAD activities during the transfer orbit and initial on-orbit operations. These activities include: CXO/IUS separation, attitude and gyro bias estimation with earth sensor and sun sensor, attitude control and disturbance torque estimation for delta-v burns, momentum build-up due to gravity gradient and solar pressure, momentum unloading with thrusters, attitude initialization with star measurements, gyro alignment calibration, maneuvering and transition to normal pointing, and PCAD pointing and stability performance.

NASA's Space Launch System: A Heavy-Lift Platform for Entirely New Missions

NASA Technical Reports Server (NTRS)

Creech, Stephen D.

2012-01-01

The National Aeronautics and Space Administration's (NASA's) Space Launch System (SLS) will contribute a new capability for human space flight and scientific missions beyond low-Earth orbit (LEO). The SLS Program, managed at NASA s Marshall Space Flight Center, will develop the heavy-lift vehicle that will launch the Orion Multi-Purpose Crew Vehicle (MPCV), equipment, supplies, and major science missions for exploration and discovery. Orion will carry crews to space, provide emergency abort capability, sustain the crew during space travel, and provide safe reentry from deep-space return velocities. Supporting Orion s first autonomous flight to lunar orbit and back in 2017 and its first crewed flight in 2021, the SLS ultimately offers a flexible platform for both human and scientific exploration. The SLS plan leverages legacy infrastructure and hardware in NASA s inventory, as well as continues with advanced technologies now in development, to deliver an initial 70 metric ton (t) lift capability in 2017, evolving to a 130-t capability, using a block upgrade approach. This paper will give an overview of the SLS design and management approach against a backdrop of the missions it will support. It will detail the plan to deliver the initial SLS capability to the launch pad in the near term, as well as summarize the innovative approaches the SLS team is applying to deliver a safe, affordable, and sustainable long-range capability for entirely new missions-opening a new realm of knowledge and a world of possibilities for multiple partners. Design reference missions that the SLS is being planned to support include Mars, Jupiter, Lagrange Points, and near-Earth asteroids (NEAs), among others. The Agency is developing its mission manifest in parallel with the development of a heavy-lift flagship that will dramatically increase total lift and volume capacity beyond current launch vehicle options, reduce trip times, and provide a robust platform for conducting new missions destined to rewrite textbooks with the information they deliver, while creating a framework for further collaboration among domestic and international partners, and potentially spurring economic expansion into new markets.

NASA's Space Launch System: A Heavy-Lift Platform for Entirely New Missions

NASA Technical Reports Server (NTRS)

Creech, Stephen A.

2012-01-01

The National Aeronautics and Space Administration s (NASA's) Space Launch System (SLS) will contribute a new capability for human space flight and scientific missions beyond low-Earth orbit. The SLS Program, managed at NASA s Marshall Space Fight Center, will develop the heavy-lift vehicle that will launch the Orion Multi-Purpose Crew Vehicle (MPCV), equipment, supplies, and major science missions. Orion will carry crews to space, provide emergency abort capability, sustain the crew during space travel, and provide safe reentry from deep-space return velocities. Supporting Orion s first autonomous flight to lunar orbit and back in 2017 and its first crewed flight in 2021, the SLS ultimately offers a flexible platform for both human and scientific exploration. The SLS plan leverages legacy infrastructure and hardware in NASA s inventory, as well as continues with advanced propulsion technologies now in development, to deliver an initial 70 metric ton (t) lift capability in 2017, evolving to a 130-t capability after 2021, using a block upgrade approach. This paper will give an overview of the SLS design and management approach against a backdrop of the missions it will support. It will detail the plan to deliver the initial SLS capability to the launch pad in the near term, as well as summarize the innovative approaches the SLS team is applying to deliver a safe, affordable, and sustainable long-range capability for entirely new missions opening a new realm of knowledge and a world of possibilities for multiple partners. Design reference missions that the SLS is being planned to support include asteroids, Lagrange Points, and Mars, among others. The Agency is developing its mission manifest in parallel with the development of a heavy-lift flagship that will dramatically increase total lift and volume capacity beyond current launch vehicle options, reduce trip times, and provide a robust platform for conducting new missions destined to rewrite textbooks with the information they deliver, while creating a framework for further collaboration among domestic and international partners, and potentially spurring economic expansion into new markets.

Graphical techniques to assist in pointing and control studies of orbiting spacecraft

NASA Technical Reports Server (NTRS)

Howell, L. W.; Ruf, J. H.

1986-01-01

Computer generated graphics are developed to assist in the modeling and assessment of pointing and control systems of orbiting spacecraft. Three-dimensional diagrams are constructed of the Earth and of geometrical models which resemble the spacecraft of interest. Orbital positioning of the spacecraft model relative to the Earth and the orbital ground track are then displayed. A star data base is also available which may be used for telescope pointing and star tracker field-of-views to visually assist in spacecraft pointing and control studies. A geometrical model of the Hubble Space Telescope (HST) is constructed and placed in Earth orbit to demonstrate the use of these programs. Simulated star patterns are then displayed corresponding to the primary mirror's FOV and the telescope's star trackers for various telescope orientations with respect to the celestial sphere.

Closeup view of the Reinforced CarbonCarbon nose cap on the ...

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

Close-up view of the Reinforced Carbon-Carbon nose cap on the front fuselage of the Orbiter Discovery. Note the 76-wheeled orbiter transfer system attached to the orbiter at the forward attach point, the same attach point used to mount the orbiter onto the External Tank. This view was taken at Kennedy Space Center. - Space Transportation System, Orbiter Discovery (OV-103), Lyndon B. Johnson Space Center, 2101 NASA Parkway, Houston, Harris County, TX

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.

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.

Exoplanet Caught on the Move

NASA Astrophysics Data System (ADS)

2010-06-01

For the first time, astronomers have been able to directly follow the motion of an exoplanet as it moves from one side of its host star to the other. The planet has the smallest orbit so far of all directly imaged exoplanets, lying almost as close to its parent star as Saturn is to the Sun. Scientists believe that it may have formed in a similar way to the giant planets in the Solar System. Because the star is so young, this discovery proves that gas giant planets can form within discs in only a few million years, a short time in cosmic terms. Only 12 million years old, or less than three-thousandths of the age of the Sun, Beta Pictoris is 75% more massive than our parent star. It is located about 60 light-years away towards the constellation of Pictor (the Painter) and is one of the best-known examples of a star surrounded by a dusty debris disc [1]. Earlier observations showed a warp of the disc, a secondary inclined disc and comets falling onto the star. "Those were indirect, but tell-tale signs that strongly suggested the presence of a massive planet, and our new observations now definitively prove this," says team leader Anne-Marie Lagrange. "Because the star is so young, our results prove that giant planets can form in discs in time-spans as short as a few million years." Recent observations have shown that discs around young stars disperse within a few million years, and that giant planet formation must occur faster than previously thought. Beta Pictoris is now clear proof that this is indeed possible. The team used the NAOS-CONICA instrument (or NACO [2]), mounted on one of the 8.2-metre Unit Telescopes of ESO's Very Large Telescope (VLT), to study the immediate surroundings of Beta Pictoris in 2003, 2008 and 2009. In 2003 a faint source inside the disc was seen (eso0842), but it was not possible to exclude the remote possibility that it was a background star. In new images taken in 2008 and spring 2009 the source had disappeared! The most recent observations, taken during autumn 2009, revealed the object on the other side of the disc after a period of hiding either behind or in front of the star (in which case it is hidden in the glare of the star). This confirmed that the source indeed was an exoplanet and that it was orbiting its host star. It also provided insights into the size of its orbit around the star. Images are available for approximately ten exoplanets, and the planet around Beta Pictoris (designated "Beta Pictoris b") has the smallest orbit known so far. It is located at a distance between 8 and 15 times the Earth-Sun separation - or 8-15 Astronomical Units - which is about the distance of Saturn from the Sun. "The short period of the planet will allow us to record the full orbit within maybe 15-20 years, and further studies of Beta Pictoris b will provide invaluable insights into the physics and chemistry of a young giant planet's atmosphere," says student researcher Mickael Bonnefoy. The planet has a mass of about nine Jupiter masses and the right mass and location to explain the observed warp in the inner parts of the disc. This discovery therefore bears some similarity to the prediction of the existence of Neptune by astronomers Adams and Le Verrier in the 19th century, based on observations of the orbit of Uranus. "Together with the planets found around the young, massive stars Fomalhaut and HR8799, the existence of Beta Pictoris b suggests that super-Jupiters could be frequent byproducts of planet formation around more massive stars," explains Gael Chauvin, a member of the team. Such planets disturb the discs around their stars, creating structures that should be readily observable with the Atacama Large Millimeter/submillimeter Array (ALMA), the revolutionary telescope being built by ESO together with international partners. A few other planetary candidates have been imaged, but they are all located further from their host star than Beta Pictoris b. If located in the Solar System, they all would lie close to or beyond the orbit of the furthest planet, Neptune. The formation processes of these distant planets are likely to be quite different from those in our Solar System and in Beta Pictoris. "The recent direct images of exoplanets - many made by the VLT - illustrate the diversity of planetary systems," says Lagrange. "Among those, Beta Pictoris b is the most promising case of a planet that could have formed in the same way as the giant planets in our Solar System." Notes [1] Debris discs are composed of dust resulting from collisions among larger bodies such as planetary embryos or asteroids. They are larger versions of the zodiacal dust band in our Solar System. The disc around Beta Pictoris was the first to be imaged and is now known to extend up to about 1000 times the distance between the Earth and the Sun. [2] NACO is an adaptive optics instrument attached to ESO's Very Large Telescope, located in Chile. Thanks to adaptive optics, astronomers can remove most of the blurring effect of the atmosphere and obtain very sharp images. More information This research was presented in a paper to appear this week in Science Express ("A Giant Planet Imaged in the disk of the Young Star Beta Pictoris," by A.-M. Lagrange et al.). The team is composed of A.-M. Lagrange, M. Bonnefoy, G. Chauvin, D. Ehrenreich, and D. Mouillet (Laboratoire d'Astrophysique de l'Observatoire de Grenoble, Université Joseph Fourier, CNRS, France), D. Apai (Space Telescope Science Institute, Baltimore, USA), A. Boccaletti, D. Gratadour, D. Rouan, and S. Lacour (LESIA, Observatoire de Paris-Meudon, France), and M. Kasper (ESO). ESO, the European Southern Observatory, is the foremost intergovernmental astronomy organisation in Europe and the world's most productive astronomical observatory. It is supported by 14 countries: Austria, Belgium, the Czech Republic, Denmark, France, Finland, Germany, Italy, the Netherlands, Portugal, Spain, Sweden, Switzerland and the United Kingdom. ESO carries out an ambitious programme focused on the design, construction and operation of powerful ground-based observing facilities enabling astronomers to make important scientific discoveries. ESO also plays a leading role in promoting and organising cooperation in astronomical research. ESO operates three unique world-class observing sites in Chile: La Silla, Paranal and Chajnantor. At Paranal, ESO operates the Very Large Telescope, the world's most advanced visible-light astronomical observatory and VISTA, the world's largest survey telescope. ESO is the European partner of a revolutionary astronomical telescope ALMA, the largest astronomical project in existence. ESO is currently planning a 42-metre European Extremely Large optical/near-infrared Telescope, the E-ELT, which will become "the world's biggest eye on the sky".

The Space Shuttle orbiter payload retention systems

NASA Technical Reports Server (NTRS)

Hardee, J. H.

1982-01-01

Payloads are secured in the orbiter payload bay by the payload retention system or are equipped with their own unique retention systems. The orbiter payload retention mechanisms provide structural attachments for each payload by using four or five attachment points to secure the payload within the orbiter payload bay during all phases of the orbiter mission. The payload retention system (PRS) is an electromechanical system that provides standarized payload carrier attachment fittings to accommodate up to five payloads for each orbiter flight. The mechanisms are able to function under either l-g or zero-g conditions. Payload berthing or deberthing on orbit is accomplished by utilizing the remote manipulator system (RMS). The retention mechanisms provide the capability for either vertical or horizontal payload installation or removal. The payload support points are selected to minimize point torsional, bending, and radial loads imparted to the payloads. In addition to the remotely controlled latching system, the passive system used for nondeployable payloads performs the same function as the RMS except it provides fixed attachments to the orbiter.

Orbital stability close to asteroid 624 Hektor using the polyhedral model

NASA Astrophysics Data System (ADS)

Jiang, Yu; Baoyin, Hexi; Li, Hengnian

2018-03-01

We investigate the orbital stability close to the unique L4-point Jupiter binary Trojan asteroid 624 Hektor. The gravitational potential of 624 Hektor is calculated using the polyhedron model with observational data of 2038 faces and 1021 vertexes. Previous studies have presented three different density values for 624 Hektor. The equilibrium points in the gravitational potential of 624 Hektor with different density values have been studied in detail. There are five equilibrium points in the gravitational potential of 624 Hektor no matter the density value. The positions, Jacobian, eigenvalues, topological cases, stability, as well as the Hessian matrix of the equilibrium points are investigated. For the three different density values the number, topological cases, and the stability of the equilibrium points with different density values are the same. However, the positions of the equilibrium points vary with the density value of the asteroid 624 Hektor. The outer equilibrium points move away from the asteroid's mass center when the density increases, and the inner equilibrium point moves close to the asteroid's mass center when the density increases. There exist unstable periodic orbits near the surface of 624 Hektor. We calculated an orbit near the primary's equatorial plane of this binary Trojan asteroid; the results indicate that the orbit remains stable after 28.8375 d.

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

Conceptual Design of a Synoptic Interplanetary Monitor Platform at L sub 1 (SIMPL).

DTIC Science & Technology

1985-11-01

solar events. -159- . . . .. . 105 II1II" -I .5 year mission at Earth-Sun- libration point plus transfer orbit eDashed line is approximate true dose as...Design .. ...................................... 27 4.1 The L Libration Point .......................... 27 4.2 L Orbit Options...34) to provide power, attitude control, communications, and other support to maintain the instruments in a halo orbit around the L libration point ; 4. a

Higher order approximation to the Hill problem dynamics about the libration points

NASA Astrophysics Data System (ADS)

Lara, Martin; Pérez, Iván L.; López, Rosario

2018-06-01

An analytical solution to the Hill problem Hamiltonian expanded about the libration points has been obtained by means of perturbation techniques. In order to compute the higher orders of the perturbation solution that are needed to capture all the relevant periodic orbits originated from the libration points within a reasonable accuracy, the normalization is approached in complex variables. The validity of the solution extends to energy values considerably far away from that of the libration points and, therefore, can be used in the computation of Halo orbits as an alternative to the classical Lindstedt-Poincaré approach. Furthermore, the theory correctly predicts the existence of the two-lane bridge of periodic orbits linking the families of planar and vertical Lyapunov orbits.

Steady Motions of Rigid Body Satellites in a Central Gravitational Field

DTIC Science & Technology

1993-12-01

been explored for several centuries. Orbiting bodies investigated include point masses, spheres, cylinders, rods, ball-and-socket connected objects...of the satellite model relative to its orbit radius could lead to 5 its treatment as a point mass, doing so would prevent analysis of satellite...8217 librational ’ motion ... and internal elastic forces in the structure balance the orbital dynamic accelerations tending to separate masses orbiting at

Program manual for HILTOP, a heliocentric interplanetary low thrust trajectory optimization program. Part 1: User's guide

NASA Technical Reports Server (NTRS)

Mann, F. I.; Horsewood, J. L.

