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.

Aerodynamic studies of delta-wing shuttle orbiters. Part 1: Low speed

NASA Technical Reports Server (NTRS)

Freeman, D. C., Jr.; Ellison, J. C.

1972-01-01

Numerous wind tunnel tests conducted on the evolving delta-wing orbiters have generated a fairly large aerodynamic data base over the entire entry operation range of these vehicles. A limited assessment is made of some of the aerodynamics of the current HO type orbiters, and several specific problem areas selected from the broad data base are discussed. These include, from a subsonic viewpoint, discussions of trim drag effect; effects of the installation of main rocket engine nozzles, OMS and RCS packages, Reynolds number effects, lateral-directional stability characteristics, and landing characteristics.

Two approaches for the gravitational self-force in black hole spacetime: Comparison of numerical results

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

Sago, Norichika; Barack, Leor; Detweiler, Steven

2008-12-15

Recently, two independent calculations have been presented of finite-mass ('self-force') effects on the orbit of a point mass around a Schwarzschild black hole. While both computations are based on the standard mode-sum method, they differ in several technical aspects, which makes comparison between their results difficult--but also interesting. Barack and Sago [Phys. Rev. D 75, 064021 (2007)] invoke the notion of a self-accelerated motion in a background spacetime, and perform a direct calculation of the local self-force in the Lorenz gauge (using numerical evolution of the perturbation equations in the time domain); Detweiler [Phys. Rev. D 77, 124026 (2008)] describesmore » the motion in terms a geodesic orbit of a (smooth) perturbed spacetime, and calculates the metric perturbation in the Regge-Wheeler gauge (using frequency-domain numerical analysis). Here we establish a formal correspondence between the two analyses, and demonstrate the consistency of their numerical results. Specifically, we compare the value of the conservative O({mu}) shift in u{sup t} (where {mu} is the particle's mass and u{sup t} is the Schwarzschild t component of the particle's four-velocity), suitably mapped between the two orbital descriptions and adjusted for gauge. We find that the two analyses yield the same value for this shift within mere fractional differences of {approx}10{sup -5}-10{sup -7} (depending on the orbital radius)--comparable with the estimated numerical error.« less

Spin-orbit scattering visualized in quasiparticle interference

NASA Astrophysics Data System (ADS)

Kohsaka, Y.; Machida, T.; Iwaya, K.; Kanou, M.; Hanaguri, T.; Sasagawa, T.

2017-03-01

In the presence of spin-orbit coupling, electron scattering off impurities depends on both spin and orbital angular momentum of electrons—spin-orbit scattering. Although some transport properties are subject to spin-orbit scattering, experimental techniques directly accessible to this effect are limited. Here we show that a signature of spin-orbit scattering manifests itself in quasiparticle interference (QPI) imaged by spectroscopic-imaging scanning tunneling microscopy. The experimental data of a polar semiconductor BiTeI are well reproduced by numerical simulations with the T -matrix formalism that include not only scalar scattering normally adopted but also spin-orbit scattering stronger than scalar scattering. To accelerate the simulations, we extend the standard efficient method of QPI calculation for momentum-independent scattering to be applicable even for spin-orbit scattering. We further identify a selection rule that makes spin-orbit scattering visible in the QPI pattern. These results demonstrate that spin-orbit scattering can exert predominant influence on QPI patterns and thus suggest that QPI measurement is available to detect spin-orbit scattering.

Trajectory optimization of spacecraft high-thrust orbit transfer using a modified evolutionary algorithm

NASA Astrophysics Data System (ADS)

Shirazi, Abolfazl

2016-10-01

This article introduces a new method to optimize finite-burn orbital manoeuvres based on a modified evolutionary algorithm. Optimization is carried out based on conversion of the orbital manoeuvre into a parameter optimization problem by assigning inverse tangential functions to the changes in direction angles of the thrust vector. The problem is analysed using boundary delimitation in a common optimization algorithm. A method is introduced to achieve acceptable values for optimization variables using nonlinear simulation, which results in an enlarged convergence domain. The presented algorithm benefits from high optimality and fast convergence time. A numerical example of a three-dimensional optimal orbital transfer is presented and the accuracy of the proposed algorithm is shown.

Exospheric perturbations by radiation pressure. 2: Solution for orbits in the ecliptic plane

NASA Technical Reports Server (NTRS)

Chamberlain, J. W.

1980-01-01

The instantaneous rates of change for the orbital elements eccentricity, longitude of perigee from the Sun, and longitude from the Sun of the ascending node are integrated simultaneously for the case of the inclination i = 0. The results confirm the validity of using mean rates when the orbits are tightly bound to the planet and serve as examples to be reproduced by the complicated numerical solutions required for arbitrary inclination. Strongly bound hydrogen atoms escaping from Earth due to radiation pressure do not seem a likely cause of the geotail extending in the anti-sun direction. Instead, radiation pressure will cause those particles' orbits to deteriorate into the Earth's atmosphere.

Direct Measurement of the Topological Charge in Elliptical Beams Using Diffraction by a Triangular Aperture.

PubMed

Melo, Leandro A; Jesus-Silva, Alcenísio J; Chávez-Cerda, Sabino; Ribeiro, Paulo H Souto; Soares, Willamys C

2018-04-23

We introduce a simple method to characterize the topological charge associated with the orbital angular momentum of a m-order elliptic light beam. This method consists in the observation of the far field pattern of the beam carrying orbital angular momentum, diffracted from a triangular aperture. We show numerically and experimentally, for Mathieu, Ince-Gaussian, and vortex Hermite-Gaussian beams, that only isosceles triangular apertures allow us to determine in a precise and direct way, the magnitude m of the order and the number and sign of unitary topological charges of isolated vortices inside the core of these beams.

NPP VIIRS Geometric Performance Status

NASA Technical Reports Server (NTRS)

Lin, Guoqing; Wolfe, Robert E.; Nishihama, Masahiro

2011-01-01

Visible Infrared Imager Radiometer Suite (VIIRS) instrument on-board the National Polar-orbiting Operational Environmental Satellite System (NPOESS) Preparatory Project (NPP) satellite is scheduled for launch in October, 2011. It is to provide satellite measured radiance/reflectance data for both weather and climate applications. Along with radiometric calibration, geometric characterization and calibration of Sensor Data Records (SDRs) are crucial to the VIIRS Environmental Data Record (EDR) algorithms and products which are used in numerical weather prediction (NWP). The instrument geometric performance includes: 1) sensor (detector) spatial response, parameterized by the dynamic field of view (DFOV) in the scan direction and instantaneous FOV (IFOV) in the track direction, modulation transfer function (MTF) for the 17 moderate resolution bands (M-bands), and horizontal spatial resolution (HSR) for the five imagery bands (I-bands); 2) matrices of band-to-band co-registration (BBR) from the corresponding detectors in all band pairs; and 3) pointing knowledge and stability characteristics that includes scan plane tilt, scan rate and scan start position variations, and thermally induced variations in pointing with respect to orbital position. They have been calibrated and characterized through ground testing under ambient and thermal vacuum conditions, numerical modeling and analysis. This paper summarizes the results, which are in general compliance with specifications, along with anomaly investigations, and describes paths forward for characterizing on-orbit BBR and spatial response, and for improving instrument on-orbit performance in pointing and geolocation.

Nontrivial paths and periodic orbits of the T-fractal billiard table

NASA Astrophysics Data System (ADS)

Lapidus, Michel L.; Miller, Robyn L.; Niemeyer, Robert G.

2016-07-01

We introduce and prove numerous new results about the orbits of the T-fractal billiard. Specifically, in section 3, we give a variety of sufficient conditions for the existence of a sequence of compatible periodic orbits. In section 4, we examine the limiting behavior of particular sequences of compatible periodic orbits. Additionally, sufficient conditions for the existence of particular nontrivial paths are given in section 4. The proofs of two results of Lapidus and Niemeyer (2013 The current state of fractal billiards Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II: Fractals in Applied Mathematics (Contemporary Mathematics vol 601) ed D Carfi et al (Providence, RI: American Mathematical Society) pp 251-88 (e-print: arXiv:math.DS.1210.0282v2, 2013) appear here for the first time, as well. In section 5, an orbit with an irrational initial direction reaches an elusive point in a way that yields a nontrivial path of finite length, yet, by our convention, constitutes a singular orbit of the fractal billiard table. The existence of such an orbit seems to indicate that the classification of orbits may not be so straightforward. A discussion of our results and directions for future research is then given in section 6.

Stationary and moving solitons in spin-orbit-coupled spin-1 Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Li, Yu-E.; Xue, Ju-Kui

2018-04-01

We investigate the matter-wave solitons in a spin-orbit-coupled spin-1 Bose-Einstein condensate using a multiscale perturbation method. Beginning with the one-dimensional spin-orbit-coupled threecomponent Gross-Pitaevskii equations, we derive a single nonlinear Schrödinger equation, which allows determination of the analytical soliton solutions of the system. Stationary and moving solitons in the system are derived. In particular, a parameter space for different existing soliton types is provided. It is shown that there exist only dark or bright solitons when the spin-orbit coupling is weak, with the solitons depending on the atomic interactions. However, when the spin-orbit coupling is strong, both dark and bright solitons exist, being determined by the Raman coupling. Our analytical solutions are confirmed by direct numerical simulations.

Numerical analysis of the angular motion of a neutrally buoyant spheroid in shear flow at small Reynolds numbers.

PubMed

Rosén, T; Einarsson, J; Nordmark, A; Aidun, C K; Lundell, F; Mehlig, B

2015-12-01

We numerically analyze the rotation of a neutrally buoyant spheroid in a shear flow at small shear Reynolds number. Using direct numerical stability analysis of the coupled nonlinear particle-flow problem, we compute the linear stability of the log-rolling orbit at small shear Reynolds number Re(a). As Re(a)→0 and as the box size of the system tends to infinity, we find good agreement between the numerical results and earlier analytical predictions valid to linear order in Re(a) for the case of an unbounded shear. The numerical stability analysis indicates that there are substantial finite-size corrections to the analytical results obtained for the unbounded system. We also compare the analytical results to results of lattice Boltzmann simulations to analyze the stability of the tumbling orbit at shear Reynolds numbers of order unity. Theory for an unbounded system at infinitesimal shear Reynolds number predicts a bifurcation of the tumbling orbit at aspect ratio λ(c)≈0.137 below which tumbling is stable (as well as log rolling). The simulation results show a bifurcation line in the λ-Re(a) plane that reaches λ≈0.1275 at the smallest shear Reynolds number (Re(a)=1) at which we could simulate with the lattice Boltzmann code, in qualitative agreement with the analytical results.

Spin-orbit coupling effects in zinc-blende InSb and wurtzite InAs nanowires: Realistic calculations with multiband k .p method

NASA Astrophysics Data System (ADS)

Campos, Tiago; Faria Junior, Paulo E.; Gmitra, Martin; Sipahi, Guilherme M.; Fabian, Jaroslav

2018-06-01

A systematic numerical investigation of spin-orbit fields in the conduction bands of III-V semiconductor nanowires is performed. Zinc-blende (ZB) InSb nanowires are considered along [001], [011], and [111] directions, while wurtzite (WZ) InAs nanowires are studied along [0001] and [10 1 ¯0 ] or [11 2 ¯0 ] directions. Robust multiband k .p Hamiltonians are solved by using plane-wave expansions of real-space parameters. In all cases, the linear and cubic spin-orbit coupling parameters are extracted for nanowire widths from 30 to 100 nm. Typical spin-orbit energies are on the μ eV scale, except for WZ InAs nanowires grown along [10 1 ¯0 ] or [11 2 ¯0 ] , in which the spin-orbit energy is about meV, largely independent of the wire diameter. Significant spin-orbit coupling is obtained by applying a transverse electric field, causing the Rashba effect. For an electric field of about 4 mV/nm, the obtained spin-orbit energies are about 1 meV for both materials in all investigated growth directions. The most favorable system, in which the spin-orbit effects are maximal, are WZ InAs nanowires grown along [1010] or [11 2 ¯0 ] since here spin-orbit energies are giant (meV) already in the absence of electric field. The least favorable are InAs WZ nanowires grown along [0001] since here even the electric field does not increase the spin-orbit energies beyond 0.1 meV. The presented results should be useful for investigations of optical orientation, spin transport, weak localization, and superconducting proximity effects in semiconductor nanowires.