1974-01-01

A performance-analysis computer program, that was developed explicitly to generate optimum electric propulsion trajectory data for missions of interest in the exploration of the solar system is presented. The program was primarily designed to evaluate the performance capabilities of electric propulsion systems, and in the simulation of a wide variety of interplanetary missions. A numerical integration of the two-body, three-dimensional equations of motion and the Euler-Lagrange equations was used in the program. Transversality conditions which permit the rapid generation of converged maximum-payload trajectory data, and the optimization of numerous other performance indices for which no transversality conditions exist are included. The ability to simulate constrained optimum solutions, including trajectories having specified propulsion time and constant thrust cone angle, is also in the program. The program was designed to handle multiple-target missions with various types of encounters, such as rendezvous, stopover, orbital capture, and flyby. Performance requirements for a variety of launch vehicles can be determined.

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

Suryanarayana, Phanish, E-mail: phanish.suryanarayana@ce.gatech.edu; Phanish, Deepa

We present an Augmented Lagrangian formulation and its real-space implementation for non-periodic Orbital-Free Density Functional Theory (OF-DFT) calculations. In particular, we rewrite the constrained minimization problem of OF-DFT as a sequence of minimization problems without any constraint, thereby making it amenable to powerful unconstrained optimization algorithms. Further, we develop a parallel implementation of this approach for the Thomas–Fermi–von Weizsacker (TFW) kinetic energy functional in the framework of higher-order finite-differences and the conjugate gradient method. With this implementation, we establish that the Augmented Lagrangian approach is highly competitive compared to the penalty and Lagrange multiplier methods. Additionally, we show that higher-ordermore » finite-differences represent a computationally efficient discretization for performing OF-DFT simulations. Overall, we demonstrate that the proposed formulation and implementation are both efficient and robust by studying selected examples, including systems consisting of thousands of atoms. We validate the accuracy of the computed energies and forces by comparing them with those obtained by existing plane-wave methods.« less

Unveiling the proton spin decomposition at a future electron-ion collider

DOE PAGES

Aschenauer, Elke C.; Sassot, Rodolfo; Stratmann, Marco

2015-11-24

We present a detailed assessment of how well a future electron-ion collider could constrain helicity parton distributions in the nucleon and, therefore, unveil the role of the intrinsic spin of quarks and gluons in the proton’s spin budget. Any remaining deficit in this decomposition will provide the best indirect constraint on the contribution due to the total orbital angular momenta of quarks and gluons. Specifically, all our studies are performed in the context of global QCD analyses based on realistic pseudodata and in the light of the most recent data obtained from polarized proton-proton collisions at BNL-RHIC that have providedmore » evidence for a significant gluon polarization in the accessible, albeit limited range of momentum fractions. We also present projections on what can be achieved on the gluon’s helicity distribution by the end of BNL-RHIC operations. As a result, all estimates of current and projected uncertainties are performed with the robust Lagrange multiplier technique.« less

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.

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.

In-Flight Guidance, Navigation, and Control Performance Results for the GOES-16 Spacecraft

NASA Technical Reports Server (NTRS)

Chapel, Jim; Stancliffe, Devin; Bevacqua, Tim; Winkler, Stephen; Clapp, Brian; Rood, Tim; Freesland, Doug; Reth, Alan; Early, Derrick; Walsh, Tim;

Keeping a Spacecraft on the Sun-Earth Line

NASA Technical Reports Server (NTRS)

Roithmayr, Carlos M.; Kay-Bunnell, Linda

2005-01-01

Measurements of Earth's atmosphere as it occults sunlight can be obtained advantageously from a spacecraft placed in the proximity of the Sun-Earth Lagrange point L2. Maintaining the condition of continuous solar occultation by all parts of the atmospheric disk requires that the displacement of the spacecraft perpendicular to the Sun-Earth line remains less than 200 km. However, the gravitational force exerted by the Earth s moon must be negated by propulsion in order to meet this rather tight constraint. We provide an estimate of propulsive force needed to keep the spacecraft coincident with L2, as well as estimates of velocity increments needed to maintain various trajectories in the close vicinity of L2.

Low Energy Transfer to the Moon

NASA Astrophysics Data System (ADS)

Koon, W. S.; Lo, M. W.; Marsden, J. E.; Ross, S. D.

In 1991, the Japanese Hiten mission used a low energy transfer with a ballistic capture at the Moon which required less Δ V than a standard Hohmann transfer. In this paper, we apply the dynamical systems techniques developed in our earlier work to reproduce systematically a Hiten-like mission. We approximate the Sun-Earth-Moon-spacecraft 4-body system as two 3-body systems. Using the invariant manifold structures of the Lagrange points of the 3-body systems, we are able to construct low energy transfer trajectories from the Earth which execute ballistic capture at the Moon. The techniques used in the design and construction of this trajectory may be applied in many situations.

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.

The research of the coupled orbital-attitude controlled motion of celestial body in the neighborhood of the collinear libration point L1

NASA Astrophysics Data System (ADS)

Shmyrov, A.; Shmyrov, V.; Shymanchuk, D.

2017-10-01

This article considers the motion of a celestial body within the restricted three-body problem of the Sun-Earth system. The equations of controlled coupled attitude-orbit motion in the neighborhood of collinear libration point L1 are investigated. The translational orbital motion of a celestial body is described using Hill's equations of circular restricted three-body problem of the Sun-Earth system. Rotational orbital motion is described using Euler's dynamic equations and quaternion kinematic equation. We investigate the problem of stability of celestial body rotational orbital motion in relative equilibrium positions and stabilization of celestial body rotational orbital motion with proposed control laws in the neighborhood of collinear libration point L1. To study stabilization problem, Lyapunov function is constructed in the form of the sum of the kinetic energy and special "kinematic function" of the Rodriguez-Hamiltonian parameters. Numerical modeling of the controlled rotational motion of a celestial body at libration point L1 is carried out. The numerical characteristics of the control parameters and rotational motion are given.

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.

Continuation of periodic orbits in the Sun-Mercury elliptic restricted three-body problem

NASA Astrophysics Data System (ADS)

Peng, Hao; Bai, Xiaoli; Xu, Shijie

2017-06-01

Starting from resonant Halo orbits in the Circular Restricted Three-Body Problem (CRTBP), Multi-revolution Elliptic Halo (ME-Halo) orbits around L1 and L2 points in the Sun-Mercury Elliptic Restricted Three-Body Problem (ERTBP) are generated systematically. Three pairs of resonant parameters M5N2, M7N3 and M9N4 are tested. The first pair shows special features and is investigated in detail. Three separated characteristic curves of periodic orbit around each libration point are obtained, showing the eccentricity varies non-monotonically along these curves. The eccentricity of the Sun-Mercury system can be achieved by continuation method in just a few cases. The stability analysis shows that these orbits are all unstable and the complex instability occurs with certain parameters. This paper shows new periodic orbits in both the CRTBP and the ERTBP. Totally four periodic orbits with parameters M5N2 around each libration points are extracted in the Sun-Mercury ERTBP.

Communication: Photoionization of degenerate orbitals for randomly oriented molecules: The effect of time-reversal symmetry on recoil-ion momentum angular distributions

NASA Astrophysics Data System (ADS)

Suzuki, Yoshi-Ichi

2018-04-01

The photoelectron asymmetry parameter β, which characterizes the direction of electrons ejected from a randomly oriented molecular ensemble by linearly polarized light, is investigated for degenerate orbitals. We show that β is totally symmetric under the symmetry operation of the point group of a molecule, and it has mixed properties under time reversal. Therefore, all degenerate molecular orbitals, except for the case of degeneracy due to time reversal, have the same β (Wigner-Eckart theorem). The exceptions are e-type complex orbitals of the Cn, Sn, Cnh, T, and Th point groups, and calculations on boric acid (C3h symmetry) are performed as an example. However, including those point groups, all degenerate orbitals have the same β if those orbitals are real. We discuss the implications of this operator formalism for molecular alignment and photoelectron circular dichroism.

Evaluation of use of MPAD trajectory tape and number of orbit points for orbiter mission thermal predictions

NASA Technical Reports Server (NTRS)

Vogt, R. A.

1979-01-01

The application of using the mission planning and analysis division (MPAD) common format trajectory data tape to predict temperatures for preflight and post flight mission analysis is presented and evaluated. All of the analyses utilized the latest Space Transportation System 1 flight (STS-1) MPAD trajectory tape, and the simplified '136 note' midsection/payload bay thermal math model. For the first 6.7 hours of the STS-1 flight profile, transient temperatures are presented for selected nodal locations with the current standard method, and the trajectory tape method. Whether the differences are considered significant or not depends upon the view point. Other transient temperature predictions are also presented. These results were obtained to investigate an initial concern that perhaps the predicted temperature differences between the two methods would not only be caused by the inaccuracies of the current method's assumed nominal attitude profile but also be affected by a lack of a sufficient number of orbit points in the current method. Comparison between 6, 12, and 24 orbit point parameters showed a surprising insensitivity to the number of orbit points.

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.

Elimination of secular terms from the differential equations for the elements of perturbed two-body motion

NASA Technical Reports Server (NTRS)

Bond, Victor R.; Fraietta, Michael F.

1991-01-01

In 1961, Sperling linearized and regularized the differential equations of motion of the two-body problem by changing the independent variable from time to fictitious time by Sundman's transformation (r = dt/ds) and by embedding the two-body energy integral and the Laplace vector. In 1968, Burdet developed a perturbation theory which was uniformly valid for all types of orbits using a variation of parameters approach on the elements which appeared in Sperling's equations for the two-body solution. In 1973, Bond and Hanssen improved Burdet's set of differential equations by embedding the total energy (which is a constant when the potential function is explicitly dependent upon time.) The Jacobian constant was used as an element to replace the total energy in a reformulation of the differential equations of motion. In the process, another element which is proportional to a component of the angular momentum was introduced. Recently trajectories computed during numerical studies of atmospheric entry from circular orbits and low thrust beginning in near-circular orbits exhibited numerical instability when solved by the method of Bond and Gottlieb (1989) for long time intervals. It was found that this instability was due to secular terms which appear on the righthand sides of the differential equations of some of the elements. In this paper, this instability is removed by the introduction of another vector integral called the delta integral (which replaces the Laplace Vector) and another scalar integral which removes the secular terms. The introduction of these integrals requires a new derivation of the differential equations for most of the elements. For this rederivation, the Lagrange method of variation of parameters is used, making the development more concise. Numerical examples of this improvement are presented.

ASPS performance with large payloads onboard the Shuttle Orbiter. [Annular Suspension and Pointing System

NASA Technical Reports Server (NTRS)

Keckler, C. R.

1980-01-01

A high fidelity digital computer simulation was used to establish the viability of the Annular Suspension and Pointing System (ASPS) for satisfying the pointing and stability requirements of facility class payloads, such as the Solar Optical Telescope, when subjected to the Orbiter disturbance environment. The ASPS and its payload were subjected to disturbances resulting from crew motions in the Orbiter aft flight deck and VRCS thruster firings. Worst case pointing errors of 0.005 arc seconds were experienced under the disturbance environment simulated; this is well within the 0.08 arc seconds requirement specified by the payload.

The structure of non-hierarchical triple system stability regions

NASA Astrophysics Data System (ADS)

Martynova, A. I.; Orlov, V. V.; Rubinov, A. V.

2009-08-01

A detailed study of the two-dimensional initial conditions region section in the planar three-body problem is performed. The initial conditions for the three well-known stable periodic orbits (the Schubart’s orbit, the Broucke’s orbit and the eight-like orbit) belong to this section. Continuous stability regions (for the fixed integration interval) generated by these periodic orbits are found. Zones of the quick stability violation are outlined. The analysis of some concrete trajectories coming from various stability regions is performed. In particular, trajectories possessing varying number of “eights” formed by moving triple system components are discovered. Orbits with librations are also found. The new periodic orbit originated from the zone siding with the Schubart’s orbit region is discovered. This orbit has reversibility points (each of the outer bodies possess a reversibility point) and two points of close double approach of the central body to each of the outer bodies. The influence of the numerical integration accuracy on the results is studied. The stability regions structure is preserved during calculations with different values of the precision parameter, numerical integration methods and regularization algorithms of the equations of motion.

Orbit Determination Error Analysis Results for the Triana Sun-Earth L2 Libration Point Mission

NASA Technical Reports Server (NTRS)

Marr, G.

2003-01-01

Using the NASA Goddard Space Flight Center's Orbit Determination Error Analysis System (ODEAS), orbit determination error analysis results are presented for all phases of the Triana Sun-Earth L1 libration point mission and for the science data collection phase of a future Sun-Earth L2 libration point mission. The Triana spacecraft was nominally to be released by the Space Shuttle in a low Earth orbit, and this analysis focuses on that scenario. From the release orbit a transfer trajectory insertion (TTI) maneuver performed using a solid stage would increase the velocity be approximately 3.1 km/sec sending Triana on a direct trajectory to its mission orbit. The Triana mission orbit is a Sun-Earth L1 Lissajous orbit with a Sun-Earth-vehicle (SEV) angle between 4.0 and 15.0 degrees, which would be achieved after a Lissajous orbit insertion (LOI) maneuver at approximately launch plus 6 months. Because Triana was to be launched by the Space Shuttle, TTI could potentially occur over a 16 orbit range from low Earth orbit. This analysis was performed assuming TTI was performed from a low Earth orbit with an inclination of 28.5 degrees and assuming support from a combination of three Deep Space Network (DSN) stations, Goldstone, Canberra, and Madrid and four commercial Universal Space Network (USN) stations, Alaska, Hawaii, Perth, and Santiago. These ground stations would provide coherent two-way range and range rate tracking data usable for orbit determination. Larger range and range rate errors were assumed for the USN stations. Nominally, DSN support would end at TTI+144 hours assuming there were no USN problems. Post-TTI coverage for a range of TTI longitudes for a given nominal trajectory case were analyzed. The orbit determination error analysis after the first correction maneuver would be generally applicable to any libration point mission utilizing a direct trajectory.

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.

Integration of Libration Point Orbit Dynamics into a Universal 3-D Autonomous Formation Flying Algorithm

NASA Technical Reports Server (NTRS)

Folta, David; Bauer, Frank H. (Technical Monitor)

2001-01-01

The autonomous formation flying control algorithm developed by the Goddard Space Flight Center (GSFC) for the New Millennium Program (NMP) Earth Observing-1 (EO-1) mission is investigated for applicability to libration point orbit formations. In the EO-1 formation-flying algorithm, control is accomplished via linearization about a reference transfer orbit with a state transition matrix (STM) computed from state inputs. The effect of libration point orbit dynamics on this algorithm architecture is explored via computation of STMs using the flight proven code, a monodromy matrix developed from a N-body model of a libration orbit, and a standard STM developed from the gravitational and coriolis effects as measured at the libration point. A comparison of formation flying Delta-Vs calculated from these methods is made to a standard linear quadratic regulator (LQR) method. The universal 3-D approach is optimal in the sense that it can be accommodated as an open-loop or closed-loop control using only state information.

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

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.

Use of libration-point orbits for space observatories

NASA Technical Reports Server (NTRS)

Farquhar, Robert W.; Dunham, David W.

1990-01-01

The sun-earth libration points, L1 and L2, are located 1.5 million kilometers from the earth toward and away from the sun. Halo orbits about these points have significant advantages for space observatories in terms of viewing geometry, thermal and radiation environment, and delta-V expediture.

Early Mission Maneuver Operations for the Deep Space Climate Observatory Sun-Earth L1 Libration Point Mission

NASA Technical Reports Server (NTRS)

Roberts, Craig; Case, Sara; Reagoso, John; Webster, Cassandra

2015-01-01

The Deep Space Climate Observatory mission launched on February 11, 2015, and inserted onto a transfer trajectory toward a Lissajous orbit around the Sun-Earth L1 libration point. This paper presents an overview of the baseline transfer orbit and early mission maneuver operations leading up to the start of nominal science orbit operations. In particular, the analysis and performance of the spacecraft insertion, mid-course correction maneuvers, and the deep-space Lissajous orbit insertion maneuvers are discussed, com-paring the baseline orbit with actual mission results and highlighting mission and operations constraints..

Trajectory Design Strategies for the NGST L2 Libration Point Mission

NASA Technical Reports Server (NTRS)

Folta, David; Cooley, Steven; Howell, Kathleen; Bauer, Frank H.

2001-01-01

The Origins' Next Generation Space Telescope (NGST) trajectory design is addressed in light of improved methods for attaining constrained orbit parameters and their control at the exterior collinear libration point, L2. The use of a dynamical systems approach, state-space equations for initial libration orbit control, and optimization to achieve constrained orbit parameters are emphasized. The NGST trajectory design encompasses a direct transfer and orbit maintenance under a constant acceleration. A dynamical systems approach can be used to provide a biased orbit and stationkeeping maintenance method that incorporates the constraint of a single axis correction scheme.

The topology of the regularized integral surfaces of the 3-body problem

NASA Technical Reports Server (NTRS)

Easton, R.

1971-01-01

Momentum, angular momentum, and energy of integral surfaces in the planar three-body problem are considered. The end points of orbits which cross an isolating block are identified. It is shown that this identification has a unique extension to an identification which pairs the end points of orbits entering the block and which end in a binary collision with the end points of orbits leaving the block and which come from a binary collision. The problem of regularization is that of showing that the identification of the end points of crossing orbits has a continuous, unique extension. The regularized phase space for the three-body problem was obtained, as were regularized integral surfaces for the problem on which the three-body equations of motion induce flows. Finally the topology of these surfaces is described.

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

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.

Sun-Earth L1 Region Halo-To-Halo Orbit and Halo-To-LisaJous Orbit Transfers

NASA Technical Reports Server (NTRS)

Roberts, Craig E.; DeFazio, Robert

2004-01-01

Practical techniques for designing transfer trajectories between Libration Point Orbits (LPOs) are presented. Motivation for development of these techniques was provided by a hardware contingency experienced by the Solar Heliospheric Observatory (SOHO), a joint mission of the European Space Agency (ESA) and the National Aeronautics and Space Administration (NASA) orbiting the L1 point of the Sun-Earth system. A potential solution to the problem involved a transfer from SOHO s periodic halo orbit to a new LPO of substantially different dimensions. Assuming the SOHO halo orbit as the departure orbit, several practical LPO transfer techniques were developed to obtain new Lissajous or periodic halo orbits that satisfy mission requirements and constraints. While not implemented for the SOHO mission, practical LPO transfer techniques were devised that are generally applicable to current and future LPO missions.

NIAC Phase II Orbiting Rainbows: Future Space Imaging with Granular Systems

NASA Technical Reports Server (NTRS)

Quadrelli, Marco B.; Basinger, Scott; Arumugam, Darmindra; Swartzlander, Grover

2017-01-01

Inspired by the light scattering and focusing properties of distributed optical assemblies in Nature, such as rainbows and aerosols, and by recent laboratory successes in optical trapping and manipulation, we propose a unique combination of space optics and autonomous robotic system technology, to enable a new vision of space system architecture with applications to ultra-lightweight space optics and, ultimately, in-situ space system fabrication. Typically, the cost of an optical system is driven by the size and mass of the primary aperture. The ideal system is a cloud of spatially disordered dust-like objects that can be optically manipulated: it is highly reconfigurable, fault-tolerant, and allows very large aperture sizes at low cost. This new concept is based on recent understandings in the physics of optical manipulation of small particles in the laboratory and the engineering of distributed ensembles of spacecraft swarms to shape an orbiting cloud of micron-sized objects. In the same way that optical tweezers have revolutionized micro- and nano-manipulation of objects, our breakthrough concept will enable new large scale NASA mission applications and develop new technology in the areas of Astrophysical Imaging Systems and Remote Sensing because the cloud can operate as an adaptive optical imaging sensor. While achieving the feasibility of constructing one single aperture out of the cloud is the main topic of this work, it is clear that multiple orbiting aerosol lenses could also combine their power to synthesize a much larger aperture in space to enable challenging goals such as exo-planet detection. Furthermore, this effort could establish feasibility of key issues related to material properties, remote manipulation, and autonomy characteristics of cloud in orbit. There are several types of endeavors (science missions) that could be enabled by this type of approach, i.e. it can enable new astrophysical imaging systems, exo-planet search, large apertures allow for unprecedented high resolution to discern continents and important features of other planets, hyperspectral imaging, adaptive systems, spectroscopy imaging through limb, and stable optical systems from Lagrange-points. Furthermore, future micro-miniaturization might hold promise of a further extension of our dust aperture concept to other more exciting smart dust concepts with other associated capabilities. Our objective in Phase II was to experimentally and numerically investigate how to optically manipulate and maintain the shape of an orbiting cloud of dust-like matter so that it can function as an adaptable ultra-lightweight surface. Our solution is based on the aperture being an engineered granular medium, instead of a conventional monolithic aperture. This allows building of apertures at a reduced cost, enables extremely fault-tolerant apertures that cannot otherwise be made, and directly enables classes of missions for exoplanet detection based on Fourier spectroscopy with tight angular resolution and innovative radar systems for remote sensing. In this task, we have examined the advanced feasibility of a crosscutting concept that contributes new technological approaches for space imaging systems, autonomous systems, and space applications of optical manipulation. The proposed investigation has matured the concept that we started in Phase I to TRL 3, identifying technology gaps and candidate system architectures for the space-borne cloud as an aperture.

Orbital loop currents in iron-based superconductors

NASA Astrophysics Data System (ADS)

Klug, Markus; Kang, Jian; Fernandes, Rafael M.; Schmalian, Jörg

2018-04-01

We show that the antiferromagnetic state commonly observed in the phase diagrams of the iron-based superconductors necessarily triggers loop currents characterized by charge transfer between different Fe 3 d orbitals. This effect is rooted on the glide-plane symmetry of these materials and on the existence of an atomic spin-orbit coupling that couples states at the X and Y points of the 1-Fe Brillouin zone. In the particular case in which the magnetic moments are aligned parallel to the magnetic ordering vector direction, which is the moment configuration most commonly found in the iron-based superconductors, these loop currents involve the dx y orbital and either the dy z orbital (if the moments point along the y axis) or the dx z orbitals (if the moments point along the x axis). We show that the two main manifestations of the orbital loop currents are the emergence of magnetic moments in the pnictide/chalcogen site and an orbital-selective band splitting in the magnetically ordered state, both of which could be detected experimentally. Our results highlight the unique intertwining between orbital and spin degrees of freedom in the iron-based superconductors, and reveal the emergence of an unusual correlated phase that may impact the normal state and superconducting properties of these materials.

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.

Spaceflight mechanics 1992; Proceedings of the 2nd AAS/AIAA Meeting, Colorado Springs, CO, Feb. 24-26, 1992. Pts. 1 & 2

NASA Astrophysics Data System (ADS)

Diehl, Roger E.; Schinnerer, Ralph G.; Williamson, Walton E.; Boden, Daryl G.

The present conference discusses topics in orbit determination, tethered satellite systems, celestial mechanics, guidance optimization, flexible body dynamics and control, attitude dynamics and control, Mars mission analyses, earth-orbiting mission analysis/debris, space probe mission analyses, and orbital computation numerical analyses. Attention is given to electrodynamic forces for control of tethered satellite systems, orbiting debris threats to asteroid flyby missions, launch velocity requirements for interceptors of short range ballistic missiles, transfers between libration-point orbits in the elliptic restricted problem, minimum fuel spacecraft reorientation, orbital guidance for hitting a fixed point at maximum speed, efficient computation of satellite visibility periods, orbit decay and reentry prediction for space debris, and the determination of satellite close approaches.

Spaceflight mechanics 1992; Proceedings of the 2nd AAS/AIAA Meeting, Colorado Springs, CO, Feb. 24-26, 1992. Pts. 1 & 2

NASA Technical Reports Server (NTRS)

Diehl, Roger E. (Editor); Schinnerer, Ralph G. (Editor); Williamson, Walton E. (Editor); Boden, Daryl G. (Editor)

1992-01-01

The present conference discusses topics in orbit determination, tethered satellite systems, celestial mechanics, guidance optimization, flexible body dynamics and control, attitude dynamics and control, Mars mission analyses, earth-orbiting mission analysis/debris, space probe mission analyses, and orbital computation numerical analyses. Attention is given to electrodynamic forces for control of tethered satellite systems, orbiting debris threats to asteroid flyby missions, launch velocity requirements for interceptors of short range ballistic missiles, transfers between libration-point orbits in the elliptic restricted problem, minimum fuel spacecraft reorientation, orbital guidance for hitting a fixed point at maximum speed, efficient computation of satellite visibility periods, orbit decay and reentry prediction for space debris, and the determination of satellite close approaches.

Space Shuttle Earth Observation sensors pointing and stabilization requirements study

NASA Technical Reports Server (NTRS)

1976-01-01

The shuttle orbiter inertial measurement unit (IMU), located in the orbiter cabin, is used to supply inertial attitude reference signals; and, in conjunction with the onboard navigation system, can provide a pointing capability of the navigation base accurate to within plus or minus 0.5 deg for earth viewing missions. This pointing accuracy can degrade to approximately plus or minus 2.0 deg for payloads located in the aft bay due to structural flexure of the shuttle vehicle, payload structural and mounting misalignments, and calibration errors with respect to the navigation base. Drawbacks to obtaining pointing accuracy by using the orbiter RCS jets are discussed. Supplemental electromechanical pointing systems are developed to provide independent pointing for individual sensors, or sensor groupings. The missions considered and the sensors required for these missions and the parameters of each sensor are described. Assumptions made to derive pointing and stabilization requirements are delineated.

A Chang'e-4 mission concept and vision of future Chinese lunar exploration activities

NASA Astrophysics Data System (ADS)

Wang, Qiong; Liu, Jizhong

2016-10-01

A novel concept for Chinese Chang'e-4 lunar exploration mission is presented in this paper at first. After the success of Chang'e-3, its backup probe, Chang'e-4 lander/rover combination, would be upgraded and land on the unexplored lunar farside by the aid of a relay satellite near the second Earth-Moon Lagrange point. Mineralogical and geochemical surveys on the farside to study the formation and evolution of lunar crust and observations at low radio frequencies to track the signals of the Universe's Dark Ages are priorities. Follow-up Chinese lunar exploration activities before 2030 are envisioned as building a robotic lunar science station by three to five missions. Finally several methods of international cooperation are proposed.

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.

Optimization of Insertion Cost for Transfer Trajectories to Libration Point Orbits

NASA Technical Reports Server (NTRS)

Howell, K. C.; Wilson, R. S.; Lo, M. W.

1999-01-01

The objective of this work is the development of efficient techniques to optimize the cost associated with transfer trajectories to libration point orbits in the Sun-Earth-Moon four body problem, that may include lunar gravity assists. Initially, dynamical systems theory is used to determine invariant manifolds associated with the desired libration point orbit. These manifolds are employed to produce an initial approximation to the transfer trajectory. Specific trajectory requirements such as, transfer injection constraints, inclusion of phasing loops, and targeting of a specified state on the manifold are then incorporated into the design of the transfer trajectory. A two level differential corrections process is used to produce a fully continuous trajectory that satisfies the design constraints, and includes appropriate lunar and solar gravitational models. Based on this methodology, and using the manifold structure from dynamical systems theory, a technique is presented to optimize the cost associated with insertion onto a specified libration point orbit.

On the use of a sunward libration-point-orbiting spacecraft as an interplanetary magnetic field monitor for magnetospheric studies

NASA Technical Reports Server (NTRS)

Kelly, T. J.; Crooker, N. U.; Siscoe, G. L.; Russell, C. T.; Smith, E. J.

1986-01-01

In order to test the accuracy of using magnetometer data from a spacecraft orbiting the sunward libration point to determine the orientation of the interplanetary magnetic field (IMF), the angle between the IMF at ISEE 3, when it was positioned around the libration point, and at ISEE 1, orbiting the earth, has been calculated for a data set of 1-hour periods covering four months. For each period, a 10-minute average of ISEE 1 data is compared with 10-minute averages of ISEE 3 data at successively lagged intervals. It is concluded that the IMF orientation at a libration-point-orbiting spacecraft, lagged by the time required for the solar wind to convect to the earth, is a convenient predictor of IMF orientation near the earth, to within about 20-degree accuracy.

Instrument pointing system applicability and orbiter stabilization for EVAL missions. Application studies

NASA Technical Reports Server (NTRS)

Spector, V. A.

1977-01-01

Related aspect of the Earth Viewing Applications Laboratory (EVAL) shuttle missions were investigated. The applicability of the gimballed Instrument Pointing System (IPS) to EVAL missions by comparing the IPS capabilities with the EVAL requirements was evaluated, and a means of stabilizing the shuttle orbiter attitude in earth viewing orientations for prolonged periods without use of the orbiter gas reaction control system was assessed.

Long Term Missions at the Sun-Earth Libration Point L1: ACE, SOHO, and WIND

NASA Technical Reports Server (NTRS)

Roberts, Craig E.

2011-01-01

Three heliophysics missions - the Solar Heliospheric Observatory (SOHO), the Advanced Composition Explorer (ACE), and the Global Geoscience WIND - have been orbiting the Sun-Earth interior libration point L1 continuously since 1996, 1997, and 2004, respectively. ACE and WIND (both NASA missions) and SOHO (an ESA-NASA joint mission) are all operated from the NASA Goddard Space Flight Center Flight Dynamics Facility. While ACE and SOHO have been dedicated libration point orbiters since their launches, WIND prior to 2004 flew a remarkable 10-year deep-space trajectory that featured 38 targeted lunar flybys. The L1 orbits and the mission histories of the three spacecraft are briefly reviewed, and the station-keeping techniques and orbit maneuver experience are discussed.

Orbit Determination Issues for Libration Point Orbits

NASA Technical Reports Server (NTRS)

Beckman, Mark; Bauer, Frank (Technical Monitor)

2002-01-01

Libration point mission designers require knowledge of orbital accuracy for a variety of analyses including station keeping control strategies, transfer trajectory design, and formation and constellation control. Past publications have detailed orbit determination (OD) results from individual libration point missions. This paper collects both published and unpublished results from four previous libration point missions (ISEE (International Sun-Earth Explorer) -3, SOHO (Solar and Heliospheric Observatory), ACE (Advanced Composition Explorer) and MAP (Microwave Anisotropy Probe)) supported by Goddard Space Flight Center's Guidance, Navigation & Control Center. The results of those missions are presented along with OD issues specific to each mission. All past missions have been limited to ground based tracking through NASA ground sites using standard range and Doppler measurement types. Advanced technology is enabling other OD options including onboard navigation using seaboard attitude sensors and the use of the Very Long Baseline Interferometry (VLBI) measurement Delta Differenced One-Way Range (DDOR). Both options potentially enable missions to reduce coherent dedicated tracking passes while maintaining orbital accuracy. With the increased projected loading of the DSN (Deep Space Network), missions must find alternatives to the standard OD scenario.