Secular Dynamical Anti-friction in Galactic Nuclei

NASA Astrophysics Data System (ADS)

Madigan, Ann-Marie; Levin, Yuri

2012-07-01

We identify a gravitational-dynamical process in near-Keplerian potentials of galactic nuclei that occurs when an intermediate-mass black hole (IMBH) is migrating on an eccentric orbit through the stellar cluster towards the central supermassive black hole. We find that, apart from conventional dynamical friction, the IMBH experiences an often much stronger systematic torque due to the secular (i.e., orbit-averaged) interactions with the cluster's stars. The force which results in this torque is applied, counterintuitively, in the same direction as the IMBH's precession and we refer to its action as "secular dynamical anti-friction" (SDAF). We argue that SDAF, and not the gravitational ejection of stars, is responsible for the IMBH's eccentricity increase seen in the initial stages of previous N-body simulations. Our numerical experiments, supported by qualitative arguments, demonstrate that (1) when the IMBH's precession direction is artificially reversed, the torque changes sign as well, which decreases the orbital eccentricity; (2) the rate of eccentricity growth is sensitive to the IMBH migration rate, with zero systematic eccentricity growth for an IMBH whose orbit is artificially prevented from inward migration; and (3) SDAF is the strongest when the central star cluster is rapidly rotating. This leads to eccentricity growth/decrease for the clusters rotating in the opposite/same direction relative to the IMBH's orbital motion.

Lunar Cube Transfer Trajectory Options

NASA Technical Reports Server (NTRS)

Folta, David; Dichmann, Donald James; Clark, Pamela E.; Haapala, Amanda; Howell, Kathleen

2015-01-01

Numerous Earth-Moon trajectory and lunar orbit options are available for Cubesat missions. Given the limited Cubesat injection infrastructure, transfer trajectories are contingent upon the modification of an initial condition of the injected or deployed orbit. Additionally, these transfers can be restricted by the selection or designs of Cubesat subsystems such as propulsion or communication. Nonetheless, many trajectory options can b e considered which have a wide range of transfer duration, fuel requirements, and final destinations. Our investigation of potential trajectories highlights several options including deployment from low Earth orbit (LEO) geostationary transfer orbits (GTO) and higher energy direct lunar transfer and the use of longer duration Earth-Moon dynamical systems. For missions with an intended lunar orbit, much of the design process is spent optimizing a ballistic capture while other science locations such as Sun-Earth libration or heliocentric orbits may simply require a reduced Delta-V imparted at a convenient location along the trajectory.

Lunar Cube Transfer Trajectory Options

NASA Technical Reports Server (NTRS)

Folta, David; Dichmann, Donald J.; Clark, Pamela; Haapala, Amanda; Howell, Kathleen

2015-01-01

Numerous Earth-Moon trajectory and lunar orbit options are available for Cubesat missions. Given the limited Cubesat injection infrastructure, transfer trajectories are contingent upon the modification of an initial condition of the injected or deployed orbit. Additionally, these transfers can be restricted by the selection or designs of Cubesat subsystems such as propulsion or communication. Nonetheless, many trajectory options can be considered which have a wide range of transfer durations, fuel requirements, and final destinations. Our investigation of potential trajectories highlights several options including deployment from low Earth orbit (LEO), geostationary transfer orbits (GTO), and higher energy direct lunar transfers and the use of longer duration Earth-Moon dynamical systems. For missions with an intended lunar orbit, much of the design process is spent optimizing a ballistic capture while other science locations such as Sun-Earth libration or heliocentric orbits may simply require a reduced Delta-V imparted at a convenient location along the trajectory.

Relativistic spin-orbit interactions of photons and electrons

NASA Astrophysics Data System (ADS)

Smirnova, D. A.; Travin, V. M.; Bliokh, K. Y.; Nori, F.

2018-04-01

Laboratory optics, typically dealing with monochromatic light beams in a single reference frame, exhibits numerous spin-orbit interaction phenomena due to the coupling between the spin and orbital degrees of freedom of light. Similar phenomena appear for electrons and other spinning particles. Here we examine transformations of paraxial photon and relativistic-electron states carrying the spin and orbital angular momenta (AM) under the Lorentz boosts between different reference frames. We show that transverse boosts inevitably produce a rather nontrivial conversion from spin to orbital AM. The converted part is then separated between the intrinsic (vortex) and extrinsic (transverse shift or Hall effect) contributions. Although the spin, intrinsic-orbital, and extrinsic-orbital parts all point in different directions, such complex behavior is necessary for the proper Lorentz transformation of the total AM of the particle. Relativistic spin-orbit interactions can be important in scattering processes involving photons, electrons, and other relativistic spinning particles, as well as when studying light emitted by fast-moving bodies.

An iterative analytical technique for the design of interplanetary direct transfer trajectories including perturbations

NASA Astrophysics Data System (ADS)

Parvathi, S. P.; Ramanan, R. V.

2018-06-01

An iterative analytical trajectory design technique that includes perturbations in the departure phase of the interplanetary orbiter missions is proposed. The perturbations such as non-spherical gravity of Earth and the third body perturbations due to Sun and Moon are included in the analytical design process. In the design process, first the design is obtained using the iterative patched conic technique without including the perturbations and then modified to include the perturbations. The modification is based on, (i) backward analytical propagation of the state vector obtained from the iterative patched conic technique at the sphere of influence by including the perturbations, and (ii) quantification of deviations in the orbital elements at periapsis of the departure hyperbolic orbit. The orbital elements at the sphere of influence are changed to nullify the deviations at the periapsis. The analytical backward propagation is carried out using the linear approximation technique. The new analytical design technique, named as biased iterative patched conic technique, does not depend upon numerical integration and all computations are carried out using closed form expressions. The improved design is very close to the numerical design. The design analysis using the proposed technique provides a realistic insight into the mission aspects. Also, the proposed design is an excellent initial guess for numerical refinement and helps arrive at the four distinct design options for a given opportunity.

Direct observations of a flare related coronal and solar wind disturbance

NASA Technical Reports Server (NTRS)

Gosling, J. T.; Hildner, E.; Macqueen, R. M.; Munro, R. H.; Poland, A. I.; Ross, C. L.

1975-01-01

Numerous mass ejections from the sun have been detected with orbiting coronagraphs. Here for the first time we document and discuss the direct association of a coronagraph observed mass ejection, which followed a 2B flare, with a large interplanetary shock wave disturbance observed at 1 AU. Estimates of the mass and energy content of the coronal disturbance are in reasonably good agreement with estimates of the mass and energy content of the solar wind disturbance at 1 AU. The energy estimates as well as the transit time of the disturbance are also in good agreement with numerical models of shock wave propagation in the solar wind.

Deadly Sunflower Orbits

NASA Astrophysics Data System (ADS)

Hamilton, Douglas P.

2018-04-01

Solar radiation pressure is usually very effective at removing hazardous millimeter-sized debris from distant orbits around asteroidsand other small solar system bodies (Hamilton and Burns 1992). Theprimary loss mechanism, driven by the azimuthal component of radiationpressure, is eccentricity growth followed by a forced collision withthe central body. One large class of orbits, however, neatly sidestepsthis fate. Orbits oriented nearly perpendicular to the solar directioncan maintain their face-on geometry, oscillating slowly around a stableequilibrium orbit. These orbits, designated sunflower orbits, arerelated to terminator orbits studied by spacecraft mission designers(Broschart etal. 2014).Destabilization of sunflower orbits occurs only for particles smallenough that radiation pressure is some tens of percent the strength ofthe central body's direct gravity. This greatly enhanced stability,which follows from the inability of radiation incident normal to theorbit to efficiently drive eccentricities, presents a threat tospacecraft missions, as numerous dangerous projectiles are potentiallyretained in orbit. We have investigated sunflower orbits insupport of the New Horizons, Aida, and Lucy missions and find thatthese orbits are stable for hazardous particle sizes at asteroids,comets, and Kuiper belt objects of differing dimensions. Weinvestigate the sources and sinks for debris that might populate suchorbits, estimate timescales and equilibrium populations, and willreport on our findings.

Dirac spin-orbit torques and charge pumping at the surface of topological insulators

NASA Astrophysics Data System (ADS)

Ndiaye, Papa B.; Akosa, C. A.; Fischer, M. H.; Vaezi, A.; Kim, E.-A.; Manchon, A.

2017-07-01

We address the nature of spin-orbit torques at the magnetic surfaces of topological insulators using the linear-response theory. We find that the so-called Dirac torques in such systems possess a different symmetry compared to their Rashba counterpart, as well as a high anisotropy as a function of the magnetization direction. In particular, the damping torque vanishes when the magnetization lies in the plane of the topological-insulator surface. We also show that the Onsager reciprocal of the spin-orbit torque, the charge pumping, induces an enhanced anisotropic damping. Via a macrospin model, we numerically demonstrate that these features have important consequences in terms of magnetization switching.

On the physical interpretation of the nuclear molecular orbital energy.

PubMed

Charry, Jorge; Pedraza-González, Laura; Reyes, Andrés

2017-06-07

Recently, several groups have extended and implemented molecular orbital (MO) schemes to simultaneously obtain wave functions for electrons and selected nuclei. Many of these schemes employ an extended Hartree-Fock approach as a first step to find approximate electron-nuclear wave functions and energies. Numerous studies conducted with these extended MO methodologies have explored various effects of quantum nuclei on physical and chemical properties. However, to the best of our knowledge no physical interpretation has been assigned to the nuclear molecular orbital energy (NMOE) resulting after solving extended Hartree-Fock equations. This study confirms that the NMOE is directly related to the molecular electrostatic potential at the position of the nucleus.

Altimetry, Orbits and Tides

NASA Technical Reports Server (NTRS)

Colombo, O. L.

1984-01-01

The nature of the orbit error and its effect on the sea surface heights calculated with satellite altimetry are explained. The elementary concepts of celestial mechanics required to follow a general discussion of the problem are included. Consideration of errors in the orbits of satellites with precisely repeating ground tracks (SEASAT, TOPEX, ERS-1, POSEIDON, amongst past and future altimeter satellites) are detailed. The theoretical conclusions are illustrated with the numerical results of computer simulations. The nature of the errors in this type of orbits is such that this error can be filtered out by using height differences along repeating (overlapping) passes. This makes them particularly valuable for the study and monitoring of changes in the sea surface, such as tides. Elements of tidal theory, showing how these principles can be combined with those pertinent to the orbit error to make direct maps of the tides using altimetry are presented.

Orbital stability of the unseen solar companion linked to periodic extinction events

NASA Technical Reports Server (NTRS)

Torbett, M. V.; Smoluchowski, R.

1984-01-01

Evidence from three-dimensional numerical modelling is presented that only cometary orbits with a limited range in inclination with respect to the galactic plane are formally stable for the length of time required to cause periodic extinction events. The calculations were done using Cowell's method employing a fourth-order Runge-Kutta integration scheme in an inertial reference frame in orbit about the Galaxy. Tidal perturbations in the radial direction due to the Galaxy and the Coriolis forces are included. The vertical component of the gravitational field of the galactic disk is superimposed on these forces. The results indicate that orbits for Nemesis that are inclined at more than 30 deg to the galactic plane are not allowed and suggests that the search for Nemesis should be concentrated toward the plane of the Galaxy. Perturbations by passing stars or molecular clouds may make even the low-inclination orbits unstable.

Exospheric perturbations by radiation pressure. II - Solution for orbits in the ecliptic plane

NASA Technical Reports Server (NTRS)

Chamberlain, J. W.

1980-01-01

A previous study (Chamberlain, 1979) gave solutions for the mean time rates of change of orbital elements of satellite atoms in an exosphere influenced by solar radiation pressure; each element was assumed to behave independently. In the present paper, the instantaneous rates of changes for three elements (e, Omega, and phi = omega + Omega) are integrated simultaneously for the case of the inclination i = 0. The results confirm the validity of using mean rates when the orbits are tighly bound to the planet, and serve as examples to be reproduced by the complicated numerical solutions required for arbitrary inclination. Strongly bound hydrogen atoms perturbed in earth orbit by radiation pressure do not seem a likely cause of the geotail extending in the anti-sun direction. Instead, radiation pressure will cause those particles' orbits to form a broad fan-shaped tail and to deteriorate into the earth's atmosphere.

Spin-orbit signatures in the dynamics of singlet-triplet qubits in double quantum dots

NASA Astrophysics Data System (ADS)

Rolon, Juan E.; Cota, Ernesto; Ulloa, Sergio E.

2017-05-01

We characterize numerically and analytically the signatures of the spin-orbit interaction in a two-electron GaAs double quantum dot in the presence of an external magnetic field. In particular, we obtain the return probability of the singlet state by simulating Landau-Zener voltage detuning sweeps which traverse the singlet-triplet (S -T+ ) resonance. Our results indicate that non-spin-conserving interdot tunneling processes arising from the spin-orbit interaction have well defined signatures. These allow direct access to the spin-orbit interaction scales and are characterized by a frequency shift and Fourier amplitude modulation of the Rabi flopping dynamics of the singlet-triplet qubits S -T0 and S -T+ . By applying the Bloch-Feshbach projection formalism, we demonstrate analytically that the aforementioned effects originate from the interplay between spin-orbit interaction and processes driven by the hyperfine interaction between the electron spins and those of the GaAs nuclei.

Theoretical study of spin Hall effect in conjugated Organic semiconductors

NASA Astrophysics Data System (ADS)

Mahani, M. R.; Delin, A.

The spin Hall effect (SHE), a direct conversion between electronic and spin currents, is a rapidly growing branch of spintronics. The study of SHE in conjugated polymers has gained momentum recently due to the weak spin-orbit couplings and hyperfine interactions in these materials. Our calculations of SHE based on the recent work, are the result of the misalignment of pi-orbitals in triads consisting of three molecules. In disordered organics, where the electronic conduction is through hopping of the electrons among randomly oriented molecules, instead of identifying a hopping triad to represent the entire system, we numerically solve the master equations for electrical and spin hall conductivities by summing the contributions from all triads in a sufficiently large system. The interference between the direct and indirect hoppings in these triads leads to SHE proportional to the orientation vector of molecule at the first order of spin-orbit coupling. Hence, our results show, the degree of molecular alignment as well as the strength of the spin-orbit coupling can be used to control the SHE in organics.

On the long-period evolution of the sun-synchronous orbits

NASA Astrophysics Data System (ADS)

Kuznetsov, E. D.; Jasim, A. T.

2016-05-01

The dynamic evolution of sun-synchronous orbits at a time interval of 20 years is considered. The numerical motion simulation has been carried out using the Celestial Mechanics software package developed at the Institute of Astronomy of the University of Bern. The dependence of the dynamic evolution on the initial value of the ascending node longitude is examined for two families of sun-synchronous orbits with altitudes of 751 and 1191 km. Variations of the semimajor axis and orbit inclination are obtained depending on the initial value of the ascending node longitude. Recommendations on the selection of orbits, in which spent sun-synchronous satellites can be moved, are formulated. Minimal changes of elements over a time interval of 20 years have been observed for orbits in which at the initial time the angle between the orbit ascending node and the direction of the Sun measured along the equator have been close to 90° or 270°. In this case, the semimajor axis of the orbit is not experiencing secular perturbations arising from the satellite's passage through the Earth's shadow.

Lifetime of a spacecraft around a synchronous system of asteroids using a dipole model

NASA Astrophysics Data System (ADS)

dos Santos, Leonardo Barbosa Torres; de Almeida Prado, Antonio F. Bertachini; Sanchez, Diogo Merguizo

2017-11-01

Space missions allow us to expand our knowledge about the origin of the solar system. It is believed that asteroids and comets preserve the physical characteristics from the time that the solar system was created. For this reason, there was an increase of missions to asteroids in the past few years. To send spacecraft to asteroids or comets is challenging, since these objects have their own characteristics in several aspects, such as size, shape, physical properties, etc., which are often only discovered after the approach and even after the landing of the spacecraft. These missions must be developed with sufficient flexibility to adjust to these parameters, which are better determined only when the spacecraft reaches the system. Therefore, conducting a dynamic investigation of a spacecraft around a multiple asteroid system offers an extremely rich environment. Extracting accurate information through analytical approaches is quite challenging and requires a significant number of restrictive assumptions. For this reason, a numerical approach to the dynamics of a spacecraft in the vicinity of a binary asteroid system is offered in this paper. In the present work, the equations of the Restricted Synchronous Four-Body Problem (RSFBP) are used to model a binary asteroid system. The main objective of this work is to construct grids of initial conditions, which relates semi-major axis and eccentricity, in order to quantify the lifetime of a spacecraft when released close to the less massive body of the binary system (modeled as a rotating mass dipole). We performed an analysis of the lifetime of the spacecraft considering several mass ratios of a binary system of asteroids and investigating the behavior of a spacecraft in the vicinity of this system. We analyze direct and retrograde orbits. This study investigated orbits that survive for at least 500 orbital periods of the system (which is approximately one year), then not colliding or escaping from the system during this time. In this work, we take into account the gravitational forces of the binary asteroid system and the solar radiation pressure (SRP). We found several regions where the direct and retrograde orbits of a spacecraft survive throughout the integration time (one year) when the solar radiation pressure is taken into account. Numerical evidence shows that retrograde orbits have a larger region initial conditions that generate orbits that survive for one year, compared to direct orbits.

A Comparison of Trajectory Optimization Methods for the Impulsive Minimum Fuel Rendezvous Problem

NASA Technical Reports Server (NTRS)

Hughes, Steven P.; Mailhe, Laurie M.; Guzman, Jose J.

2003-01-01

In this paper we present, a comparison of trajectory optimization approaches for the minimum fuel rendezvous problem. Both indirect and direct methods are compared for a variety of test cases. The indirect approach is based on primer vector theory. The direct approaches are implemented numerically and include Sequential Quadratic Programming (SQP). Quasi- Newton and Nelder-Meade Simplex. Several cost function parameterizations are considered for the direct approach. We choose one direct approach that appears to be the most flexible. Both the direct and indirect methods are applied to a variety of test cases which are chosen to demonstrate the performance of each method in different flight regimes. The first test case is a simple circular-to-circular coplanar rendezvous. The second test case is an elliptic-to-elliptic line of apsides rotation. The final test case is an orbit phasing maneuver sequence in a highly elliptic orbit. For each test case we present a comparison of the performance of all methods we consider in this paper.

Phonon-drag magnetothermopower in Rashba spin-split two-dimensional electron systems.

PubMed

Biswas, Tutul; Ghosh, Tarun Kanti

2013-10-16

We study the phonon-drag contribution to the thermoelectric power in a quasi-two-dimensional electron system confined in GaAs/AlGaAs heterostructure in the presence of both Rashba spin-orbit interaction and perpendicular magnetic field at very low temperature. It is observed that the peaks in the phonon-drag thermopower split into two when the Rashba spin-orbit coupling constant is strong. This splitting is a direct consequence of the Rashba spin-orbit interaction. We show the dependence of phonon-drag thermopower on both magnetic field and temperature numerically. A power-law dependence of phonon-drag magnetothermopower on the temperature in the Bloch-Gruneisen regime is found. We also extract the exponent of the temperature dependence of phonon-drag thermopower for different parameters like electron density, magnetic field, and the spin-orbit coupling constant.

Emergent low-energy bound states in the two-orbital Hubbard model

DOE PAGES

Nunez-Fernandez, Y.; Kotliar, G.; Hallberg, K.

2018-03-30

A repulsive Coulomb interaction between electrons in different orbitals in correlated materials can give rise to bound quasiparticle states. We study the nonhybridized two-orbital Hubbard model with intra- (inter)orbital interaction U (U 12) and different bandwidths using an improved dynamical mean-field theory numerical technique which leads to reliable spectra on the real energy axis directly at zero temperature. We find that a finite density of states at the Fermi energy in one band is correlated with the emergence of well-defined quasiparticle states at excited energies Δ = U - U 12 in the other band. These excitations are interband holon-doublonmore » bound states. At the symmetric point U = U 12, the quasiparticle peaks are located at the Fermi energy, leading to a simultaneous and continuous Mott transition settling a long-standing controversy.« less

Emergent low-energy bound states in the two-orbital Hubbard model

NASA Astrophysics Data System (ADS)

Núñez-Fernández, Y.; Kotliar, G.; Hallberg, K.

2018-03-01

A repulsive Coulomb interaction between electrons in different orbitals in correlated materials can give rise to bound quasiparticle states. We study the nonhybridized two-orbital Hubbard model with intra- (inter)orbital interaction U (U12) and different bandwidths using an improved dynamical mean-field theory numerical technique which leads to reliable spectra on the real energy axis directly at zero temperature. We find that a finite density of states at the Fermi energy in one band is correlated with the emergence of well-defined quasiparticle states at excited energies Δ =U -U12 in the other band. These excitations are interband holon-doublon bound states. At the symmetric point U =U12 , the quasiparticle peaks are located at the Fermi energy, leading to a simultaneous and continuous Mott transition settling a long-standing controversy.

Evolution of Cometary Dust Particles to the Orbit of the Earth: Particle Size, Shape, and Mutual Collisions

NASA Astrophysics Data System (ADS)

Yang, Hongu; Ishiguro, Masateru

2018-02-01

In this study, we numerically investigated the orbital evolution of cometary dust particles, with special consideration of the initial size–frequency distribution (SFD) and different evolutionary tracks according to the initial orbit and particle shape. We found that close encounters with planets (mostly Jupiter) are the dominating factor determining the orbital evolution of dust particles. Therefore, the lifetimes of cometary dust particles (∼250,000 yr) are shorter than the Poynting–Robertson lifetime, and only a small fraction of large cometary dust particles can be transferred into orbits with small semimajor axes. The exceptions are dust particles from 2P/Encke and, potentially, active asteroids that have little interaction with Jupiter. We also found that the effects of dust shape, mass density, and SFD were not critical in the total mass supply rate to the interplanetary dust particle (IDP) cloud complex when these quantities are confined by observations of zodiacal light brightness and SFD around the Earth’s orbit. When we incorporate a population of fluffy aggregates discovered in the Earth’s stratosphere and the coma of 67P/Churyumov–Gerasimenko within the initial ejection, the initial SFD measured at the comae of comets (67P and 81P/Wild 2) can produce the observed SFD around the Earth’s orbit. Considering the above effects, we derived the probability of mutual collisions among dust particles within the IDP cloud for the first time in a direct manner via numerical simulation and concluded that mutual collisions can mostly be ignored.

Navigation strategy and filter design for solar electric missions

NASA Technical Reports Server (NTRS)

Tapley, B. D.; Hagar, H., Jr.