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

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

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.

Symmetrical polyhedra (simple crystal forms) as orbits of noncrystallographic point symmetry groups

NASA Astrophysics Data System (ADS)

Ovsetsina, T. I.; Chuprunov, E. V.

2017-09-01

Simple crystal forms are analyzed as the orbits of noncrystallographic point symmetry groups on a set of smooth or structured ("hatched") planes of crystal space. Polyhedra with symmetrically equivalent faces, obtained using noncrystallographic point symmetry groups, are considered. All possible versions of simple forms for all noncrystallographic groups are listed in a unified table.

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.

Dynamics and Control of Tethered Antennas/Reflectors in Orbit

DTIC Science & Technology

1992-02-01

reflector system. The optimal linear quadratic Gaussian (LQG) digital con- trol of the orbiting tethered antenna/reflector system is analyzed. The...flexibility of both the antenna and the tether are included in this high order system model. With eight point actuators optimally positioned together with...able to maintain satisfactory pointing accuracy for low and moderate altitude orbits under the influence of solar pressure. For the higher altitudes a

On Space Warfare: A Space Power Doctrine

DTIC Science & Technology

1998-06-01

called Panama Theory: that there are strategic places (geostationary orbits , libration points ) in space that have military value similar to the...initial training courses for the orbital analyst career field. In 1969, Lupton was transferred to the Headquarters Strategic Air Command, Directorate...over a point on the equator even though the satellite is moving in a circular orbit through space. This altitude (19,360 nautical miles) is the only

Cuntz-Krieger algebras representations from orbits of interval maps

NASA Astrophysics Data System (ADS)

Correia Ramos, C.; Martins, Nuno; Pinto, Paulo R.; Sousa Ramos, J.

2008-05-01

Let f be an expansive Markov interval map with finite transition matrix Af. Then for every point, we yield an irreducible representation of the Cuntz-Krieger algebra and show that two such representations are unitarily equivalent if and only if the points belong to the same generalized orbit. The restriction of each representation to the gauge part of is decomposed into irreducible representations, according to the decomposition of the orbit.

Impact of Multi-GNSS Observations on Precise Orbit Determination and Precise Point Positioning Solutions

NASA Astrophysics Data System (ADS)

Amiri, N.; Bertiger, W. I.; Lu, W.; Miller, M. A.; David, M. W.; Ries, P.; Romans, L.; Sibois, A. E.; Sibthorpe, A.; Sakumura, C.

2017-12-01

Impact of Multi-GNSS Observations on Precise Orbit Determination and Precise Point Positioning Solutions Authors: Nikta Amiri, Willy Bertiger, Wenwen Lu, Mark Miller, David Murphy, Paul Ries, Larry Romans, Carly Sakumura, Aurore Sibois, Anthony Sibthorpe All at the Jet Propulsion Laboratory, California Institute of Technology Multiple Global Navigation Satellite Systems (GNSS) are now in various stages of completion. The four current constellations (GPS, GLONASS, BeiDou, Galileo) comprise more than 80 satellites as of July 2017, with 120 satellites expected to be available when all four constellations become fully operational. We investigate the impact of simultaneous observations to these four constellations on global network precise orbit determination (POD) solutions, and compare them to available sets of orbit and clock products submitted to the Multi-GNSS Experiment (MGEX). Using JPL's GipsyX software, we generate orbit and clock products for the four constellations. The resulting solutions are evaluated based on a number of metrics including day-to-day internal and external orbit and/or clock overlaps and estimated constellation biases. Additionally, we examine estimated station positions obtained from precise point positioning (PPP) solutions by comparing results generated from multi-GNSS and GPS-only orbit and clock products.

The Spacelab Instrument Pointing System (IPS) and its first flight

NASA Astrophysics Data System (ADS)

Heusmann, H.; Wolf, P.

1985-11-01

The development of the Instrument Pointing System (IPS) as part of Spacelab's experimental apparatus for open Pallet direct space exposure, and its test flight aboard the Shuttle Orbiter are discussed. The IPS is a three-axis-controlled platform with stellar, sun and earth pointing modes, and a better than 1 arcsec pointing ability. The development of an 'inside-out gimbal' configuration with the platform acting like a joint between the unstable Shuttle and the inertially stabilized payload facilitated close to hemispherical pointing and the adaptability for payloads of almost any size. Gimbal axes torquers counteract Orbiter acceleration due to crew movement and thruster firings, and facilitate target acquisition and precision pointing, by command from a crew-engaged computer preprogrammed for all possible control steps. Carrying an experimental solar-physics payload, the IPS correctly performed all intended functions and withstood launch and orbital loads. Several anomalies were detected and successfully corrected in-flight.

Lissajous Orbit Control for the Deep Space Climate Observatory Sun-Earth L1 Libration Point Mission

NASA Technical Reports Server (NTRS)

Roberts, Craig; Case, Sarah; Reagoso, John

2015-01-01

DSCOVR Lissajous Orbit sized such that orbit track never extends beyond 15 degrees from Earth-Sun line (as seen from Earth). Requiring delta-V maneuvers, control orbit to obey a Solar Exclusion Zone (SEZ) cone of half-angle 4 degrees about the Earth-Sun line. Spacecraft should never be less than 4 degrees from solar center as seen from Earth. Following Lissajous Orbit Insertion (LOI), DSCOVR should be in an opening phase that just skirts the 4-degree SEZ. Maximizes time to the point where a closing Lissajous will require avoidance maneuvers to keep it out of the SEZ. Station keeping maneuvers should take no more than 15 minutes.

Libration Orbit Mission Design: Applications of Numerical & Dynamical Methods

NASA Technical Reports Server (NTRS)

Bauer, Frank (Technical Monitor); Folta, David; Beckman, Mark

2002-01-01

Sun-Earth libration point orbits serve as excellent locations for scientific investigations. These orbits are often selected to minimize environmental disturbances and maximize observing efficiency. Trajectory design in support of libration orbits is ever more challenging as more complex missions are envisioned in the next decade. Trajectory design software must be further enabled to incorporate better understanding of the libration orbit solution space and thus improve the efficiency and expand the capabilities of current approaches. The Goddard Space Flight Center (GSFC) is currently supporting multiple libration missions. This end-to-end support consists of mission operations, trajectory design, and control. It also includes algorithm and software development. The recently launched Microwave Anisotropy Probe (MAP) and upcoming James Webb Space Telescope (JWST) and Constellation-X missions are examples of the use of improved numerical methods for attaining constrained orbital parameters and controlling their dynamical evolution at the collinear libration points. This paper presents a history of libration point missions, a brief description of the numerical and dynamical design techniques including software used, and a sample of future GSFC mission designs.

Advanced Communication Technology Satellite (ACTS) Multibeam Antenna On-Orbit Performance

NASA Technical Reports Server (NTRS)

1995-01-01

The NASA Lewis Research Center's Advanced Communication Technology Satellite (ACTS) was launched in September 1993. ACTS introduced several new technologies, including a multibeam antenna (MBA) operating at extremely short wavelengths never before used in communications. This antenna, which has both fixed and rapidly reconfigurable high-energy spot beams (150 miles in diameter), serves users equipped with small antenna terminals. Extensive structural and thermal analyses have been performed for simulating the ACTS MBA on-orbit performance. The results show that the reflector surfaces (mainly the front subreflector), antenna support assembly, and metallic surfaces on the spacecraft body will be distorted because of the thermal effects of varying solar heating, which degrade the ACTS MBA performance. Since ACTS was launched, a number of evaluations have been performed to assess MBA performance in the space environment. For example, the on-orbit performance measurements found systematic environmental disturbances to the MBA beam pointing. These disturbances were found to be imposed by the attitude control system, antenna and spacecraft mechanical alignments, and on-orbit thermal effects. As a result, the MBA may not always exactly cover the intended service area. In addition, the on-orbit measurements showed that antenna pointing accuracy is the performance parameter most sensitive to thermal distortions on the front subreflector surface and antenna support assemblies. Several compensation approaches were tested and evaluated to restore on-orbit pointing stability. A combination of autotrack (75 percent of the time) and Earth sensor control (25 percent of the time) was found to be the best way to compensate for antenna pointing error during orbit. This approach greatly minimizes the effects of thermal distortions on antenna beam pointing.

Formation Flying in Earth, Libration, and Distant Retrograde Orbits

NASA Technical Reports Server (NTRS)

Folta, David C.

2004-01-01

This slide presentation examines the current and future state of formation flying, LEO formations, control strategies for flight in the vicinity of the libration points, and distant retrograde orbit formations. This discussion of LEO formations includes background on perturbation theory/accelerations and LEO formation flying. The discussion of strategies for formation flight in the vicinity of the libration points includes libration missions and natural and controlled libration orbit formations. A reference list is included.

Equilibrium points and associated periodic orbits in the gravity of binary asteroid systems: (66391) 1999 KW4 as an example

NASA Astrophysics Data System (ADS)

Shi, Yu; Wang, Yue; Xu, Shijie

2018-04-01

The motion of a massless particle in the gravity of a binary asteroid system, referred as the restricted full three-body problem (RF3BP), is fundamental, not only for the evolution of the binary system, but also for the design of relevant space missions. In this paper, equilibrium points and associated periodic orbit families in the gravity of a binary system are investigated, with the binary (66391) 1999 KW4 as an example. The polyhedron shape model is used to describe irregular shapes and corresponding gravity fields of the primary and secondary of (66391) 1999 KW4, which is more accurate than the ellipsoid shape model in previous studies and provides a high-fidelity representation of the gravitational environment. Both of the synchronous and non-synchronous states of the binary system are considered. For the synchronous binary system, the equilibrium points and their stability are determined, and periodic orbit families emanating from each equilibrium point are generated by using the shooting (multiple shooting) method and the homotopy method, where the homotopy function connects the circular restricted three-body problem and RF3BP. In the non-synchronous binary system, trajectories of equivalent equilibrium points are calculated, and the associated periodic orbits are obtained by using the homotopy method, where the homotopy function connects the synchronous and non-synchronous systems. Although only the binary (66391) 1999 KW4 is considered, our methods will also be well applicable to other binary systems with polyhedron shape data. Our results on equilibrium points and associated periodic orbits provide general insights into the dynamical environment and orbital behaviors in proximity of small binary asteroids and enable the trajectory design and mission operations in future binary system explorations.

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), ...

Efficient Development of High Fidelity Structured Volume Grids for Hypersonic Flow Simulations

NASA Technical Reports Server (NTRS)

Alter, Stephen J.

2003-01-01

A new technique for the control of grid line spacing and intersection angles of a structured volume grid, using elliptic partial differential equations (PDEs) is presented. Existing structured grid generation algorithms make use of source term hybridization to provide control of grid lines, imposing orthogonality implicitly at the boundary and explicitly on the interior of the domain. A bridging function between the two types of grid line control is typically used to blend the different orthogonality formulations. It is shown that utilizing such a bridging function with source term hybridization can result in the excessive use of computational resources and diminishes robustness. A new approach, Anisotropic Lagrange Based Trans-Finite Interpolation (ALBTFI), is offered as a replacement to source term hybridization. The ALBTFI technique captures the essence of the desired grid controls while improving the convergence rate of the elliptic PDEs when compared with source term hybridization. Grid generation on a blunt cone and a Shuttle Orbiter is used to demonstrate and assess the ALBTFI technique, which is shown to be as much as 50% faster, more robust, and produces higher quality grids than source term hybridization.

STM contrast of a CO dimer on a Cu(1 1 1) surface: a wave-function analysis.

PubMed

Gustafsson, Alexander; Paulsson, Magnus

2017-12-20

We present a method used to intuitively interpret the scanning tunneling microscopy (STM) contrast by investigating individual wave functions originating from the substrate and tip side. We use localized basis orbital density functional theory, and propagate the wave functions into the vacuum region at a real-space grid, including averaging over the lateral reciprocal space. Optimization by means of the method of Lagrange multipliers is implemented to perform a unitary transformation of the wave functions in the middle of the vacuum region. The method enables (i) reduction of the number of contributing tip-substrate wave function combinations used in the corresponding transmission matrix, and (ii) to bundle up wave functions with similar symmetry in the lateral plane, so that (iii) an intuitive understanding of the STM contrast can be achieved. The theory is applied to a CO dimer adsorbed on a Cu(1 1 1) surface scanned by a single-atom Cu tip, whose STM image is discussed in detail by the outlined method.

STM contrast of a CO dimer on a Cu(1 1 1) surface: a wave-function analysis

NASA Astrophysics Data System (ADS)

Gustafsson, Alexander; Paulsson, Magnus

2017-12-01

We present a method used to intuitively interpret the scanning tunneling microscopy (STM) contrast by investigating individual wave functions originating from the substrate and tip side. We use localized basis orbital density functional theory, and propagate the wave functions into the vacuum region at a real-space grid, including averaging over the lateral reciprocal space. Optimization by means of the method of Lagrange multipliers is implemented to perform a unitary transformation of the wave functions in the middle of the vacuum region. The method enables (i) reduction of the number of contributing tip-substrate wave function combinations used in the corresponding transmission matrix, and (ii) to bundle up wave functions with similar symmetry in the lateral plane, so that (iii) an intuitive understanding of the STM contrast can be achieved. The theory is applied to a CO dimer adsorbed on a Cu(1 1 1) surface scanned by a single-atom Cu tip, whose STM image is discussed in detail by the outlined method.

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

Applying Dynamical Systems Theory to Optimize Libration Point Orbit Stationkeeping Maneuvers for WIND

NASA Technical Reports Server (NTRS)

Brown, Jonathan M.; Petersen, Jeremy D.

2014-01-01

NASA's WIND mission has been operating in a large amplitude Lissajous orbit in the vicinity of the interior libration point of the Sun-Earth/Moon system since 2004. Regular stationkeeping maneuvers are required to maintain the orbit due to the instability around the collinear libration points. Historically these stationkeeping maneuvers have been performed by applying an incremental change in velocity, or (delta)v along the spacecraft-Sun vector as projected into the ecliptic plane. Previous studies have shown that the magnitude of libration point stationkeeping maneuvers can be minimized by applying the (delta)v in the direction of the local stable manifold found using dynamical systems theory. This paper presents the analysis of this new maneuver strategy which shows that the magnitude of stationkeeping maneuvers can be decreased by 5 to 25 percent, depending on the location in the orbit where the maneuver is performed. The implementation of the optimized maneuver method into operations is discussed and results are presented for the first two optimized stationkeeping maneuvers executed by WIND.

Robust superconductivity with nodes in the superconducting topological insulator CuxBi2Se3 : Zeeman orbital field and nonmagnetic impurities

NASA Astrophysics Data System (ADS)

Nagai, Yuki

2015-02-01

We study the robustness against nonmagnetic impurities in the topological superconductor with point nodes, focusing on an effective model of CuxBi2Se3 . We find that the topological superconductivity with point nodes is not fragile against nonmagnetic impurities, although the superconductivity with nodes in past studies is usually fragile. Exchanging the role of spin with the one of orbital, and vice versa, we find that in the "dual" space the topological superconductor with point nodes is regarded as the intraorbital spin-singlet s -wave one. From the viewpoint of the dual space, we deduce that the point-node state is not fragile against nonmagnetic impurity, when the orbital imbalance in the normal states is small. Since the spin imbalance is induced by the Zeeman magnetic field, we shall name this key quantity for the impurity effects the Zeeman "orbital" field. The numerical calculations support that the deduction is correct. If the Zeeman orbital field is small, the topological superconductivity is not fragile in dirty materials, even with nodes. Thus, the topological superconductors cannot be simply regarded as one of the conventional unconventional superconductors.