1972-01-01

Methods which have been proposed to improve the navigation accuracy for the low-thrust space vehicle include modifications to the standard Sequential- and Batch-type orbit determination procedures and the use of inertial measuring units (IMU) which measures directly the acceleration applied to the vehicle. The navigation accuracy obtained using one of the more promising modifications to the orbit determination procedures is compared with a combined IMU-Standard. The unknown accelerations are approximated as both first-order and second-order Gauss-Markov processes. The comparison is based on numerical results obtained in a study of the navigation requirements of a numerically simulated 152-day low-thrust mission to the asteroid Eros. The results obtained in the simulation indicate that the DMC algorithm will yield a significant improvement over the navigation accuracies achieved with previous estimation algorithms. In addition, the DMC algorithms will yield better navigation accuracies than the IMU-Standard Orbit Determination algorithm, except for extremely precise IMU measurements, i.e., gyroplatform alignment .01 deg and accelerometer signal-to-noise ratio .07. Unless these accuracies are achieved, the IMU navigation accuracies are generally unacceptable.

Numerical simulation of runaway electrons: 3-D effects on synchrotron radiation and impurity-based runaway current dissipation

NASA Astrophysics Data System (ADS)

del-Castillo-Negrete, D.; Carbajal, L.; Spong, D.; Izzo, V.

2018-05-01

Numerical simulations of runaway electrons (REs) with a particular emphasis on orbit dependent effects in 3-D magnetic fields are presented. The simulations were performed using the recently developed Kinetic Orbit Runaway electron Code (KORC) that computes the full-orbit relativistic dynamics in prescribed electric and magnetic fields including radiation damping and collisions. The two main problems of interest are synchrotron radiation and impurity-based RE dissipation. Synchrotron radiation is studied in axisymmetric fields and in 3-D magnetic configurations exhibiting magnetic islands and stochasticity. For passing particles in axisymmetric fields, neglecting orbit effects might underestimate or overestimate the total radiation power depending on the direction of the radial shift of the drift orbits. For trapped particles, the spatial distribution of synchrotron radiation exhibits localized "hot" spots at the tips of the banana orbits. In general, the radiation power per particle for trapped particles is higher than the power emitted by passing particles. The spatial distribution of synchrotron radiation in stochastic magnetic fields, obtained using the MHD code NIMROD, is strongly influenced by the presence of magnetic islands. 3-D magnetic fields also introduce a toroidal dependence on the synchrotron spectra, and neglecting orbit effects underestimates the total radiation power. In the presence of magnetic islands, the radiation damping of trapped particles is larger than the radiation damping of passing particles. Results modeling synchrotron emission by RE in DIII-D quiescent plasmas are also presented. The computation uses EFIT reconstructed magnetic fields and RE energy distributions fitted to the experimental measurements. Qualitative agreement is observed between the numerical simulations and the experiments for simplified RE pitch angle distributions. However, it is noted that to achieve quantitative agreement, it is necessary to use pitch angle distributions that depart from simplified 2-D Fokker-Planck equilibria. Finally, using the guiding center orbit model (KORC-GC), a preliminary study of pellet mitigated discharges in DIII-D is presented. The dependence of RE energy decay and current dissipation on initial energy and ionization levels of neon impurities is studied. The computed decay rates are within the range of experimental observations.

On analytic modeling of lunar perturbations of artificial satellites of the earth

NASA Astrophysics Data System (ADS)

Lane, M. T.

1989-06-01

Two different procedures for analytically modeling the effects of the moon's direct gravitational force on artificial earth satellites are discussed from theoretical and numerical viewpoints. One is developed using classical series expansions of inclination and eccentricity for both the satellite and the moon, and the other employs the method of averaging. Both solutions are seen to have advantages, but it is shown that while the former is more accurate in special situations, the latter is quicker and more practical for the general orbit determination problem where observed data are used to correct the orbit in near real time.

Studying the energy variation in the powered Swing-By in the Sun-Mercury system

NASA Astrophysics Data System (ADS)

Ferreira, A. F. S.; Prado, A. F. B. A.; Winter, O. C.; Santos, D. P. S.

2017-10-01

A maneuver where a spacecraft passes close to Mercury and uses the gravity of this body combined with an impulse applied at the periapsis, with different magnitudes and directions, is presented. The main objective of this maneuver is the fuel economy in space missions. Using this maneuver, it is possible to insert the spacecraft into an orbit captured around the Sun or Mercury. Trajectories escaping the Solar System are also obtained and mapped. Maps of the spacecraft energy variation relative to the Sun and the types of orbits resulting from the maneuver are presented, based in numerical integrations. The results show that applying the impulse out of the direction of motion can optimize the maneuver due to the effect of the combination of the impulse and the gravity.

Stability and evolution of orbits around the binary asteroid 175706 (1996 FG3): Implications for the MarcoPolo-R mission

NASA Astrophysics Data System (ADS)

Hussmann, Hauke; Oberst, Jürgen; Wickhusen, Kai; Shi, Xian; Damme, Friedrich; Lüdicke, Fabian; Lupovka, Valery; Bauer, Sven

2012-09-01

In support of the MarcoPolo-R mission, we have carried out numerical simulations of spacecraft trajectories about the binary asteroid 175706 (1996 FG3) under the influence of solar radiation pressure. We study the effects of (1) the asteroid's mass, shape, and rotational parameters, (2) the secondary's mass, shape, and orbit parameters, (3) the spacecraft's mass, surface area, and reflectivity, and (4) the time of arrival, and therefore the relative position to the sun and planets. We have considered distance regimes between 5 and 20 km, the typical range for a detailed characterization of the asteroids - primary and secondary - with imaging systems, spectrometers and by laser altimetry. With solar radiation pressure and gravity forces of the small asteroid competing, orbits are found to be unstable, in general. However, limited orbital stability can be found in the so-called Self-Stabilized Terminator Orbits (SSTO), where initial orbits are circular, orbital planes are oriented approximately perpendicular to the solar radiation pressure, and where the orbital plane of the spacecraft is shifted slightly (between 0.2 and 1 km) from the asteroid in the direction away from the sun. Under the effect of radiation pressure, the vector perpendicular to the orbit plane is observed to follow the sun direction. Shape and rotation parameters of the asteroid as well as gravitational perturbations by the secondary (not to mention sun and planets) were found not to affect the results. Such stable orbits may be suited for long radio tracking runs, which will allow for studying the gravity field. As the effect of the solar radiation pressure depends on the spacecraft mass, shape, and albedo, good knowledge of the spacecraft model and persistent monitoring of the spacecraft orientation are required.

Characterizing the three-orbital Hubbard model with determinant quantum Monte Carlo

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

Kung, Y. F.; Chen, C. -C.; Wang, Yao

Here, we characterize the three-orbital Hubbard model using state-of-the-art determinant quantum Monte Carlo (DQMC) simulations with parameters relevant to the cuprate high-temperature superconductors. The simulations find that doped holes preferentially reside on oxygen orbitals and that the (π,π) antiferromagnetic ordering vector dominates in the vicinity of the undoped system, as known from experiments. The orbitally-resolved spectral functions agree well with photoemission spectroscopy studies and enable identification of orbital content in the bands. A comparison of DQMC results with exact diagonalization and cluster perturbation theory studies elucidates how these different numerical techniques complement one another to produce a more complete understandingmore » of the model and the cuprates. Interestingly, our DQMC simulations predict a charge-transfer gap that is significantly smaller than the direct (optical) gap measured in experiment. Most likely, it corresponds to the indirect gap that has recently been suggested to be on the order of 0.8 eV, and demonstrates the subtlety in identifying charge gaps.« less

Characterizing the three-orbital Hubbard model with determinant quantum Monte Carlo

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

Kung, Y. F.; Chen, C. -C.; Wang, Yao

We characterize the three-orbital Hubbard model using state-of-the-art determinant quantum Monte Carlo (DQMC) simulations with parameters relevant to the cuprate high-temperature superconductors. The simulations find that doped holes preferentially reside on oxygen orbitals and that the (π,π) antiferromagnetic ordering vector dominates in the vicinity of the undoped system, as known from experiments. The orbitally-resolved spectral functions agree well with photoemission spectroscopy studies and enable identification of orbital content in the bands. A comparison of DQMC results with exact diagonalization and cluster perturbation theory studies elucidates how these different numerical techniques complement one another to produce a more complete understanding ofmore » the model and the cuprates. Interestingly, our DQMC simulations predict a charge-transfer gap that is significantly smaller than the direct (optical) gap measured in experiment. Most likely, it corresponds to the indirect gap that has recently been suggested to be on the order of 0.8 eV, and demonstrates the subtlety in identifying charge gaps.« less

"Diffusion" region of magnetic reconnection: electron orbits and the phase space mixing

NASA Astrophysics Data System (ADS)

Kropotkin, Alexey P.

2018-05-01

The nonlinear dynamics of electrons in the vicinity of magnetic field neutral lines during magnetic reconnection, deep inside the diffusion region where the electron motion is nonadiabatic, has been numerically analyzed. Test particle orbits are examined in that vicinity, for a prescribed planar two-dimensional magnetic field configuration and with a prescribed uniform electric field in the neutral line direction. On electron orbits, a strong particle acceleration occurs due to the reconnection electric field. Local instability of orbits in the neighborhood of the neutral line is pointed out. It combines with finiteness of orbits due to particle trapping by the magnetic field, and this should lead to the effect of mixing in the phase space, and the appearance of dynamical chaos. The latter may presumably be viewed as a mechanism producing finite conductivity in collisionless plasma near the neutral line. That conductivity is necessary to provide violation of the magnetic field frozen-in condition, i.e., for magnetic reconnection to occur in that region.

Characterizing the three-orbital Hubbard model with determinant quantum Monte Carlo

DOE PAGES

Kung, Y. F.; Chen, C. -C.; Wang, Yao; ...

2016-04-29

Here, we characterize the three-orbital Hubbard model using state-of-the-art determinant quantum Monte Carlo (DQMC) simulations with parameters relevant to the cuprate high-temperature superconductors. The simulations find that doped holes preferentially reside on oxygen orbitals and that the (π,π) antiferromagnetic ordering vector dominates in the vicinity of the undoped system, as known from experiments. The orbitally-resolved spectral functions agree well with photoemission spectroscopy studies and enable identification of orbital content in the bands. A comparison of DQMC results with exact diagonalization and cluster perturbation theory studies elucidates how these different numerical techniques complement one another to produce a more complete understandingmore » of the model and the cuprates. Interestingly, our DQMC simulations predict a charge-transfer gap that is significantly smaller than the direct (optical) gap measured in experiment. Most likely, it corresponds to the indirect gap that has recently been suggested to be on the order of 0.8 eV, and demonstrates the subtlety in identifying charge gaps.« less

Characterizing the three-orbital Hubbard model with determinant quantum Monte Carlo

NASA Astrophysics Data System (ADS)

Kung, Y. F.; Chen, C.-C.; Wang, Yao; Huang, E. W.; Nowadnick, E. A.; Moritz, B.; Scalettar, R. T.; Johnston, S.; Devereaux, T. P.

2016-04-01

We characterize the three-orbital Hubbard model using state-of-the-art determinant quantum Monte Carlo (DQMC) simulations with parameters relevant to the cuprate high-temperature superconductors. The simulations find that doped holes preferentially reside on oxygen orbitals and that the (π ,π ) antiferromagnetic ordering vector dominates in the vicinity of the undoped system, as known from experiments. The orbitally-resolved spectral functions agree well with photoemission spectroscopy studies and enable identification of orbital content in the bands. A comparison of DQMC results with exact diagonalization and cluster perturbation theory studies elucidates how these different numerical techniques complement one another to produce a more complete understanding of the model and the cuprates. Interestingly, our DQMC simulations predict a charge-transfer gap that is significantly smaller than the direct (optical) gap measured in experiment. Most likely, it corresponds to the indirect gap that has recently been suggested to be on the order of 0.8 eV, and demonstrates the subtlety in identifying charge gaps.