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.

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.

A New Guidance Method for a Delta V and Re-entry Constrained Orbit Transfer Problem

DTIC Science & Technology

2005-06-01

a vehicle that undertakes a maneuver with the objective of precisely flying through a point in space at a particular time. The spacecraft must...for the Example Spacecraft . . . . 50 4-1 Graphical Results of Large Changes in Orbital Velocity . . . . . . . . . . . 62 4-2 Contours of Perigee...Orbit Relative to Rendezvous Point . . . . . . . . . . 98 6-2 Angular Rate and Angles for GEM-CR Maneuver with ∆θ = 90◦ . . . . . . 101 6-3 Position

Halo-orbit and lunar-swingby missions of the 1990's

NASA Technical Reports Server (NTRS)

Farquhar, Robert W.

1990-01-01

A significant number of spacecraft are planning to use halo orbits and lunar-swingby trajectories in the next decade. Four spacecraft will be placed into halo orbits around the earth's sunward libration point, while two others will be stationed near the sun-earth L2 libration point in the distant geomagnetic tail. Six spacecraft, including two of the aforementioned halo orbiters, will make use of lunar-swingby maneuvers to fulfill their mission objectives. Thus, a total of ten spacecraft, five from the Soviet Union, two from Japan, two from the United States, and one from the European Space Agency, will employ halo orbits and/or lunar-swingby trajectories in the 1990's. Pertinent facts are presented for each of these missions.

Open Solar Physics Questions - What Can Orbiter Do That Could Not Be Addressed By Existing Missions?

NASA Technical Reports Server (NTRS)

Antiochos, S. K.

2009-01-01

Solar Orbiter represents a revolutionary advance in observing the Sun. Orbiter will have optical and XUV telescopes that will deliver high-resolution images and spectra from vantages points that have never been possible before, dose to the Sun and at high latitudes. At the same time, Orbiter will measure in situ the properties of the solar wind that originate from the observed solar photosphere and corona. In this presentation, Ivvi|/ describe how with its unique vantage points and capabilities, Orbiter will allow us to answer, for the first time, some of the major question in solar physics, such as: Where does the slow wind originate? How do CMEs initiate and evolve? What is the heating mechanism in corona/ loops.

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.

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.

Impacts of Satellite Orbit and Clock on Real-Time GPS Point and Relative Positioning.

PubMed

Shi, Junbo; Wang, Gaojing; Han, Xianquan; Guo, Jiming

2017-06-12

Satellite orbit and clock corrections are always treated as known quantities in GPS positioning models. Therefore, any error in the satellite orbit and clock products will probably cause significant consequences for GPS positioning, especially for real-time applications. Currently three types of satellite products have been made available for real-time positioning, including the broadcast ephemeris, the International GNSS Service (IGS) predicted ultra-rapid product, and the real-time product. In this study, these three predicted/real-time satellite orbit and clock products are first evaluated with respect to the post-mission IGS final product, which demonstrates cm to m level orbit accuracies and sub-ns to ns level clock accuracies. Impacts of real-time satellite orbit and clock products on GPS point and relative positioning are then investigated using the P3 and GAMIT software packages, respectively. Numerical results show that the real-time satellite clock corrections affect the point positioning more significantly than the orbit corrections. On the contrary, only the real-time orbit corrections impact the relative positioning. Compared with the positioning solution using the IGS final product with the nominal orbit accuracy of ~2.5 cm, the real-time broadcast ephemeris with ~2 m orbit accuracy provided <2 cm relative positioning error for baselines no longer than 216 km. As for the baselines ranging from 574 to 2982 km, the cm-dm level positioning error was identified for the relative positioning solution using the broadcast ephemeris. The real-time product could result in <5 mm relative positioning accuracy for baselines within 2982 km, slightly better than the predicted ultra-rapid product.

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.

Orbital dynamics of high area-to-mass ratio spacecraft with J2 and solar radiation pressure for novel Earth observation and communication services

NASA Astrophysics Data System (ADS)

Colombo, Camilla; Lücking, Charlotte; McInnes, Colin R.

2012-12-01

This paper investigates the effect of planetary oblateness and solar radiation pressure on the orbits of high area-to-mass spacecraft. A planar Hamiltonian model shows the existence of equilibrium orbits with the orbit apogee pointing towards or away from the Sun. These solutions are numerically continued to non-zero inclinations and considering the obliquity of the ecliptic plane relative to the equator. Quasi-frozen orbits are identified in eccentricity, inclination and the angle between the Sun-line and the orbit perigee. The long-term evolution of these orbits is then verified through numerical integration. A set of 'heliotropic' orbits with apogee pointing in the direction of the Sun is proposed for enhancing imaging and telecommunication on the day side of the Earth. The effects of J2 and solar radiation pressure are exploited to obtain a passive rotation of the apsides line following the Sun; moreover the effect of solar radiation pressure enables such orbits at higher eccentricities with respect to the J2 only case.

results obtained by the application of two different methods for the calculation of optimal coplanar orbital maneuvers with time limit

NASA Astrophysics Data System (ADS)

Rocco, Emr; Prado, Afbap; Souza, Mlos

In this work, the problem of bi-impulsive orbital transfers between coplanar elliptical orbits with minimum fuel consumption but with a time limit for this transfer is studied. As a first method, the equations presented by Lawden (1993) were used. Those equations furnishes the optimal transfer orbit with fixed time for this transfer, between two elliptical coplanar orbits considering fixed terminal points. The method was adapted to cases with free terminal points and those equations was solved to develop a software for orbital maneuvers. As a second method, the equations presented by Eckel and Vinh (1984) were used, those equations provide the transfer orbit between non-coplanar elliptical orbits with minimum fuel and fixed time transfer, or minimum time transfer for a prescribed fuel consumption, considering free terminal points. But in this work only the problem with fixed time transfer was considered, the case of minimum time for a prescribed fuel consumption was already studied in Rocco et al. (2000). Then, the method was modified to consider cases of coplanar orbital transfer, and develop a software for orbital maneuvers. Therefore, two software that solve the same problem using different methods were developed. The first method, presented by Lawden, uses the primer vector theory. The second method, presented by Eckel and Vinh, uses the ordinary theory of maxima and minima. So, to test the methods we choose the same terminal orbits and the same time as input. We could verify that we didn't obtain exactly the same result. In this work, that is an extension of Rocco et al. (2002), these differences in the results are explored with objective of determining the reason of the occurrence of these differences and which modifications should be done to eliminate them.

Normal orbit skeletal changes in adolescents as determined through cone-beam computed tomography.

PubMed

Lee, B; Flores-Mir, C; Lagravère, M O

2016-11-10

To determine three-dimensional spatial orbit skeletal changes in adolescents over a 19 to 24 months observation period assessed through cone-beam computed tomography (CBCT). The sample consisted of 50 adolescents aged 11 to 17. All were orthodontic patients who had two CBCTs taken with an interval of 19 to 24 months between images. The CBCTs were analyzed using the third-party software Avizo. Sixteen anatomical landmarks resulting in 24 distances were used to measure spatial structural changes of both orbits. Reliability and measurement error of all landmarks were calculated using ten CBCTs. Descriptive and t-test statistical analyses were used to determine the overall changes in the orbits. All landmarks showed excellent reliability with the largest measurement error being the Y-coordinate of the left most medial point of the temporalis grooves at 0.95 mm. The mean differences of orbital changes between time 1 and time 2 in the transverse, antero-posterior and vertical directions were 0.97, 0.36 and 0.33 mm respectively. Right to left most antero-inferior superior orbital rim distance had the greatest overall transverse change of 4.37 mm. Right most posterior point of lacrimal crest to right most postero-lateral point of the superior orbital fissure had the greatest overall antero-posterior change of 0.52 mm. Lastly, left most antero-inferior superior orbital rim to left most antero-superior inferior orbital rim had the greatest overall vertical change of 0.63 mm. The orbit skeletal changes in a period of 19-24 months in a sample of 11-17 year olds were statistically significant, but are not considered to be clinically significant. The overall average changes of orbit measurements were less than 1 mm.

Hubble Space Telescope Reduced-Gyro Control Law Design, Implementation, and On-Orbit Performance

NASA Technical Reports Server (NTRS)

Clapp, Brian R.; Ramsey, Patrick R.; Wirzburger, John H.; Smith, Daniel C.; VanArsadall, John C.

2008-01-01

Following gyro failures in April 2001 and April 2003, HST Pointing Control System engineers designed reduced-gyro control laws to extend the spacecraft science mission. The Two-Gyro Science (TGS) and One-Gyro Science (OGS) control laws were designed and implemented using magnetometers, star trackers, and Fine Guidance Sensors in succession to control vehicle rate about the missing gyro axes. Both TGS and OGS have demonstrated on-orbit pointing stability of 7 milli-arcseconds or less, which depends upon the guide star magnitude used by the Fine Guidance Sensor. This paper describes the design, implementation, and on-orbit performance of the TGS and OGS control law fine-pointing modes using Fixed Head Star Trackers and Fine Guidance Sensors, after successfully achieving coarse-pointing control using magnetometers.

Equilibrium and Stability of a Pendulum in an Orbiting Spaceship.

ERIC Educational Resources Information Center

Blitzer, Leon

1979-01-01

Investigates the behavior of a simple pendulum attached to a fixed point inside a satellite moving in a circular orbit about the earth. It is found that the number of equilibrium positions depends on the length of the pendulum and the location of the point of attachment. (HM)

Convergence Time towards Periodic Orbits in Discrete Dynamical Systems

PubMed Central

San Martín, Jesús; Porter, Mason A.

2014-01-01

We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we use linearized equations to examine the evolution near that neighborhood. The underlying idea is that points of stable periodic orbit are associated with intervals. We state and prove a theorem that details what regions of phase space are mapped into these intervals (once they are known) and how many iterations are required to get there. We also construct algorithms that allow our theoretical results to be implemented successfully in practice. PMID:24736594

Control Of Flexible Structures-2 (COFS-2) flight control, structure and gimbal system interaction study

NASA Technical Reports Server (NTRS)

Fay, Stanley; Gates, Stephen; Henderson, Timothy; Sackett, Lester; Kirchwey, Kim; Stoddard, Isaac; Storch, Joel

1988-01-01

The second Control Of Flexible Structures Flight Experiment (COFS-2) includes a long mast as in the first flight experiment, but with the Langley 15-m hoop column antenna attached via a gimbal system to the top of the mast. The mast is to be mounted in the Space Shuttle cargo bay. The servo-driven gimbal system could be used to point the antenna relative to the mast. The dynamic interaction of the Shuttle Orbiter/COFS-2 system with the Orbiter on-orbit Flight Control System (FCS) and the gimbal pointing control system has been studied using analysis and simulation. The Orbiter pointing requirements have been assessed for their impact on allowable free drift time for COFS experiments. Three fixed antenna configurations were investigated. Also simulated was Orbiter attitude control behavior with active vernier jets during antenna slewing. The effect of experiment mast dampers was included. Control system stability and performance and loads on various portions of the COFS-2 structure were investigated. The study indicates possible undesirable interaction between the Orbiter FCS and the flexible, articulated COFS-2 mast/antenna system, even when restricted to vernier reaction jets.

Precise Orbit Determination of the GOCE Re-Entry Phase

NASA Astrophysics Data System (ADS)

Gini, Francesco; Otten, Michiel; Springer, Tim; Enderle, Werner; Lemmens, Stijn; Flohrer, Tim

2015-03-01

During the last days of the GOCE mission, after the GOCE spacecraft ran out of fuel, it slowly decayed before finally re-entering the atmosphere on the 11th November 2013. As an integrated part of the AOCS, GOCE carried a GPS receiver that was in operations during the re-entry phase. This feature provided a unique opportunity for Precise Orbit Determination (POD) analysis. As part of the activities carried out by the Navigation Support Office (HSO-GN) at ESOC, precise ephemerides of the GOCE satellite have been reconstructed for the entire re-entry phase based on the available GPS observations of the onboard LAGRANGE receiver. All the data available from the moment the thruster was switched off on the 21st of October 2013 to the last available telemetry downlink on the 10th November 2013 have been processed, for a total of 21 daily arcs. For this period a dedicated processing sequence has been defined and implemented within the ESA/ESOC NAvigation Package for Earth Observation Satellites (NAPEOS) software. The computed results show a post-fit RMS of the GPS undifferenced carrier phase residuals (ionospheric-free linear combination) between 6 and 14 mm for the first 16 days which then progressively increases up to about 80 mm for the last available days. An orbit comparison with the Precise Science Orbits (PSO) generated at the Astronomical Institute of the University of Bern (AIUB, Bern, Switzerland) shows an average difference around 9 cm for the first 8 daily arcs and progressively increasing up to 17 cm for the following days. During this reentry phase (21st of October - 10th November 2013) a substantial drop in the GOCE altitude is observed, starting from about 230 km to 130 km where the last GPS measurements were taken. During this orbital decay an increment of a factor of 100 in the aerodynamic acceleration profile is observed. In order to limit the mis-modelling of the non-gravitational forces (radiation pressure and aerodynamic effects) the newly developed software ARPA (Aerodynamics and Radiation Pressure Analysis) has been adopted to compute the forces acting on GOCE. An overview of the software techniques and the results of its implementation is presented in this paper. The use of the ARPA modelling leads to an average reduction of the carrier phase post-fit RMS of about 2 mm and decrement of the difference with the PSO orbits of more than 1 cm.

Generalized Roche potential for misaligned binary systems - Properties of the critical lobe

NASA Technical Reports Server (NTRS)

Avni, Y.; Schiller, N.

1982-01-01

The paper considers the Roche potential for binary systems where the stellar rotation axis is not aligned with the orbital revolution axis. It is shown that, as the degree of misalignment varies, internal Lagrangian points and external Lagrangian points may switch their roles. A systematic method to identify the internal Lagrangian point and to calculate the volume of the critical lobe is developed, and numerical results for a wide range of parameters of binary systems with circular orbits are presented. For binary systems with large enough misalignment, discrete changes occur in the topological structure of the equipotential surfaces as the orbital phase varies. The volume of the critical lobe has minima, as a function of orbital phase, at the two instances when the secondary crosses the equatorial plane of the primary. In semidetached systems, mass transfer may be confined to the vicinity of these two instances.

Observing the Interstellar Neutral He Gas Flow with a Variable IBEX Pointing Strategy

NASA Astrophysics Data System (ADS)

Leonard, T.; Moebius, E.; Bzowski, M.; Fuselier, S. A.; Heirtzler, D.; Kubiak, M. A.; Kucharek, H.; Lee, M. A.; McComas, D. J.; Schwadron, N.; Wurz, P.