Pursuit-evasion games with information uncertainties for elusive orbital maneuver and space object tracking

NASA Astrophysics Data System (ADS)

Shen, Dan; Jia, Bin; Chen, Genshe; Blasch, Erik; Pham, Khanh

2015-05-01

This paper develops and evaluates a pursuit-evasion (PE) game approach for elusive orbital maneuver and space object tracking. Unlike the PE games in the literature, where the assumption is that either both players have perfect knowledge of the opponents' positions or use primitive sensing models, the proposed PE approach solves the realistic space situation awareness (SSA) problem with imperfect information, where the evaders will exploit the pursuers' sensing and tracking models to confuse their opponents by maneuvering their orbits to increase the uncertainties, which the pursuers perform orbital maneuvers to minimize. In the game setup, each game player P (pursuer) and E (evader) has its own motion equations with a small continuous low-thrust. The magnitude of the low thrust is fixed and the direction can be controlled by the associated game player. The entropic uncertainty is used to generate the cost functions of game players. The Nash or mixed Nash equilibrium is composed of the directional controls of low-thrusts. Numerical simulations are emulated to demonstrate the performance. Simplified perturbations models (SGP4/SDP4) are exploited to calculate the ground truth of the satellite states (position and speed).

Cutting-edge Kinetic Physics with Parker Solar Probe and Solar Orbiter: The Arbitrary Linear Plasma Solver (ALPS)

NASA Astrophysics Data System (ADS)

Verscharen, D.; Klein, K. G.; Chandran, B. D. G.; Stevens, M. L.; Salem, C. S.; Bale, S. D.

2017-12-01

The Arbitrary Linear Plasma Solver (ALPS) is a parallelized numerical code that solves the dispersion relation in a hot (even relativistic) magnetized plasma with an arbitrary number of particle species with arbitrary gyrotropic equilibrium distribution functions for any direction of wave propagation with respect to the background field. In this way, ALPS retains generality and overcomes the shortcomings of previous (bi-)Maxwellian solvers for the plasma dispersion relations. The unprecedented high-resolution particle and field data products from Parker Solar Probe (PSP) and Solar Orbiter (SO) will require novel theoretical tools. ALPS is one such tool, and its use will make possible new investigations into the role of non-Maxwellian distributions in the near-Sun solar wind. It can be applied to numerous high-velocity-resolution systems, ranging from current space missions to numerical simulations. We will briefly discuss the ALPS algorithm and demonstrate its functionality based on previous solar-wind measurements. We will then highlight our plans for future applications of ALPS to PSP and SO observations.

Anisotropic optical absorption induced by Rashba spin-orbit coupling in monolayer phosphorene

NASA Astrophysics Data System (ADS)

Li, Yuan; Li, Xin; Wan, Qi; Bai, R.; Wen, Z. C.

2018-04-01

We obtain the effective Hamiltonian of the phosphorene including the effect of Rashba spin-orbit coupling in the frame work of the low-energy theory. The spin-splitting energy bands show an anisotropy feature for the wave vectors along kx and ky directions, where kx orients to ΓX direction in the k space. We numerically study the optical absorption of the electrons for different wave vectors with Rashba spin-orbit coupling. We find that the spin-flip transition from the valence band to the conduction band induced by the circular polarized light closes to zero with increasing the x-component wave vector when ky equals to zero, while it can be significantly increased to a large value when ky gets a small value. When the wave vector varies along the ky direction, the spin-flip transition can also increase to a large value, however, which shows an anisotropy feature for the optical absorption. Especially, the spin-conserved transitions keep unchanged and have similar varying trends for different wave vectors. This phenomenon provides a novel route for the manipulation of the spin-dependent property of the fermions in the monolayer phosphorene.

Thrust vector control of upper stage with a gimbaled thruster during orbit transfer

NASA Astrophysics Data System (ADS)

Wang, Zhaohui; Jia, Yinghong; Jin, Lei; Duan, Jiajia

2016-10-01

In launching Multi-Satellite with One-Vehicle, the main thruster provided by the upper stage is mounted on a two-axis gimbal. During orbit transfer, the thrust vector of this gimbaled thruster (GT) should theoretically pass through the mass center of the upper stage and align with the command direction to provide orbit transfer impetus. However, it is hard to be implemented from the viewpoint of the engineering mission. The deviations of the thrust vector from the command direction would result in large velocity errors. Moreover, the deviations of the thrust vector from the upper stage mass center would produce large disturbance torques. This paper discusses the thrust vector control (TVC) of the upper stage during its orbit transfer. Firstly, the accurate nonlinear coupled kinematic and dynamic equations of the upper stage body, the two-axis gimbal and the GT are derived by taking the upper stage as a multi-body system. Then, a thrust vector control system consisting of the special attitude control of the upper stage and the gimbal rotation of the gimbaled thruster is proposed. The special attitude control defined by the desired attitude that draws the thrust vector to align with the command direction when the gimbal control makes the thrust vector passes through the upper stage mass center. Finally, the validity of the proposed method is verified through numerical simulations.

Analytical formulation of impulsive collision avoidance dynamics

NASA Astrophysics Data System (ADS)

Bombardelli, Claudio

2014-02-01

The paper deals with the problem of impulsive collision avoidance between two colliding objects in three dimensions and assuming elliptical Keplerian orbits. Closed-form analytical expressions are provided that accurately predict the relative dynamics of the two bodies in the encounter b-plane following an impulsive delta-V manoeuvre performed by one object at a given orbit location prior to the impact and with a generic three-dimensional orientation. After verifying the accuracy of the analytical expressions for different orbital eccentricities and encounter geometries the manoeuvre direction that maximises the miss distance is obtained numerically as a function of the arc length separation between the manoeuvre point and the predicted collision point. The provided formulas can be used for high-accuracy instantaneous estimation of the outcome of a generic impulsive collision avoidance manoeuvre and its optimisation.

GPS Satellite Orbit Prediction at User End for Real-Time PPP System.

PubMed

Yang, Hongzhou; Gao, Yang

2017-08-30

This paper proposed the high-precision satellite orbit prediction process at the user end for the real-time precise point positioning (PPP) system. Firstly, the structure of a new real-time PPP system will be briefly introduced in the paper. Then, the generation of satellite initial parameters (IP) at the sever end will be discussed, which includes the satellite position, velocity, and the solar radiation pressure (SRP) parameters for each satellite. After that, the method for orbit prediction at the user end, with dynamic models including the Earth's gravitational force, lunar gravitational force, solar gravitational force, and the SRP, are presented. For numerical integration, both the single-step Runge-Kutta and multi-step Adams-Bashforth-Moulton integrator methods are implemented. Then, the comparison between the predicted orbit and the international global navigation satellite system (GNSS) service (IGS) final products are carried out. The results show that the prediction accuracy can be maintained for several hours, and the average prediction error of the 31 satellites are 0.031, 0.032, and 0.033 m for the radial, along-track and cross-track directions over 12 h, respectively. Finally, the PPP in both static and kinematic modes are carried out to verify the accuracy of the predicted satellite orbit. The average root mean square error (RMSE) for the static PPP of the 32 globally distributed IGS stations are 0.012, 0.015, and 0.021 m for the north, east, and vertical directions, respectively; while the RMSE of the kinematic PPP with the predicted orbit are 0.031, 0.069, and 0.167 m in the north, east and vertical directions, respectively.

GPS Satellite Orbit Prediction at User End for Real-Time PPP System

PubMed Central

Yang, Hongzhou; Gao, Yang

2017-01-01

This paper proposed the high-precision satellite orbit prediction process at the user end for the real-time precise point positioning (PPP) system. Firstly, the structure of a new real-time PPP system will be briefly introduced in the paper. Then, the generation of satellite initial parameters (IP) at the sever end will be discussed, which includes the satellite position, velocity, and the solar radiation pressure (SRP) parameters for each satellite. After that, the method for orbit prediction at the user end, with dynamic models including the Earth’s gravitational force, lunar gravitational force, solar gravitational force, and the SRP, are presented. For numerical integration, both the single-step Runge–Kutta and multi-step Adams–Bashforth–Moulton integrator methods are implemented. Then, the comparison between the predicted orbit and the international global navigation satellite system (GNSS) service (IGS) final products are carried out. The results show that the prediction accuracy can be maintained for several hours, and the average prediction error of the 31 satellites are 0.031, 0.032, and 0.033 m for the radial, along-track and cross-track directions over 12 h, respectively. Finally, the PPP in both static and kinematic modes are carried out to verify the accuracy of the predicted satellite orbit. The average root mean square error (RMSE) for the static PPP of the 32 globally distributed IGS stations are 0.012, 0.015, and 0.021 m for the north, east, and vertical directions, respectively; while the RMSE of the kinematic PPP with the predicted orbit are 0.031, 0.069, and 0.167 m in the north, east and vertical directions, respectively. PMID:28867771

Generic effective source for scalar self-force calculations

NASA Astrophysics Data System (ADS)

Wardell, Barry; Vega, Ian; Thornburg, Jonathan; Diener, Peter

2012-05-01

A leading approach to the modeling of extreme mass ratio inspirals involves the treatment of the smaller mass as a point particle and the computation of a regularized self-force acting on that particle. In turn, this computation requires knowledge of the regularized retarded field generated by the particle. A direct calculation of this regularized field may be achieved by replacing the point particle with an effective source and solving directly a wave equation for the regularized field. This has the advantage that all quantities are finite and require no further regularization. In this work, we present a method for computing an effective source which is finite and continuous everywhere, and which is valid for a scalar point particle in arbitrary geodesic motion in an arbitrary background spacetime. We explain in detail various technical and practical considerations that underlie its use in several numerical self-force calculations. We consider as examples the cases of a particle in a circular orbit about Schwarzschild and Kerr black holes, and also the case of a particle following a generic timelike geodesic about a highly spinning Kerr black hole. We provide numerical C code for computing an effective source for various orbital configurations about Schwarzschild and Kerr black holes.

Navigation and guidance of Japanese deepspace probes encountering Halley's comet

NASA Astrophysics Data System (ADS)

Nishimura, T.; Matsuo, H.; Takano, T.; Kawaguchi, J.

The techniques used by ISAS in the guidance of the Sakigake and Suisei probes, which encountered Comet Halley in March 1986, are reviewed. Consideration is given to the guidance of the last rocket stage in the direct ascent phase, midcourse maneuvers, tracking systems and communication links, the tracking strategy, trajectory-generation and orbit-determination software, and orbit-determination accuracy. Diagrams, drawings, graphs, photographs, and tables of numerical data are provided, and the ISAS positions of both probes during the first 10 days after launch are shown to be within 100 km in distance and 1 m/sec in velocity of NASA coordinate estimates.

Orbital effects of spatial variations of fundamental coupling constants

NASA Astrophysics Data System (ADS)

Iorio, Lorenzo

2011-11-01

We deal with the effects induced on the orbit of a test particle revolving around a central body by putative spatial variations of dimensionless fundamental coupling constants ζ. In particular, we assume a dipole gradient for ? along a generic direction ? in space. We analytically work out the long-term variations of all the six standard osculating Keplerian orbital elements parameterizing the orbit of a test particle in a gravitationally bound two-body system. Apart from the semimajor axis a, the eccentricity e, the inclination I, the longitude of the ascending node Ω, the longitude of pericentre ϖ and the mean anomaly ? undergo non-zero long-term changes. By using the usual decomposition along the radial (R), transverse (T) and normal (N) directions, we also analytically work out the long-term changes ΔR, ΔT, ΔN and ΔvR, ΔvT, ΔvN experienced by the position and the velocity vectors r and v of the test particle. Apart from ΔN, all the other five shifts do not vanish over one full orbital revolution. In the calculation we do not use a priori simplifying assumptions concerning e and I. Thus, our results are valid for a generic orbital geometry; moreover, they hold for any gradient direction ?. We compare our predictions to the latest observational results for some of the major bodies of the solar system. The largest predicted planetary perihelion precessions occur for the rocky planets, amounting to some 10-2-10-3 mas per century. Apart from the Earth, they are 2 - 3 orders of magnitude smaller than the present-day accuracy in empirically determining the corrections ? to the standard Newtonian-Einsteinian planetary perihelion rates. Numerically integrated time-series of the interplanetary range for some Earth-planet pairs yield Stark-like signatures as large as 0.1-10 mm; future planned planetary laser ranging facilities should be accurate at a cm level. The long-term variations of the lunar eccentricity and perigee are of the order of 10-14 yr-1 and 10-4 mas yr-1, respectively, while the change ΔR in the radial component of the Moon's geocentric orbit is as large as 0.8 μm per orbit. A numerically calculated geocentric lunar range time-series has a maximum nominal peak-to-peak amplitude of just a few mm, with an average of 0.3 μm over 30 yr. The present-day accuracies in determining ? and ? for the Moon are 10-12 yr-1 and 10-1 mas yr-1, respectively. The Apollo facility should be able to determine on a continuous basis of the Earth-Moon range with a mm accuracy.