2015-12-01

The Interstellar Neutral (ISN) gas flow can be observed at Earth's orbit due to the motion of the solar system relative to the surrounding interstellar gas. Since He is minimally influenced by ionization and charge exchange, the ISN He flow provides a sample of the pristine interstellar environment. The Interstellar Boundary Explorer (IBEX) has observed the ISN gas flow over the past 7 years from a highly elliptical orbit around the Earth. IBEX is a Sun-pointing spinning spacecraft with energetic neutral atom (ENA) detectors observing perpendicular to the spacecraft spin axis. Due to the Earth's orbital motion around the Sun, it is necessary for IBEX to perform spin axis pointing maneuvers every few days to maintain a sunward pointed spin axis. The IBEX operations team has successfully pointed the spin axis in a variety of latitude orientations during the mission, including in the ecliptic during the 2012 and 2013 seasons, about 5 degrees below the ecliptic during the 2014 season, and recently about 5 degrees above the ecliptic during the 2015 season, as well as optimizing observations with the spin axis pointed along the Earth-Sun line. These observations include a growing number of measurements near the perihelion of the interstellar atom trajectories, which allow for an improved determination of the ISN He bulk flow longitude at Earth orbit. Combining these bulk flow measurements with an analytical model (Lee et al. 2012 ApJS, 198, 10) based upon orbital mechanics improves the knowledge of the narrow ISN parameter tube, obtained with IBEX, which couples the interstellar inflow longitude, latitude, speed, and temperature.

Explore Stochastic Instabilities of Periodic Points by Transition Path Theory

NASA Astrophysics Data System (ADS)

Cao, Yu; Lin, Ling; Zhou, Xiang

2016-06-01

We consider the noise-induced transitions from a linearly stable periodic orbit consisting of T periodic points in randomly perturbed discrete logistic map. Traditional large deviation theory and asymptotic analysis at small noise limit cannot distinguish the quantitative difference in noise-induced stochastic instabilities among the T periodic points. To attack this problem, we generalize the transition path theory to the discrete-time continuous-space stochastic process. In our first criterion to quantify the relative instability among T periodic points, we use the distribution of the last passage location related to the transitions from the whole periodic orbit to a prescribed disjoint set. This distribution is related to individual contributions to the transition rate from each periodic points. The second criterion is based on the competency of the transition paths associated with each periodic point. Both criteria utilize the reactive probability current in the transition path theory. Our numerical results for the logistic map reveal the transition mechanism of escaping from the stable periodic orbit and identify which periodic point is more prone to lose stability so as to make successful transitions under random perturbations.

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.

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.

Revisiting the Bohr Atom 100 Years Later

NASA Astrophysics Data System (ADS)

Wall, Ernst

2013-03-01

We use a novel electron model wherein the electron is modeled as a point charge behaving as a trapped photon revolving in a Compton wavelength orbit at light speed. The revolving point charge gives rise to spiraling Compton wavelets around the electron, which give rise to de Broglie waves. When applied to the Bohr model, the orbital radius of the electron scales to the first Bohr orbit's radius via the fine structure constant. The orbiting electron's orbital velocity, Vb, scales to that of the electron's charge's internal velocity (the velocity of light, c) via the fine structure constant. The Compton wavelets, if they reflect off the nucleus, have a round trip time just long enough to allow the electron to move one of its diameters in distance in the first Bohr orbit. The ratio of the electron's rotational frequency, fe, to its rotational frequency in the Bohr orbit fb, is fe/fb = 1/α2, which is also the number of electron rotations in single orbit. If we scale the electron's rotational energy (h*fe) to that of the orbit using this, the orbital energy value (h*fb) would be 27.2114 eV. However, the virial theorem reduces it to 13.6057, the ground state energy of the first Bohr orbit. Ref: www.tachyonmodel.com.

Libration-point staging concepts for Earth-Mars transportation

NASA Technical Reports Server (NTRS)

Farquhar, Robert; Dunham, David

1986-01-01

The use of libration points as transfer nodes for an Earth-Mars transportation system is briefly described. It is assumed that a reusable Interplanetary Shuttle Vehicle (ISV) operates between the libration point and Mars orbit. Propellant for the round-trip journey to Mars and other supplies would be carried from low Earth orbit (LEO) to the ISV by additional shuttle vehicles. Different types of trajectories between LEO and libration points are presented, and approximate delta-V estimates for these transfers are given. The possible use of lunar gravity-assist maneuvers is also discussed.

Point-to-point sub-orbital space tourism: Some initial considerations

NASA Astrophysics Data System (ADS)

Webber, Derek

2010-06-01

Several public statements have been made about the possible, or even likely, extension of initial sub-orbital space tourism operations to encompass point-to-point travel. It is the purpose of this paper to explore some of the basic considerations for such a plan, in order to understand both its merits and its problems. The paper will discuss a range of perspectives, from basic physics to market segmentation, from ground segment logistics to spacecraft design considerations. It is important that these initial considerations are grasped before more detailed planning and design takes place.

Drift-free solar sail formations in elliptical Sun-synchronous orbits

NASA Astrophysics Data System (ADS)

Parsay, Khashayar; Schaub, Hanspeter

2017-10-01

To study the spatial and temporal variations of plasma in the highly dynamic environment of the magnetosphere, multiple spacecraft must fly in a formation. The objective for this study is to investigate the feasibility of solar sail formation flying in the Earth-centered, Sun-synchronous orbit regime. The focus of this effort is to enable formation flying for a group of solar sails that maintain a nominally fixed Sun-pointing attitude during formation flight, solely for the purpose of precessing their orbit apse lines Sun-synchronously. A fixed-attitude solar sail formation is motivated by the difficulties in the simultaneous control of orbit and attitude in flying solar sails. First, the secular rates of the orbital elements resulting from the effects of solar radiation pressure (SRP) are determined using averaging theory for a Sun-pointing attitude sail. These averaged rates are used to analytically derive the first-order necessary conditions for a drift-free solar sail formation in Sun-synchronous orbits, assuming a fixed Sun-pointing orientation for each sail in formation. The validity of the first-order necessary conditions are illustrated by designing quasi-periodic relative motions. Next, nonlinear programming is applied to design truly drift-free two-craft solar sail formations. Lastly, analytic expressions are derived to determine the long-term dynamics and sensitivity of the formation with respect to constant attitude errors, uncertainty in orbital elements, and uncertainty in a sail's characteristic acceleration.

Relative attitude dynamics and control for a satellite inspection mission

NASA Astrophysics Data System (ADS)

Horri, Nadjim M.; Kristiansen, Kristian U.; Palmer, Phil; Roberts, Mark

2012-02-01

The problem of conducting an inspection mission from a chaser satellite orbiting a target spaceraft is considered. It is assumed that both satellites follow nearly circular orbits. The relative orbital motion is described by the Hill-Clohessy-Wiltshire equation. In the case of an elliptic relative orbit, it is shown that an inspection mission is feasible when the chaser is inertially pointing, provided that the camera mounted on the chaser satellite has sufficiently large field of view. The same possibility is shown when the optical axis of the chaser's camera points in, or opposite to, the tangential direction of the local vertical local horizontal frame. For an arbitrary relative orbit and arbitrary initial conditions, the concept of relative Euler angles is defined for this inspection mission. The expression of the desired relative angular velocity vector is derived as a function of Cartesian coordinates of the relative orbit. A quaternion feedback controller is then designed and shown to perform relative attitude control with admissible internal torques. Three different types of relative orbits are considered, namely the elliptic, Pogo and drifting relative orbits. Measurements of the relative orbital motion are assumed to be available from optical navigation.

On E-discretization of tori of compact simple Lie groups. II

NASA Astrophysics Data System (ADS)

Hrivnák, Jiří; Juránek, Michal

2017-10-01

Ten types of discrete Fourier transforms of Weyl orbit functions are developed. Generalizing one-dimensional cosine, sine, and exponential, each type of the Weyl orbit function represents an exponential symmetrized with respect to a subgroup of the Weyl group. Fundamental domains of even affine and dual even affine Weyl groups, governing the argument and label symmetries of the even orbit functions, are determined. The discrete orthogonality relations are formulated on finite sets of points from the refinements of the dual weight lattices. Explicit counting formulas for the number of points of the discrete transforms are deduced. Real-valued Hartley orbit functions are introduced, and all ten types of the corresponding discrete Hartley transforms are detailed.

orbit-estimation: Fast orbital parameters estimator

NASA Astrophysics Data System (ADS)

Mackereth, J. Ted; Bovy, Jo

2018-04-01

orbit-estimation tests and evaluates the Stäckel approximation method for estimating orbit parameters in galactic potentials. It relies on the approximation of the Galactic potential as a Stäckel potential, in a prolate confocal coordinate system, under which the vertical and horizontal motions decouple. By solving the Hamilton Jacobi equations at the turning points of the horizontal and vertical motions, it is possible to determine the spatial boundary of the orbit, and hence calculate the desired orbit parameters.

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).

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.

Closeup view of the underside of the forward fuselage of ...

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

Close-up view of the underside of the forward fuselage of the Orbiter Discovery looking at the nose landing-gear and into the landing-gear well. The vehicle is elevated and supported by jack stands attached to the hoist attach points and the rear External Tank attach points on the propellant disconnect plate assemblies. This photo was taken inside the Orbiter Processing Facility at Kennedy Space Center. - Space Transportation System, Orbiter Discovery (OV-103), Lyndon B. Johnson Space Center, 2101 NASA Parkway, Houston, Harris County, TX

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.

Prebifurcation periodic ghost orbits in semiclassical quantization

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

Kus, M.; Haake, F.; Delande, D.

1993-10-04

Classical periodic orbits are stationary-phase points in path integral representations of quantum propagators. We show that complex solutions of the stationary-phase equation, not corresponding to real classical periodic orbits, give additional contributions to the propagator which can be important, especially near bifurcations. We reveal the existence and relevance of such periodic ghost orbits for a kicked top.

SCIAMACHY In-orbit Operations until 2013

NASA Astrophysics Data System (ADS)

Gottwald, Manfred; Krieg, Eckhart; Lichtenberg, Günter; Noël, Stefan; Bramstedt, Klaus; Bovensmann, Heinrich

In 2010 ENVISAT enters its next mission extension phase when a manoeuvre transfers the plat-form from its nominal into a modified orbit. This modified orbit is not only characterized by the lower altitude but also by slightly drifting parameters such as e.g. the inclination or the Mean Local Solar Time at ascending node crossing. Thus all SCIAMACHY measurements requiring an accurate pointing knowledge are affected. How the line-of-sight evolves along the orbit de-pends on orbit altitude and orbital period. Therefore adjustments to SCIAMACHY's on-board instrument configuration are necessary reflecting this orbit chance. Based on a detailed analysis simulating SCIAMACHY operations in the modified orbit until the end of 2013, the impacts on nadir, limb and solar and lunar occultation measurements when orbiting the Earth at a reduced altitude was studied. By modifying SCIAMACHY's configuration these impacts can be compensated for. Thus the current performance of instrument operations, including the pointing knowledge, can be maintained. It ensures acquisition of high quality measurement data for the entire duration of the mission. This presentation describes how the instrument will be configured for achieving successful operations until the end of 2013. In addition a brief outlook is given how the drifting modified orbit may impact an operations phase even beyond 2013 and potential corrective countermeasures.

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.

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.

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.

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)

An Investigation of Spinup Dynamics of Axial Gyrostats Using Elliptic Integrals and the Method of Averaging

DTIC Science & Technology

1991-01-01

is a gyrostat near one of the five libration points . She identified the equilibria and determined their stability regions. Also, Mavraga- nis [71] has...defines a family of periodic orbits , depending on how close the all-spun motion is to an equilibrium point of the equations of motion for a single...determined by the relationship between the mission orbit and the object the platform is supposed to track. As a limiting case, one might wish to point

Comparison of Sigma-Point and Extended Kalman Filters on a Realistic Orbit Determination Scenario

NASA Technical Reports Server (NTRS)

Gaebler, John; Hur-Diaz. Sun; Carpenter, Russell

2010-01-01

Sigma-point filters have received a lot of attention in recent years as a better alternative to extended Kalman filters for highly nonlinear problems. In this paper, we compare the performance of the additive divided difference sigma-point filter to the extended Kalman filter when applied to orbit determination of a realistic operational scenario based on the Interstellar Boundary Explorer mission. For the scenario studied, both filters provided equivalent results. The performance of each is discussed in detail.

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.

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.

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.

Measurements of the STS orbiter's angular stability during in-orbit operations

NASA Technical Reports Server (NTRS)

Neupert, Werner M.; Epstein, Gabriel L.; Houston, James; Zarechnak, Andrew

1995-01-01

We report on measurements of the angular stability, commonly called 'jitter', of the STS Orbiter during normal operations in space. Measurements were carried out by measuring optically the Orbiter's roll and pitch orientation relative to the solar vector as the orbiter was held in a -Z(sub 0) solar inertial orientation (orbiter bay oriented toward the Sun). We also report observations of an interesting perturbation to the orbiter's orientation noted by the crew during the STS-60 mission. These data may be useful in analyzing the in-orbit response of the Orbiter to thruster firings and other applied torques, and may aid in the planning of future experiments that require fine-pointed operations by the orbiter.

The structural, electronic and magnetic properties of CoS2 under pressure

NASA Astrophysics Data System (ADS)

Feng, Zhong-Ying; Yang, Yan; Zhang, Jian-Min

2018-05-01

The structural, electronic and magnetic properties of CoS2 under pressure have been investigated by the first-principles calculations. The lattice constant and volume decrease with increasing pressure. The CoS2 is stable and behaves a brittle characteristic under the pressures of 0-5 GPa. The CoS2 presents metallic characteristic under the pressures of 1-5 GPa although it is nearly half-metal (HM) under the pressure of 0 GPa. The lowest conduction bands for spin-up and spin-down channels shift towards higher and lower energy region, respectively, with the pressure increasing from 0 to 5 GPa. In spin-up channel the conduction band minimum (CBM) is mainly contributed by Co-3d(eg) orbitals at R point but the valence band maximum (VBM) is contributed by Co-3d(t2g) orbitals near M point. While in spin-down channel the CBM is contributed by S-3p orbitals at Γ point but the VBM is contributed by Co-3d(t2g) orbitals near X point. The CoS2 is still suitable to be used in the supercapacitor under the environmental pressures of 0-5 GPa due to the high conductivity.

Analytical and numerical construction of vertical periodic orbits about triangular libration points based on polynomial expansion relations among directions

NASA Astrophysics Data System (ADS)

Qian, Ying-Jing; Yang, Xiao-Dong; Zhai, Guan-Qiao; Zhang, Wei

2017-08-01

Innovated by the nonlinear modes concept in the vibrational dynamics, the vertical periodic orbits around the triangular libration points are revisited for the Circular Restricted Three-body Problem. The ζ -component motion is treated as the dominant motion and the ξ and η -component motions are treated as the slave motions. The slave motions are in nature related to the dominant motion through the approximate nonlinear polynomial expansions with respect to the ζ -position and ζ -velocity during the one of the periodic orbital motions. By employing the relations among the three directions, the three-dimensional system can be transferred into one-dimensional problem. Then the approximate three-dimensional vertical periodic solution can be analytically obtained by solving the dominant motion only on ζ -direction. To demonstrate the effectiveness of the proposed method, an accuracy study was carried out to validate the polynomial expansion (PE) method. As one of the applications, the invariant nonlinear relations in polynomial expansion form are used as constraints to obtain numerical solutions by differential correction. The nonlinear relations among the directions provide an alternative point of view to explore the overall dynamics of periodic orbits around libration points with general rules.