Analysis of direct transfer trajectories from LL2 halo orbits to LLOs

NASA Astrophysics Data System (ADS)

Cao, Pengfei; He, Boyong; Li, Haiyang

2017-09-01

A convenient procedure for designing the direct transfer trajectory from lunar L2 point (LL2) halo orbit to a low lunar orbit (LLO) is presented in this paper. The trajectory characteristics are analyzed to support the manned lunar missions design aimed at lunar surface global access. The concise procedure is established based on the circular restricted three-body problem (CR3BP) model. An analytical algorithm is employed to estimate an initial maneuver vector for approaching the Moon in its close vicinity. An iteration process is adopted to generate favorable trajectory that satisfies the constraints at perilune. By introducing a number of intermediate coordinate frames, an algorithm to compute the arriving LLO inclination and right ascension of ascending node (RAAN) is proposed. The orbital inclination and RAAN in this paper are defined and established in the J2000 frame rather than in the synodical frame. Numerical results show that, regardless of value of out-of-plane amplitude (Az) of the halo orbit, the overall maneuver cost of the trajectory largely depends on departure position, and it has two minima around 0.65 km/s. Further study shows that the values of the arriving LLO inclination and RAAN largely depend on the choices of the departure time and the value of Az. The periodicity, due to the natural motion of the Moon, is discovered to play a role in this time dependency. It is concluded that the fuel optimal trajectory permits access to almost any final lunar orbit, including a polar orbit, by means of varying the departure time and Az value.

Augmentation method of XPNAV in Mars orbit based on Phobos and Deimos observations

NASA Astrophysics Data System (ADS)

Rong, Jiao; Luping, Xu; Zhang, Hua; Cong, Li

2016-11-01

Autonomous navigation for Mars probe spacecraft is required to reduce the operation costs and enhance the navigation performance in the future. X-ray pulsar-based navigation (XPNAV) is a potential candidate to meet this requirement. This paper addresses the use of the Mars' natural satellites to improve XPNAV for Mars probe spacecraft. Two observation variables of the field angle and natural satellites' direction vectors of Mars are added into the XPNAV positioning system. The measurement model of field angle and direction vectors is formulated by processing satellite image of Mars obtained from optical camera. This measurement model is integrated into the spacecraft orbit dynamics to build the filter model. In order to estimate position and velocity error of the spacecraft and reduce the impact of the system noise on navigation precision, an adaptive divided difference filter (ADDF) is applied. Numerical simulation results demonstrate that the performance of ADDF is better than Unscented Kalman Filter (UKF) DDF and EKF. In view of the invisibility of Mars' natural satellites in some cases, a visibility condition analysis is given and the augmented XPNAV in a different visibility condition is numerically simulated. The simulation results show that the navigation precision is evidently improved by using the augmented XPNAV based on the field angle and natural satellites' direction vectors of Mars in a comparison with the conventional XPNAV.

Uncertainty propagation in orbital mechanics via tensor decomposition

NASA Astrophysics Data System (ADS)

Sun, Yifei; Kumar, Mrinal

2016-03-01

Uncertainty forecasting in orbital mechanics is an essential but difficult task, primarily because the underlying Fokker-Planck equation (FPE) is defined on a relatively high dimensional (6-D) state-space and is driven by the nonlinear perturbed Keplerian dynamics. In addition, an enormously large solution domain is required for numerical solution of this FPE (e.g. encompassing the entire orbit in the x-y-z subspace), of which the state probability density function (pdf) occupies a tiny fraction at any given time. This coupling of large size, high dimensionality and nonlinearity makes for a formidable computational task, and has caused the FPE for orbital uncertainty propagation to remain an unsolved problem. To the best of the authors' knowledge, this paper presents the first successful direct solution of the FPE for perturbed Keplerian mechanics. To tackle the dimensionality issue, the time-varying state pdf is approximated in the CANDECOMP/PARAFAC decomposition tensor form where all the six spatial dimensions as well as the time dimension are separated from one other. The pdf approximation for all times is obtained simultaneously via the alternating least squares algorithm. Chebyshev spectral differentiation is employed for discretization on account of its spectral ("super-fast") convergence rate. To facilitate the tensor decomposition and control the solution domain size, system dynamics is expressed using spherical coordinates in a noninertial reference frame. Numerical results obtained on a regular personal computer are compared with Monte Carlo simulations.

Capture of Planetesimals into a Circumterrestrial Swarm

NASA Technical Reports Server (NTRS)

Weidenschilling, S. J.

1985-01-01

The lunar origin model considered in this report involves processing of protolunar material through a circumterrestrial swarm of particles. Once such a swarm has formed, it can gain mass by capturing infalling planetesimals and ejecta from giant impacts on the Earth, although the angular momentum supply from these sources remains a problem. The first stage of formation of a geocentric swarm by capture of planetesimals from initially heliocentric orbits is examined. The only plausible capture mechanism that is not dependent on very low approach velocities is the mutual collision of planetesimals passing within Earth's sphere of influence. The dissipation of energy in inelastic collisions or accretion events changes the value of the Jacobi parameter, allowing capture into bound geocentric orbits. This capture scenario was tested directly by many body numerical integration of planetesimal orbits in near Earth space.

Comparative DMFT study of the eg-orbital Hubbard model in thin films

NASA Astrophysics Data System (ADS)

Rüegg, Andreas; Hung, Hsiang-Hsuan; Gull, Emanuel; Fiete, Gregory A.

2014-02-01

Heterostructures of transition-metal oxides have emerged as a new route to engineer electronic systems with desired functionalities. Motivated by these developments, we study a two-orbital Hubbard model in a thin-film geometry confined along the cubic [001] direction using the dynamical mean-field theory. We contrast the results of two approximate impurity solvers (exact diagonalization and one-crossing approximation) to the results of the numerically exact continuous-time quantum Monte Carlo solver. Consistent with earlier studies, we find that the one-crossing approximation performs well in the insulating regime, while the advantage of the exact-diagonalization-based solver is more pronounced in the metallic regime. We then investigate various aspects of strongly correlated eg-orbital systems in thin-film geometries. In particular, we show how the interfacial orbital polarization dies off quickly a few layers from the interface and how the film thickness affects the location of the interaction-driven Mott transition. In addition, we explore the changes in the electronic structure with varying carrier concentration and identify large variations of the orbital polarization in the strongly correlated regime.

Projector Augmented Wave formulation of orbital-dependent exchange-correlation functionals

NASA Astrophysics Data System (ADS)

Xu, Xiao; Holzwarth, N. A. W.

2012-02-01

The use of orbital-dependent exchange-correlation functionals within electronic structure calculations has recently received renewed attention for improving the accuracy of the calculations, especially correcting self-interaction errors. Since the Projector Augmented Wave (PAW) methodootnotetext P. Bl"ochl, Phys. Rev. B 50, 17953 (1994). is an efficient pseudopotential-like scheme which ensures accurate evaluation of all multipole moments of direct and exchange Coulomb integrals, it is a natural choice for implementing orbital-dependent formalisms. Using Fock exchange as an example of an orbital-dependent functional, we developed the formulation and numerical implementation of the approximate optimized effective potential formalism of Kreiger, Li, and Iafrate (KLI)ootnotetext J. B. Krieger, Y. Li, and G. J. Iafrate Phys. Rev. A 45, 101 (1992). within the PAW method, comparing results with the analogous Hartree-Fock treatment.ootnotetext Xiao Xu and N. A. W. Holzwarth, Phys. Rev. B 81, 245105 (2010); 84, 155113 (2011). Test results are presented for ground state properties of two well-known materials -- diamond and LiF. This formalism can be extended to treat orbital-dependent functionals more generally.

Modeling and analysis of the space shuttle nose-gear tire with semianalytic finite elements

NASA Technical Reports Server (NTRS)

Kim, Kyun O.; Noor, Ahmed K.; Tanner, John A.

1990-01-01

A computational procedure is presented for the geometrically nonlinear analysis of aircraft tires. The Space Shuttle Orbiter nose gear tire was modeled by using a two-dimensional laminated anisotropic shell theory with the effects of variation in material and geometric parameters included. The four key elements of the procedure are: (1) semianalytic finite elements in which the shell variables are represented by Fourier series in the circumferential direction and piecewise polynominals in the meridional direction; (2) a mixed formulation with the fundamental unknowns consisting of strain parameters, stress-resultant parameters, and generalized displacements; (3) multilevel operator splitting to effect successive simplifications, and to uncouple the equations associated with different Fourier harmonics; and (4) multilevel iterative procedures and reduction techniques to generate the response of the shell. Numerical results of the Space Shuttle Orbiter nose gear tire model are compared with experimental measurements of the tire subjected to inflation loading.

Preliminary Assessment of New Orbital Debris Shielding for Unmanned Satellites

NASA Astrophysics Data System (ADS)

Wilkinson, J.; Stokes, H.; Walker, R.

The numerous rocket launches and spacecraft deployments carried out since the dawn of the space age have generated a large orbiting population of man-made debris. Without the adoption of mitigation measures, it is likely that this population will continue to increase in the future. The ever-growing collision threat posed to operating spacecraft from these debris objects is therefore fast becoming a driver in the design of new spacecraft missions. DERA, under contract from the European Space Agency (ESA), is developing new techniques to provide mass- and cost-effective solutions to this spacecraft protection problem. Direct shielding methods such as enhancing a spacecraft's thermal blankets with strong materials and adapting the honeycomb panel structure are being investigated, as are indirect shielding methods such as reconfiguration of critical or susceptible units. This paper reports the latest results of the direct shielding research.

Centrifugal photovoltaic and photogalvanic effects driven by structured light

PubMed Central

Wätzel, J.; Berakdar, J.

2016-01-01

Much efforts are devoted to material structuring in a quest to enhance the photovoltaic effect. We show that structuring light in a way it transfers orbital angular momentum to semiconductor-based rings results in a steady charge accumulation at the outer boundaries that can be utilized for the generation of an open circuit voltage or a photogalvanic (bulk photovoltaic) type current. This effect which stems both from structuring light and matter confinement potentials, can be magnified even at fixed moderate intensities, by increasing the orbital angular momentum of light which strengthens the effective centrifugal potential that repels the charge outwards. Based on a full numerical time propagation of the carriers wave functions in the presence of light pulses we demonstrate how the charge buildup leads to a useable voltage or directed photocurrent whose amplitudes and directions are controllable by the light pulse parameters. PMID:26900105

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.

Consistency of Post-Newtonian Waveforms with Numerical Relativity

NASA Technical Reports Server (NTRS)

Baker, John G.; vanMeter, James R.; McWilliams, Sean T.; Cewntrella, Joan; Kelly, Bernard J.