James Webb Space Telescope Core 2 Test - Cryogenic Thermal Balance Test of the Observatorys Core Area Thermal Control Hardware

NASA Technical Reports Server (NTRS)

Cleveland, Paul; Parrish, Keith; Thomson, Shaun; Marsh, James; Comber, Brian

2016-01-01

The James Webb Space Telescope (JWST), successor to the Hubble Space Telescope, will be the largest astronomical telescope ever sent into space. To observe the very first light of the early universe, JWST requires a large deployed 6.5-meter primary mirror cryogenically cooled to less than 50 Kelvin. Three scientific instruments are further cooled via a large radiator system to less than 40 Kelvin. A fourth scientific instrument is cooled to less than 7 Kelvin using a combination pulse-tube Joule-Thomson mechanical cooler. Passive cryogenic cooling enables the large scale of the telescope which must be highly folded for launch on an Ariane 5 launch vehicle and deployed once on orbit during its journey to the second Earth-Sun Lagrange point. Passive cooling of the observatory is enabled by the deployment of a large tennis court sized five layer Sunshield combined with the use of a network of high efficiency radiators. A high purity aluminum heat strap system connects the three instrument's detector systems to the radiator systems to dissipate less than a single watt of parasitic and instrument dissipated heat. JWST's large scale features, while enabling passive cooling, also prevent the typical flight configuration fully-deployed thermal balance test that is the keystone of most space missions' thermal verification plans. This paper describes the JWST Core 2 Test, which is a cryogenic thermal balance test of a full size, high fidelity engineering model of the Observatory's 'Core' area thermal control hardware. The 'Core' area is the key mechanical and cryogenic interface area between all Observatory elements. The 'Core' area thermal control hardware allows for temperature transition of 300K to approximately 50 K by attenuating heat from the room temperature IEC (instrument electronics) and the Spacecraft Bus. Since the flight hardware is not available for test, the Core 2 test uses high fidelity and flight-like reproductions.

Thermal System Verification and Model Validation for NASA's Cryogenic Passively Cooled James Webb Space Telescope

NASA Technical Reports Server (NTRS)

Cleveland, Paul E.; Parrish, Keith A.

2005-01-01

A thorough and unique thermal verification and model validation plan has been developed for NASA s James Webb Space Telescope. The JWST observatory consists of a large deployed aperture optical telescope passively cooled to below 50 Kelvin along with a suite of several instruments passively and actively cooled to below 37 Kelvin and 7 Kelvin, respectively. Passive cooling to these extremely low temperatures is made feasible by the use of a large deployed high efficiency sunshield and an orbit location at the L2 Lagrange point. Another enabling feature is the scale or size of the observatory that allows for large radiator sizes that are compatible with the expected power dissipation of the instruments and large format Mercury Cadmium Telluride (HgCdTe) detector arrays. This passive cooling concept is simple, reliable, and mission enabling when compared to the alternatives of mechanical coolers and stored cryogens. However, these same large scale observatory features, which make passive cooling viable, also prevent the typical flight configuration fully-deployed thermal balance test that is the keystone to most space missions thermal verification plan. JWST is simply too large in its deployed configuration to be properly thermal balance tested in the facilities that currently exist. This reality, when combined with a mission thermal concept with little to no flight heritage, has necessitated the need for a unique and alternative approach to thermal system verification and model validation. This paper describes the thermal verification and model validation plan that has been developed for JWST. The plan relies on judicious use of cryogenic and thermal design margin, a completely independent thermal modeling cross check utilizing different analysis teams and software packages, and finally, a comprehensive set of thermal tests that occur at different levels of JWST assembly. After a brief description of the JWST mission and thermal architecture, a detailed description of the three aspects of the thermal verification and model validation plan is presented.

Micrometeorite Science with LISA Pathfinder

NASA Astrophysics Data System (ADS)

Pagane, Nicole; Thorpe, James Ira; Littenberg, Tyson; Littenberg, Tyson; Baker, John; Slutsky, Jacob; Hourihane, Sophie; LISA Pathfinder Team

2018-01-01

The primary objective of LISA Pathfinder (LPF) was to demonstrate drag-free control of test masses—along with the technology necessary to maintain the inertial motion—that LISA (Laser Interferometer Space Antenna) would later utilize as a space-based gravitational wave observatory. Due to the precise interferometry used during the mission, LPF could be employed as an accelerometer and used to detect micrometeorite impacts while in orbit about the Sun-Earth Lagrange Point L1. To infer micrometeorite impacts, the flight data was processed for event reconstruction to determine external acceleration of LPF; impact parameters were then estimated through a Markov-Chain Monte-Carlo (MCMC) tool via Bayesian analysis by fitting delta functions in the acceleration domain. As impact candidates were collected, a catalog of event data was curated with the reconstructed estimated parameters, among which were impact sky localizations that were later rotated into more intuitive reference frames. To infer the results of this dust modeling technique, current micrometeorite models were compared to the impact data. In the final reference frame common to the available micrometeorite models, the reconstructed impacts appear to cluster at (±90°, 0°)—where impacts prograde in this longitude-latitude frame were at (-90°, 0°), retrograde were (90°, 0°), and the sun was centered at the origin. The two available models used for comparison were of the Jupiter-family comets (JFC) and Halley-type comets (HTC), which clustered primarily around (±90°, 0°) and (0°, ±20°) respectively. This suggests that the JFC population seems to account for the majority of the impacts detected by LPF. The models’ expected rates given localization and velocity are currently being compared to the reconstructed data to further characterize the micrometeorite populations at L1. We will present our current analysis of this data set and discuss possibilities of extending such an analysis for LISA.

User and technical documentation

NASA Astrophysics Data System (ADS)

1988-09-01

The program LIBRATE calculates velocities for trajectories from low earth orbit (LEO) to four of the five libration points (L2, L3, L4, and L5), and from low lunar orbit (LLO) to libration points L1 and L2. The flight to be analyzed departs from a circular orbit of any altitude and inclination about the Earth or Moon and finishes in a circular orbit about the Earth at the desired libration point within a specified flight time. This program produces a matrix of the delta V's needed to complete the desired flight. The user specifies the departure orbit, and the maximum flight time. A matrix is then developed with 10 inclinations, ranging from 0 to 90 degrees, forming the columns, and 19 possible flight times, ranging from the flight time (input) to 36 hours less than the input value, in decrements of 2 hours, forming the rows. This matrix is presented in three different reports including the total delta V's, and both of the delta V components discussed. The input required from the user to define the flight is discussed. The contents of the three reports that are produced as outputs are also described. The instructions are also included which are needed to execute the program.

Minimum Number of Observation Points for LEO Satellite Orbit Estimation by OWL Network

NASA Astrophysics Data System (ADS)

Park, Maru; Jo, Jung Hyun; Cho, Sungki; Choi, Jin; Kim, Chun-Hwey; Park, Jang-Hyun; Yim, Hong-Suh; Choi, Young-Jun; Moon, Hong-Kyu; Bae, Young-Ho; Park, Sun-Youp; Kim, Ji-Hye; Roh, Dong-Goo; Jang, Hyun-Jung; Park, Young-Sik; Jeong, Min-Ji

2015-12-01

By using the Optical Wide-field Patrol (OWL) network developed by the Korea Astronomy and Space Science Institute (KASI) we generated the right ascension and declination angle data from optical observation of Low Earth Orbit (LEO) satellites. We performed an analysis to verify the optimum number of observations needed per arc for successful estimation of orbit. The currently functioning OWL observatories are located in Daejeon (South Korea), Songino (Mongolia), and Oukaïmeden (Morocco). The Daejeon Observatory is functioning as a test bed. In this study, the observed targets were Gravity Probe B, COSMOS 1455, COSMOS 1726, COSMOS 2428, SEASAT 1, ATV-5, and CryoSat-2 (all in LEO). These satellites were observed from the test bed and the Songino Observatory of the OWL network during 21 nights in 2014 and 2015. After we estimated the orbit from systematically selected sets of observation points (20, 50, 100, and 150) for each pass, we compared the difference between the orbit estimates for each case, and the Two Line Element set (TLE) from the Joint Space Operation Center (JSpOC). Then, we determined the average of the difference and selected the optimal observation points by comparing the average values.

Interplay between resonant tunneling and spin precession oscillations in all-electric all-semiconductor spin transistors

NASA Astrophysics Data System (ADS)

Alomar, M. I.; Serra, Llorenç; Sánchez, David

2016-08-01

We investigate the transmission properties of a spin transistor coupled to two quantum point contacts acting as a spin injector and detector. In the Fabry-Pérot regime, transport is mediated by quasibound states formed between tunnel barriers. Interestingly, the spin-orbit interaction of the Rashba type can be tuned in such a way that nonuniform spin-orbit fields can point along distinct directions at different points of the sample. We discuss both spin-conserving and spin-flipping transitions as the spin-orbit angle of orientation increases from parallel to antiparallel configurations. Spin precession oscillations are clearly seen as a function of the length of the central channel. Remarkably, we find that these oscillations combine with the Fabry-Pérot motion, giving rise to quasiperiodic transmissions in the purely one-dimensional case. Furthermore, we consider the more realistic case of a finite width in the transverse direction and find that the coherent oscillations become deteriorated for moderate values of the spin-orbit strength. Our results then determine the precise role of the spin-orbit intersubband coupling potential in the Fabry-Pérot-Datta-Das intermixed oscillations.

Method of determining the orbits of the small bodies in the solar system based on an exhaustive search of orbital planes

NASA Astrophysics Data System (ADS)

Bondarenko, Yu. S.; Vavilov, D. E.; Medvedev, Yu. D.

2014-05-01

A universal method of determining the orbits of newly discovered small bodies in the Solar System using their positional observations has been developed. The proposed method suggests determining geocentric distances of a small body by means of an exhaustive search for heliocentric orbital planes and subsequent determination of the distance between the observer and the points at which the chosen plane intersects with the vectors pointing to the object. Further, the remaining orbital elements are determined using the classical Gauss method after eliminating those heliocentric distances that have a fortiori low probabilities. The obtained sets of elements are used to determine the rms between the observed and calculated positions. The sets of elements with the least rms are considered to be most probable for newly discovered small bodies. Afterwards, these elements are improved using the differential method.

47 CFR 25.208 - Power flux density limits.

Code of Federal Regulations, 2012 CFR

2012-10-01

... emissions from all co-frequency space stations of a single non-geostationary-satellite orbit (NGSO) system... point on the geostationary satellite orbit (GSO) by the emissions from all co-frequency earth stations in a non-geostationary satellite orbit fixed-satellite service (NGSO FSS) system, for all conditions...

47 CFR 25.208 - Power flux density limits.

Code of Federal Regulations, 2010 CFR

2010-10-01

... emissions from all co-frequency space stations of a single non-geostationary-satellite orbit (NGSO) system... point on the geostationary satellite orbit (GSO) by the emissions from all co-frequency earth stations in a non-geostationary satellite orbit fixed-satellite service (NGSO FSS) system, for all conditions...

47 CFR 25.208 - Power flux density limits.

Code of Federal Regulations, 2011 CFR

2011-10-01

... emissions from all co-frequency space stations of a single non-geostationary-satellite orbit (NGSO) system... point on the geostationary satellite orbit (GSO) by the emissions from all co-frequency earth stations in a non-geostationary satellite orbit fixed-satellite service (NGSO FSS) system, for all conditions...

UV Spectroscopy of Lucy Mission Targets

NASA Astrophysics Data System (ADS)

Thomas, Cristina

2017-08-01

The Trojan asteroids are a significant population of primitive bodies trapped in Jupiter's stable L4 and L5 Lagrange regions. Their physical properties and existence in these particular orbits constrain the chemical and dynamical processes in our early Solar System. NASA's recently selected Lucy mission will perform the first reconnaissance of these asteroids and will answer many fundamental questions about the population. The compositions of the Trojans are not well understood. Spectroscopy and spectrophotometry in visible and near-infrared wavelengths show red slopes (spectra with reflectivity increasing towards the long wavelength end of the spectrum) and no diagnostic spectral absorption features. However, past spectral and photometric observations suggest there are unobserved features in ultraviolet wavelengths. We propose to obtain ultraviolet spectroscopy with WFC3 of four Trojan asteroids that are targets of the Lucy mission. Lucy will not have the capability to obtain ultraviolet spectra. The proposed observations can only be made using Hubble. We will determine if there are UV spectral features, as suggested by visible wavelength observations, and connect these features to candidate compositional components. These observations will enable connections between the compositions of Trojans and dynamical models of the early Solar System.

Long Term Missions at the Sun-Earth Libration Point L1: ACE, SOHO, and WIND

NASA Technical Reports Server (NTRS)

Roberts, Craig E.

2011-01-01

Three heliophysics missions -- the Advanced Composition Explorer (ACE), Solar Heliospheric Observatory (SOHO), and the Global Geoscience WIND -- have been orbiting the Sun-Earth interior libration point L1 continuously since 1997, 1996, and 2004, respectively. ACE and WIND (both NASA missions) and SOHO (an ESA-NASA joint mission) are all operated from the NASA Goddard Space Flight Center (GSFC). While ACE and SOHO have been dedicated libration point orbiters since their launches, WIND has had also a remarkable 10-year career flying a deep-space, multiple lunar-flyby trajectory prior to 2004. That era featured 36 targeted lunar flybys with excursions to both L1 and L2 before its final insertion in L1 orbit. A figure depicts the orbits of the three spacecraft, showing projections of the orbits onto the orthographic planes of a solar rotating ecliptic frame of reference. The SOHO orbit is a quasi-periodic halo orbit, where the frequencies of the in-plane and out-of-plane motions are practically equal. Such an orbit is seen to repeat itself with a period of approximately 178 days. For ACE and WIND, the frequencies of the in-plane and out-of-plane motions are unequal, giving rise to the characteristic Lissajous motion. ACE's orbit is of moderately small amplitude, whereas WIND's orbit is a large-amplitude Lissajous of dimensions close to those of the SOHO halo orbit. As motion about the collinear points is inherently unstable, stationkeeping maneuvers are necessary to prevent orbital decay and eventual escape from the L1 region. Though the three spacecraft are dissimilar (SOHO is a 3-axis stabilized Sun pointer, WIND is a spin-stabilized ecliptic pole pointer, and ACE is also spin-stabilized with its spin axis maintained between 4 and 20 degrees of the Sun), the stationkeeping technique for the three is fundamentally the same. The technique consists of correcting the energy of the orbit via a delta-V directed parallel or anti-parallel to the Spacecraft-to-Sun line. SOHO achieves this using thrusters oriented in line with the solar direction. WIND achieves the delta-V via pulsing radial thrusters when aligned with the Sun. ACE uses axial thrusters to apply delta-V with a component that is 94% or more aligned with the ACE-Sun line. Sunward thrust adds energy to the orbit preventing decay back toward Earth. Thrust directed anti-Sunward takes energy out of the L1 orbit, thereby preventing escape from the Earth-Moon system into independent heliocentric orbit. Libration point orbit stationkeeping delta-V costs grow exponentially with time elapsed from the last maneuver performed. The doubling time constant is approximately 16 days. For the sake of fuel conservation, and for limiting the absolute magnitude of propulsion performance errors, stationkeeping maneuvers should be performed before the delta-V grows too large; for our purposes 'too large' is considered to be greater than 0.5 m/sec. In practice, the typical interval between burns for this trio is about three months, and the typical delta-V is much smaller than 0.5 m/sec. Typical annual stationkeeping costs have been around 1.0 m/sec for ACE and WIND, and much less than that for SOHO. All three spacecraft have ample fuel remaining; barring contingencies all three could, in principle, be maintained at L1 for decades to come. This paper will review the L1 orbits and the mission history of ACE, WIND, and SOHO, and describe the stationkeeping techniques and orbit maneuver experience. The Lissajous phase control that was practiced for ACE during the period from 1999 to 2001 will also be briefly discussed. The final section will consider the future of these ongoing missions.