2006-01-01

General relativity predicts the gravitational radiation signatures of mergers of compact binaries, such as coalescing binary black hole systems. Derivations of waveform predictions for such systems are required for optimal scientific analysis of observational gravitational wave data, and have so far been achieved primarily with the aid of the post-Newtonian (PN) approximation. The quality of this treatment is unclear, however, for the important late inspiral portion. We derive late-inspiral waveforms via a complementary approach, direct numerical simulation of Einstein's equations, which has recently matured sufficiently for such applications. We compare waveform phasing from simulations covering the last approximately 14 cycles of gravitational radiation from an equal-mass binary system of nonspinning black holes with the corresponding 3PN and 3.5PN orbital phasing. We find agreement consistent with internal error estimates based on either approach at the level of one radian over approximately 10 cycles. The result suggests that PN waveforms for this system are effective roughly until the system reaches its last stable orbit just prior to the final merger/

Optimal aeroassisted orbital transfer with plane change using collocation and nonlinear programming

NASA Technical Reports Server (NTRS)

Shi, Yun. Y.; Nelson, R. L.; Young, D. H.

1990-01-01

The fuel optimal control problem arising in the non-planar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) with orbital plane change. The basic strategy here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the aeroassisted HEO to LEO transfer consists of three phases. In the first phase, the orbital transfer begins with a deorbit impulse at HEO which injects the vehicle into an elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and bank angle modulations to perform the desired orbital plane change and to satisfy heating constraints. Because of the energy loss during the turn, an impulse is required to initiate the third phase to boost the vehicle back to the desired LEO orbital altitude. The third impulse is then used to circularize the orbit at LEO. The problem is solved by a direct optimization technique which uses piecewise polynomial representation for the state and control variables and collocation to satisfy the differential equations. This technique converts the optimal control problem into a nonlinear programming problem which is solved numerically. Solutions were obtained for cases with and without heat constraints and for cases of different orbital inclination changes. The method appears to be more powerful and robust than other optimization methods. In addition, the method can handle complex dynamical constraints.

Size Dependence of Dust Distribution around the Earth Orbit

NASA Astrophysics Data System (ADS)

Ueda, Takahiro; Kobayashi, Hiroshi; Takeuchi, Taku; Ishihara, Daisuke; Kondo, Toru; Kaneda, Hidehiro

2017-05-01

In the solar system, interplanetary dust particles (IDPs) originating mainly from asteroid collisions and cometary activities drift to Earth orbit due to Poynting-Robertson drag. We analyzed the thermal emission from IDPs that was observed by the first Japanese infrared astronomical satellite, AKARI. The observed surface brightness in the trailing direction of the Earth orbit is 3.7% greater than that in the leading direction in the 9 μm band and 3.0% in the 18 μm band. In order to reveal dust properties causing leading-trailing surface brightness asymmetry, we numerically integrated orbits of the Sun, the Earth, and a dust particle as a restricted three-body problem including radiation from the Sun. The initial orbits of particles are determined according to the orbits of main-belt asteroids or Jupiter-family comets. Orbital trapping in mean motion resonances results in a significant leading-trailing asymmetry so that intermediate sized dust (˜10-100 μm) produces a greater asymmetry than zodiacal light. The leading-trailing surface brightness difference integrated over the size distribution of the asteroidal dust is obtained to be 27.7% and 25.3% in the 9 μm and 18 μm bands, respectively. In contrast, the brightness difference for cometary dust is calculated as 3.6% and 3.1% in the 9 μm and 18 μm bands, respectively, if the maximum dust radius is set to be s max = 3000 μm. Taking into account these values and their errors, we conclude that the contribution of asteroidal dust to the zodiacal infrared emission is less than ˜10%, while cometary dust of the order of 1 mm mainly accounts for the zodiacal light in infrared.

Size Dependence of Dust Distribution around the Earth Orbit

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

Ueda, Takahiro; Takeuchi, Taku; Kobayashi, Hiroshi

In the solar system, interplanetary dust particles (IDPs) originating mainly from asteroid collisions and cometary activities drift to Earth orbit due to Poynting–Robertson drag. We analyzed the thermal emission from IDPs that was observed by the first Japanese infrared astronomical satellite, AKARI . The observed surface brightness in the trailing direction of the Earth orbit is 3.7% greater than that in the leading direction in the 9 μ m band and 3.0% in the 18 μ m band. In order to reveal dust properties causing leading–trailing surface brightness asymmetry, we numerically integrated orbits of the Sun, the Earth, and amore » dust particle as a restricted three-body problem including radiation from the Sun. The initial orbits of particles are determined according to the orbits of main-belt asteroids or Jupiter-family comets. Orbital trapping in mean motion resonances results in a significant leading–trailing asymmetry so that intermediate sized dust (∼10–100 μ m) produces a greater asymmetry than zodiacal light. The leading–trailing surface brightness difference integrated over the size distribution of the asteroidal dust is obtained to be 27.7% and 25.3% in the 9 μ m and 18 μ m bands, respectively. In contrast, the brightness difference for cometary dust is calculated as 3.6% and 3.1% in the 9 μ m and 18 μ m bands, respectively, if the maximum dust radius is set to be s {sub max} = 3000 μ m. Taking into account these values and their errors, we conclude that the contribution of asteroidal dust to the zodiacal infrared emission is less than ∼10%, while cometary dust of the order of 1 mm mainly accounts for the zodiacal light in infrared.« less

Mixing of t2 g-eg orbitals in 4 d and 5 d transition metal oxides

NASA Astrophysics Data System (ADS)

Stamokostas, Georgios L.; Fiete, Gregory A.

2018-02-01

Using exact diagonalization, we study the spin-orbit coupling and interaction-induced mixing between t2 g and egd -orbital states in a cubic crystalline environment, as commonly occurs in transition metal oxides. We make a direct comparison with the widely used t2 g-only or eg-only models, depending on electronic filling. We consider all electron fillings of the d shell and compute the total magnetic moment, the spin, the occupancy of each orbital, and the effective spin-orbit coupling strength (renormalized through interaction effects) in terms of the bare interaction parameters, spin-orbit coupling, and crystal-field splitting, focusing on the parameter ranges relevant to 4 d and 5 d transition metal oxides. In various limits, we provide perturbative results consistent with our numerical calculations. We find that the t2 g-eg mixing can be large, with up to 20% occupation of orbitals that are nominally "empty," which has experimental implications for the interpretation of the branching ratio in experiments, and can impact the effective local moment Hamiltonian used to study magnetic phases and magnetic excitations in transition metal oxides. Our results can aid the theoretical interpretation of experiments on these materials, which often fall in a regime of intermediate coupling with respect to electron-electron interactions.

A Numerical-Analytical Approach Based on Canonical Transformations for Computing Optimal Low-Thrust Transfers

NASA Astrophysics Data System (ADS)

da Silva Fernandes, S.; das Chagas Carvalho, F.; Bateli Romão, J. V.

2018-04-01

A numerical-analytical procedure based on infinitesimal canonical transformations is developed for computing optimal time-fixed low-thrust limited power transfers (no rendezvous) between coplanar orbits with small eccentricities in an inverse-square force field. The optimization problem is formulated as a Mayer problem with a set of non-singular orbital elements as state variables. Second order terms in eccentricity are considered in the development of the maximum Hamiltonian describing the optimal trajectories. The two-point boundary value problem of going from an initial orbit to a final orbit is solved by means of a two-stage Newton-Raphson algorithm which uses an infinitesimal canonical transformation. Numerical results are presented for some transfers between circular orbits with moderate radius ratio, including a preliminary analysis of Earth-Mars and Earth-Venus missions.

Numerical orbit generators of artificial earth satellites

NASA Astrophysics Data System (ADS)

Kugar, H. K.; Dasilva, W. C. C.

1984-04-01

A numerical orbit integrator containing updatings and improvements relative to the previous ones that are being utilized by the Departmento de Mecanica Espacial e Controle (DMC), of INPE, besides incorporating newer modellings resulting from the skill acquired along the time is presented. Flexibility and modularity were taken into account in order to allow future extensions and modifications. Characteristics of numerical accuracy, processing quickness, memory saving as well as utilization aspects were also considered. User's handbook, whole program listing and qualitative analysis of accuracy, processing time and orbit perturbation effects were included as well.

Evolution of asteroidal orbits with high inclinations

NASA Astrophysics Data System (ADS)

Solovaya, Nina A.; Pittich, Eduard M.

1993-10-01

The 20,000 years orbital evolution of massless fictitious asteroid located at a border of the Hill's gravitational sphere has been investigated. The eleven orbits with the eccentricities from 0.0 to 0.4 in five groups of inclinations from 40 deg to 80 deg were numerically integrated with planetary perturbations of six major planets, using the numerical integration n-body program with the Everhart's integrator RA 15. For each group time evolution of orbital elements of the asteroids is presented.

Spin-Orbit Qubits of Rare-Earth-Metal Ions in Axially Symmetric Crystal Fields

NASA Astrophysics Data System (ADS)

Bertaina, S.; Shim, J. H.; Gambarelli, S.; Malkin, B. Z.; Barbara, B.

2009-11-01

Contrary to the well-known spin qubits, rare-earth-metal qubits are characterized by a strong influence of crystal field due to large spin-orbit coupling. At low temperature and in the presence of resonance microwaves, it is the magnetic moment of the crystal-field ground state which nutates (for several μs) and the Rabi frequency ΩR is anisotropic. Here, we present a study of the variations of ΩR(H→0) with the magnitude and direction of the static magnetic field H→0 for the odd Er167 isotope in a single crystal CaWO4:Er3+. The hyperfine interactions split the ΩR(H→0) curve into eight different curves which are fitted numerically and described analytically. These “spin-orbit qubits” should allow detailed studies of decoherence mechanisms which become relevant at high temperature and open new ways for qubit addressing using properly oriented magnetic fields.

Spin-orbit qubits of rare-earth-metal ions in axially symmetric crystal fields.

PubMed

Bertaina, S; Shim, J H; Gambarelli, S; Malkin, B Z; Barbara, B

2009-11-27

Contrary to the well-known spin qubits, rare-earth-metal qubits are characterized by a strong influence of crystal field due to large spin-orbit coupling. At low temperature and in the presence of resonance microwaves, it is the magnetic moment of the crystal-field ground state which nutates (for several micros) and the Rabi frequency Omega(R) is anisotropic. Here, we present a study of the variations of Omega(R)(H(0)) with the magnitude and direction of the static magnetic field H(0) for the odd 167Er isotope in a single crystal CaWO(4):Er(3+). The hyperfine interactions split the Omega(R)(H(0)) curve into eight different curves which are fitted numerically and described analytically. These "spin-orbit qubits" should allow detailed studies of decoherence mechanisms which become relevant at high temperature and open new ways for qubit addressing using properly oriented magnetic fields.

Capture of planetesimals into a circumterrestrial swarm

NASA Technical Reports Server (NTRS)

Weidenschilling, S. J.

1984-01-01

The lunar origin model considered involves processing of protolunar material through a circumterrestrial swarm of particles. Once such a swarm has formed, it can gain mass by capturing infalling planetesimals and ejecta from giant impacts on the Earth, although the angular momentum supply from these sources remains a problem. Examined is the first stage of formation of a geocentric swarm by capture of planetesimals from initialy heliocentric orbits. The only plausible capture mechanism that is not dependent on very low approach velocities is the mutual collision of planetesimals passing within Earth's sphere of influence. This capture scenario was tested directly by many body numerical integration of planetesimal orbits in near Earth space. Results agree that the systematic contribution of angular momentum is insufficient to maintain an orbiting swarm under heavy bombardment. Thus, a circumterrestrial swarm can be formed rather easily, but is hard to sustain because the mean net angular momentum of a many body swarm is small.

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.