Prospects for tracking spacecrafts within 2 million Km of Earth with phased array antennas

NASA Technical Reports Server (NTRS)

Amoozegar, F.; Jamnejad, V.; Cesarone, R.

2003-01-01

Recent advances in space technology for Earth observations, global communications, and positioning systems have created heavy traffic at a variety of orbits. These include smart sensors in low Earth orbits (LEO), internet satellites in LEO and GEO orbits, Earth observing satellites in high Earth orbits (HEO), observatory class satellites at Lagrangian libration points, and those heading for deep space.

14 CFR 420.19 - Launch site location review-general.

Code of Federal Regulations, 2011 CFR

2011-01-01

... nm orbit Weight class Small Medium Medium large Large 28 degrees inclination * ≤4400 >4400 to ≤11100.... Orbital expendable launch vehicles are further classified by weight class, based on the weight of payload... class of orbital expendable launch vehicles flown from a launch point, the applicant shall demonstrate...

14 CFR 420.19 - Launch site location review-general.

Code of Federal Regulations, 2010 CFR

2010-01-01

... site, at least one type of expendable or reusable launch vehicle can be flown from the launch point... × 10−6). (2) Types of launch vehicles include orbital expendable launch vehicles, guided sub-orbital expendable launch vehicles, unguided sub-orbital expendable launch vehicles, and reusable launch vehicles...

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.

Feasibility evaluation and study of adapting the attitude reference system to the Orbiter camera payload system's large format camera

NASA Technical Reports Server (NTRS)

1982-01-01

A design concept that will implement a mapping capability for the Orbital Camera Payload System (OCPS) when ground control points are not available is discussed. Through the use of stellar imagery collected by a pair of cameras whose optical axis are structurally related to the large format camera optical axis, such pointing information is made available.

Orbit determination singularities in the Doppler tracking of a planetary orbiter

NASA Technical Reports Server (NTRS)

Wood, L. J.

1985-01-01

On a number of occasions, spacecraft launched by the U.S. have been placed into orbit about the moon, Venus, or Mars. It is pointed out that, in particular, in planetary orbiter missions two-way coherent Doppler data have provided the principal data type for orbit determination applications. The present investigation is concerned with the problem of orbit determination on the basis of Doppler tracking data in the case of a spacecraft in orbit about a natural body other than the earth or the sun. Attention is given to Doppler shift associated with a planetary orbiter, orbit determination using a zeroth-order model for the Doppler shift, and orbit determination using a first-order model for the Doppler shift.

Invariant Solar Sail Formations in Elliptical Sun-Synchronous Orbits

NASA Astrophysics Data System (ADS)

Parsay, Khashayar

Current and past missions that study the Earth's geomagnetic tail require multiple spacecraft to fly in formation about a highly eccentric Keplerian reference orbit that has its apogee inside a predefined science region of interest. Because the geomagnetic tail is directed along the Sun-Earth line and therefore rotates annually, inertially fixed Keplerian orbits are only aligned with the geomagnetic tail once per year. This limitation reduces the duration of the science phase to less than a few months annually. Solar sails are capable of creating non-Keplerian, Sun-synchronous orbits that rotate with the geomagnetic tail. A solar sail flying in a Sun-synchronous orbit will have a continuous presence in the geomagnetic tail throughout the entire year, which significantly improves the in situ observations of the magnetosphere. To achieve a Sun-synchronous orbit, a solar sail is required to maintain a Sun-pointing attitude, which leads to the artificial precession of the orbit apse line in a Sun-synchronous manner, leaving the orbit apogee inside the science region of interest throughout entire the year. To study the spatial and temporal variations of plasma in the highly dynamic environment of the magnetosphere, multiple spacecraft must fly in a formation. The objective for this dissertation is to investigate the feasibility of solar sail formation flying in the Earth-centered, Sun-synchronous orbit regime. The focus of this effort is to enable formation flying for a group of solar sails that maintain a nominally fixed Sun-pointing attitude during formation flight, solely for the purpose of precessing their orbit apse lines Sun-synchronously. A fixed-attitude solar sail formation is motivated by the difficulties in the simultaneous control of orbit and attitude in flying solar sails. First, the secular rates of the orbital elements resulting from the effects of solar radiation pressure (SRP) are determined using averaging theory for a Sun-pointing attitude sail. These averaged rates are used to analytically derive the necessary conditions for a drift-free solar sail formation in Sun-synchronous orbits, assuming a fixed Sun-pointing orientation for each sail in formation. Next, the problem of formation design is solved using nonlinear programming for optimal two-craft, three-craft, and four-craft solar sail formations, in terms of formation quality and stability. Finally, the problem of formation establishment is addressed using optimal control theory, assuming that the sails are capable of making small changes to their orientations with respect to the Sun. These studies demonstrate the feasibility of solar sail formation flying for exploring the geomagnetic tail and improve upon previous work, which only considered unnatural relative motions that require continuous use of active control to remain in formation.

Optimal solar sail planetocentric trajectories

NASA Technical Reports Server (NTRS)

Sackett, L. L.

1977-01-01

The analysis of solar sail planetocentric optimal trajectory problem is described. A computer program was produced to calculate optimal trajectories for a limited performance analysis. A square sail model is included and some consideration is given to a heliogyro sail model. Orbit to a subescape point and orbit to orbit transfer are considered. Trajectories about the four inner planets can be calculated and shadowing, oblateness, and solar motion may be included. Equinoctial orbital elements are used to avoid the classical singularities, and the method of averaging is applied to increase computational speed. Solution of the two-point boundary value problem which arises from the application of optimization theory is accomplished with a Newton procedure. Time optimal trajectories are emphasized, but a penalty function has been considered to prevent trajectories which intersect a planet's surface.

Libration Point Orbit Utilization for Tactical Advantage in Communications, Surveillance, and Risk Mitigation

DTIC Science & Technology

2014-10-27

Ephemeris model in the orbit analysis software Satellite Took Kit ( STK ). As the first step, a study was conducted to find the visibility coverage using...northern L1 and L3 halo orbits. Figure 55. Average visibility by latitude at different ephemeris epochs for an L1 orbiter from STK analysis . Figure...56. Average visibility by latitude at different ephemeris epochs for an L3 orbiter from STK analysis . Figure 57. Average percent visibility of the

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.

Eclipse-Free-Time Assessment Tool for IRIS

NASA Technical Reports Server (NTRS)

Eagle, David

2012-01-01

IRIS_EFT is a scientific simulation that can be used to perform an Eclipse-Free- Time (EFT) assessment of IRIS (Infrared Imaging Surveyor) mission orbits. EFT is defined to be those time intervals longer than one day during which the IRIS spacecraft is not in the Earth s shadow. Program IRIS_EFT implements a special perturbation of orbital motion to numerically integrate Cowell's form of the system of differential equations. Shadow conditions are predicted by embedding this integrator within Brent s method for finding the root of a nonlinear equation. The IRIS_EFT software models the effects of the following types of orbit perturbations on the long-term evolution and shadow characteristics of IRIS mission orbits. (1) Non-spherical Earth gravity, (2) Atmospheric drag, (3) Point-mass gravity of the Sun, and (4) Point-mass gravity of the Moon. The objective of this effort was to create an in-house computer program that would perform eclipse-free-time analysis. of candidate IRIS spacecraft mission orbits in an accurate and timely fashion. The software is a suite of Fortran subroutines and data files organized as a "computational" engine that is used to accurately predict the long-term orbit evolution of IRIS mission orbits while searching for Earth shadow conditions.

Mars Express Forward Link Capabilities for the Mars Relay Operations Service (MaROS)

NASA Technical Reports Server (NTRS)

Allard, Daniel A.; Wallick, Michael N.; Gladden, Roy E.; Wang, Paul

2012-01-01

This software provides a new capability for landed Mars assets to perform forward link relay through the Mars Express (MEX) European Union orbital spacecraft. It solves the problem of standardizing the relay interface between lander missions and MEX. The Mars Operations Relay Service (MaROS) is intended as a central point for relay planning and post-pass analysis for all Mars landed and orbital assets. Through the first two phases of implementation, MaROS supports relay coordination through the Odyssey orbiter and the Mars Reconnaissance Orbiter (MRO). With this new software, MaROS now fully integrates the Mars Express spacecraft into the relay picture. This new software generates and manages a new set of file formats that allows for relay request to MEX for forward and return link relay, including the parameters specific to MEX. Existing MEX relay planning interactions were performed via email exchanges and point-to-point file transfers. By integrating MEX into MaROS, all transactions are managed by a centralized service for tracking and analysis. Additionally, all lander missions have a single, shared interface with MEX and do not have to integrate on a mission-by mission basis. Relay is a critical element of Mars lander data management. Landed assets depend largely upon orbital relay for data delivery, which can be impacted by the availability and health of each orbiter in the network. At any time, an issue may occur to prevent relay. For this reason, it is imperative that all possible orbital assets be integrated into the overall relay picture.

The SPQR experiment: detecting damage to orbiting spacecraft with ground-based telescopes

NASA Astrophysics Data System (ADS)

Paolozzi, Antonio; Porfilio, Manfredi; Currie, Douglas G.; Dantowitz, Ronald F.

2007-09-01

The objective of the Specular Point-like Quick Reference (SPQR) experiment was to evaluate the possibility of improving the resolution of ground-based telescopic imaging of manned spacecraft in orbit. The concept was to reduce image distortions due to atmospheric turbulence by evaluating the Point Spread Function (PSF) of a point-like light reference and processing the spacecraft image accordingly. The target spacecraft was the International Space Station (ISS) and the point-like reference was provided by a laser beam emitted by the ground station and reflected back to the telescope by a Cube Corner Reflector (CCR) mounted on an ISS window. The ultimate objective of the experiment was to demonstrate that it is possible to image spacecraft in Low Earth Orbit (LEO) with a resolution of 20 cm, which would have probably been sufficient to detect the damage which caused the Columbia disaster. The experiment was successfully performed from March to May 2005. The paper provides an overview of the SPQR experiment.

Codimension-Two Bifurcation, Chaos and Control in a Discrete-Time Information Diffusion Model

NASA Astrophysics Data System (ADS)

Ren, Jingli; Yu, Liping

2016-12-01

In this paper, we present a discrete model to illustrate how two pieces of information interact with online social networks and investigate the dynamics of discrete-time information diffusion model in three types: reverse type, intervention type and mutualistic type. It is found that the model has orbits with period 2, 4, 6, 8, 12, 16, 20, 30, quasiperiodic orbit, and undergoes heteroclinic bifurcation near 1:2 point, a homoclinic structure near 1:3 resonance point and an invariant cycle bifurcated by period 4 orbit near 1:4 resonance point. Moreover, in order to regulate information diffusion process and information security, we give two control strategies, the hybrid control method and the feedback controller of polynomial functions, to control chaos, flip bifurcation, 1:2, 1:3 and 1:4 resonances, respectively, in the two-dimensional discrete system.

Photogrammetric analysis of horizon panoramas: The Pathfinder landing site in Viking orbiter images

USGS Publications Warehouse

Oberst, J.; Jaumann, R.; Zeitler, W.; Hauber, E.; Kuschel, M.; Parker, T.; Golombek, M.; Malin, M.; Soderblom, L.

1999-01-01

Tiepoint measurements, block adjustment techniques, and sunrise/sunset pictures were used to obtain precise pointing data with respect to north for a set of 33 IMP horizon images. Azimuth angles for five prominent topographic features seen at the horizon were measured and correlated with locations of these features in Viking orbiter images. Based on this analysis, the Pathfinder line/sample coordinates in two raw Viking images were determined with approximate errors of 1 pixel, or 40 m. Identification of the Pathfinder location in orbit imagery yields geological context for surface studies of the landing site. Furthermore, the precise determination of coordinates in images together with the known planet-fixed coordinates of the lander make the Pathfinder landing site the most important anchor point in current control point networks of Mars. Copyright 1999 by the American Geophysical Union.

Navigation of a Satellite Cluster with Realistic Dynamics

DTIC Science & Technology

1991-12-01

20 2.2.1 Dynamics ( Clohessy - Wiltshire Equations) ............ 21 2.2.2 Iterated, Extended Kalman Filter.................26 iv I1l...8 Figure 4. Point mass and Clohessy - Wiltshire orbits (10 orbits) .......... 16 Figure 5. Real dynamics and Clohessy - Wiltshire orbits (10...filter ..... 31 Figure 8. Comparison of the Clohessy - Wiltshire and truth model solutions

Magnetic attitude control torque generation of a gravity gradient stabilized satellite

NASA Astrophysics Data System (ADS)

Suhadis, N. M.; Salleh, M. B.; Rajendran, P.

2018-05-01

Magnetic torquer is used to generate a magnetic dipole moment onboard satellites whereby a control torque for attitude control purposes is generated when it couples with the geomagnetic field. This technique has been considered very attractive for satellites operated in Low Earth Orbit (LEO) as the strength of the geomagnetic field is relatively high below the altitude of 1000 km. This paper presents the algorithm used to generate required magnetic dipole moment by 3 magnetic torquers mounted onboard a gravity gradient stabilized satellite operated at an altitude of 540 km with nadir pointing mission. As the geomagnetic field cannot be altered and its magnitude and direction vary with respect to the orbit altitude and inclination, a comparison study of attitude control torque generation performance with various orbit inclination is performed where the structured control algorithm is simulated for 13°, 33° and 53° orbit inclinations to see how the variation of the satellite orbit affects the satellite's attitude control torque generation. Results from simulation show that the higher orbit inclination generates optimum magnetic attitude control torque for accurate nadir pointing mission.

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.

Worst case estimation of homology design by convex analysis

NASA Technical Reports Server (NTRS)

Yoshikawa, N.; Elishakoff, Isaac; Nakagiri, S.

1998-01-01

The methodology of homology design is investigated for optimum design of advanced structures. for which the achievement of delicate tasks by the aid of active control system is demanded. The proposed formulation of homology design, based on the finite element sensitivity analysis, necessarily requires the specification of external loadings. The formulation to evaluate the worst case for homology design caused by uncertain fluctuation of loadings is presented by means of the convex model of uncertainty, in which uncertainty variables are assigned to discretized nodal forces and are confined within a conceivable convex hull given as a hyperellipse. The worst case of the distortion from objective homologous deformation is estimated by the Lagrange multiplier method searching the point to maximize the error index on the boundary of the convex hull. The validity of the proposed method is demonstrated in a numerical example using the eleven-bar truss structure.

Application of GA, PSO, and ACO algorithms to path planning of autonomous underwater vehicles

NASA Astrophysics Data System (ADS)

Aghababa, Mohammad Pourmahmood; Amrollahi, Mohammad Hossein; Borjkhani, Mehdi

2012-09-01

In this paper, an underwater vehicle was modeled with six dimensional nonlinear equations of motion, controlled by DC motors in all degrees of freedom. Near-optimal trajectories in an energetic environment for underwater vehicles were computed using a numerical solution of a nonlinear optimal control problem (NOCP). An energy performance index as a cost function, which should be minimized, was defined. The resulting problem was a two-point boundary value problem (TPBVP). A genetic algorithm (GA), particle swarm optimization (PSO), and ant colony optimization (ACO) algorithms were applied to solve the resulting TPBVP. Applying an Euler-Lagrange equation to the NOCP, a conjugate gradient penalty method was also adopted to solve the TPBVP. The problem of energetic environments, involving some energy sources, was discussed. Some near-optimal paths were found using a GA, PSO, and ACO algorithms. Finally, the problem of collision avoidance in an energetic environment was also taken into account.