Stable regions around Exoplanets: the search for Exomoons

NASA Astrophysics Data System (ADS)

Fernandes Guimaraes, Ana Helena; Moretto Tusnski, Luis Ricardo; Vieira-Neto, Ernesto; Silva Valio, Adriana

2015-08-01

There are hundreds of exoplanets which the data are available to a dynamical investigation. We extracted from the data base (exoplanets.org) all planets and candidates which have the necessary data available for the numerical investigation of the orbital stability of a body around a exoplanet in a total of 2749 of those.There is a wealth diversity of exoplanets types and the expectation in find our Earth-living conditions in another planet motivates the search for extra-solar planets, and a satellite around a planet would, in addiction, help to keep a favorable climate.Using the planets class according to PHL@Arecibo, those planets were sorted out in groups. Analyses of density, distance from the primary body, and mass ratios were done beside the suggested classification to fit some no-classified planets into one of the groups.The aim of this work is to derive the upper stability limit (or upper critical orbit) of fictitious direct satellites around exoplanets of any density, or size, orbiting single stars. Our search is for stable regions around the planet, the called S-type orbits. This orbit type determines if there is any chance to exist (or not) bodies around the planets. The investigation is limited to single stars, excluding binaries.We derived such limit purely through numerical simulations. Our proposal involved long-term integration of the circular restricted three bodies problem . Basically, the cut off of the stability zone determined in the previous work by Domingos et al. (2006) were confirmed for any planet type. However, the limitation due the Roche limit of the own satellite showed to be lower. We used this to determined possible size and to adjust orbital range were a third body could orbit the exoplanet.Independently of densities, distance, and sizes of the objects involved, the idea was to delimit where to find celestial bodies in any given system around single stars. Furthermore, we aim to provide tracks to the search for exomoons using planetary transits.

Distant retrograde orbits and the asteroid hazard

NASA Astrophysics Data System (ADS)

Perozzi, Ettore; Ceccaroni, Marta; Valsecchi, Giovanni B.; Rossi, Alessandro

2017-08-01

Distant Retrograde Orbits (DROs) gained a novel wave of fame in space mission design because of their numerous advantages within the framework of the US plans for bringing a large asteroid sample in the vicinity of the Earth as the next target for human exploration. DROs are stable solutions of the three-body problem that can be used whenever an object, whether of natural or artificial nature, is required to remain in the neighborhood of a celestial body without being gravitationally captured by it. As such, they represent an alternative option to Halo orbits around the collinear Lagrangian points L1 and L2. Also known under other names ( e.g., quasi-satellite orbits, cis-lunar orbits, family- f orbits) these orbital configurations found interesting applications in several mission profiles, like that of a spacecraft orbiting around the small irregularly shaped satellite of Mars Phobos or the large Jovian moon Europa. In this paper a basic explanation of the DRO dynamics is presented in order to clarify some geometrical properties that characterize them. Their accessibility is then discussed from the point of view of mission analysis under different assumptions. Finally, their relevance within the framework of the present asteroid hazard protection programs is shown, stressing the significant increase in warning time they would provide in the prediction of impactors coming from the direction of the Sun.

System Simulation by Recursive Feedback: Coupling a Set of Stand-Alone Subsystem Simulations

NASA Technical Reports Server (NTRS)

Nixon, D. D.

2001-01-01

Conventional construction of digital dynamic system simulations often involves collecting differential equations that model each subsystem, arran g them to a standard form, and obtaining their numerical gin solution as a single coupled, total-system simultaneous set. Simulation by numerical coupling of independent stand-alone subsimulations is a fundamentally different approach that is attractive because, among other things, the architecture naturally facilitates high fidelity, broad scope, and discipline independence. Recursive feedback is defined and discussed as a candidate approach to multidiscipline dynamic system simulation by numerical coupling of self-contained, single-discipline subsystem simulations. A satellite motion example containing three subsystems (orbit dynamics, attitude dynamics, and aerodynamics) has been defined and constructed using this approach. Conventional solution methods are used in the subsystem simulations. Distributed and centralized implementations of coupling have been considered. Numerical results are evaluated by direct comparison with a standard total-system, simultaneous-solution approach.

Energy analysis in the elliptic restricted three-body problem

NASA Astrophysics Data System (ADS)

Qi, Yi; de Ruiter, Anton

2018-07-01

The gravity assist or flyby is investigated by analysing the inertial energy of a test particle in the elliptic restricted three-body problem (ERTBP), where two primary bodies are moving in elliptic orbits. First, the expression of the derivation of energy is obtained and discussed. Then, the approximate expressions of energy change in a circular neighbourhood of the smaller primary are derived. Numerical computation indicates that the obtained expressions can be applied to study the flyby problem of the nine planets and the Moon in the Solar system. Parameters related to the flyby are discussed analytically and numerically. The optimal conditions, including the position and time of the periapsis, for a flyby orbit are found to make a maximum energy gain or loss. Finally, the mechanical process of a flyby orbit is uncovered by an approximate expression in the ERTBP. Numerical computations testify that our analytical results well approximate the mechanical process of flyby orbits obtained by the numerical simulation in the ERTBP. Compared with the previous research established in the patched-conic method and numerical calculation, our analytical investigations based on a more elaborate derivation get more original results.

Energy Analysis in the Elliptic Restricted Three-body Problem

NASA Astrophysics Data System (ADS)

Qi, Yi; de Ruiter, Anton

2018-05-01

The gravity assist or flyby is investigated by analyzing the inertial energy of a test particle in the elliptic restricted three-body problem (ERTBP), where two primary bodies are moving in elliptic orbits. Firstly, the expression of the derivation of energy is obtained and discussed. Then, the approximate expressions of energy change in a circular neighborhood of the smaller primary are derived. Numerical computation indicates that the obtained expressions can be applied to study the flyby problem of the nine planets and the Moon in the solar system. Parameters related to the flyby are discussed analytically and numerically. The optimal conditions, including the position and time of the periapsis, for a flyby orbit are found to make a maximum energy gain or loss. Finally, the mechanical process of a flyby orbit is uncovered by an approximate expression in the ERTBP. Numerical computations testify that our analytical results well approximate the mechanical process of flyby orbits obtained by the numerical simulation in the ERTBP. Compared with the previous research established in the patched-conic method and numerical calculation, our analytical investigations based on a more elaborate derivation get more original results.

First calibration results and antenna placement studies of the RPW ANT instrument on Solar Orbiter

NASA Astrophysics Data System (ADS)

Sampl, M.; Oswald, T. H.; Rucker, H. O.; Plettemeier, D.; Maksimovic, M.; Macher, W.

2010-12-01

We report our analyses of the Radio and Plasma Wave Analyzer (RPW ANT) onboard the Solar Orbiter spacecraft with a focus on the high-frequency electric antennas. The aim of the Solar Orbiter mission is to determine in-situ properties and dynamics of solarwind plasma, electric and magnetic fields in the near-Sun heliosphere. The mission is planned to be launched in 2017 with a spacecraft trajectory of, for the first time, partial co-rotation with the Sun, providing a full suite of in-situ and remote sensing instruments from as close as 0.25 AU. The RPW ANT high-frequency electric sensors, consist of three cylindrical antennas mounted on appendant booms extruded from the central body of the spacecraft. Due to the parasitic effects of the conducting spacecraft body and solar panels the true antenna properties (effective axes and length; capacitances) do not coincide with their physical representations. In order to analyze the antenna system we applied a numerical method. The current distribution on the spacecraft body and the effective length vector was calculated, by solving the underlying field equations using electromagnetic codes. In the applied method the spacecraft is modelled as a patch-grid. The numerical analysis of the reception properties, including several placement options of these antennas, is presented. Since the Solar Orbiter spacecraft body and antennas are not yet finally specified, the results can be used to evaluate the performance of the proposed sensors. In particular, goniopolarimetry techniques like polarization analysis, direction finding and ray tracing depend crucially on the effective axes and the therefore the corresponding data analysis significantly improves. Software model (patch-grid) of the Solar Orbiter spacecraft

Chaotic dynamics outside Saturn’s main rings: The case of Atlas

NASA Astrophysics Data System (ADS)

Renner, Stéfan; Cooper, Nicholas J.; El Moutamid, Maryame; Evans, Mike W.; Murray, Carl D.; Sicardy, Bruno

2014-11-01

We revisit in detail the dynamics of Atlas. From a fit to new Cassini ISS astrometric observations spanning February 2004 to August 2013, we estimate GM_Atlas=0.384+/-0.001 x 10^(-3)km^3s^(-2), a value 13% smaller than the previously published estimate but with an order of magnitude reduction in the uncertainty. Our numerically-derived orbit shows that Atlas is currently librating in both a 54:53 corotation eccentricity resonance (CER) and a 54:53 Lindblad eccentricity resonance (LER) with Prometheus. We demonstrate that the orbit of Atlas is chaotic, with a Lyapunov time of order 10 years, as a direct consequence of the coupled resonant interaction (CER/LER) with Prometheus. The interactions between the two resonances is investigated using the CoraLin analytical model (El Moutamid et al., 2014), showing that the chaotic zone fills almost all the corotation site occupied by the satellite’s orbit. Four 70 :67 apse-type mean motion resonances with Pandora are also overlapping, but these resonances have a much weaker effect on Atlas.We estimate the capture probabilities of Atlas into resonances with Prometheus as the orbits expand through tidal effects, and discuss the implications for the orbital evolution.

Numerical Researches on Dynamical Systems with Relativistic Spin

NASA Astrophysics Data System (ADS)

Han, W. B.

2010-04-01

It is well known that spinning compact binaries are one of the most important research objects in the universe. Especially, EMRIs (extreme mass ratio inspirals) involving stellar compact objects which orbit massive black holes, are considered to be primary sources of gravitational radiation (GW) which could be detected by the space-based interferometer LISA. GW signals from EMRIs can be used to test general relativity, measure the masses and spins of central black holes and study essential physics near horizons. Compared with the situation without spin, the complexity of extreme objects, most of which rotate very fast, is much higher. So the dynamics of EMRI systems are numerically and analytically studied. We focus on how the spin effects on the dynamics of these systems and the produced GW radiations. Firstly, an ideal model of spinning test particles around Kerr black hole is considered. For equatorial orbits, we present the correct expression of effective potential and analyze the stability of circular orbits. Especially, the gravitational binding energy and frame-dragging effect of extreme Kerr black hole are much bigger than those without spin. For general orbits, spin can monotonically enlarge orbital inclination and destroy the symmetry of orbits about equatorial plane. It is the most important that extreme spin can produce orbital chaos. By carefully investigating the relations between chaos and orbital parameters, we point out that chaos usually appears for orbits with small pericenter, big eccentricity and orbital inclination. It is emphasized that Poincaré section method is invalid to detect the chaos of spinning particles, and the way of systems toward chaos is the period-doubling bifurcation. Furthermore, we study how spins effect on GW radiations from spinning test particles orbiting Kerr black holes. It is found that spins can increase orbit eccentricity and then make h+ component be detected more easily. But for h× component, because spins change orbital inclination in a complicated way, it is more difficult to build GW signal templates. Secondly, based on the scalar gravity theory, a numerical relativistic model of EMRIs is constructed to consider the self-gravity and radiation reaction of low-mass objects. Finally, we develop a new method with multiple steps for Hamilton systems to meet the needs of numerical researches. This method can effectively maintain each conserved quantity of the separable Hamilton system. In addition, for constrained system with a few first integrals, we present a new numerical stabilization method named as adjustment-stabilization method, which can maintain all known conserved quantities in a given dynamical system and greatly improve the numerical accuracy. Our new method is the most complete stabilization method up to now.

Using Real and Simulated TNOs to Constrain the Outer Solar System

NASA Astrophysics Data System (ADS)

Kaib, Nathan

2018-04-01

Over the past 2-3 decades our understanding of the outer solar system’s history and current state has evolved dramatically. An explosion in the number of detected trans-Neptunian objects (TNOs) coupled with simultaneous advances in numerical models of orbital dynamics has driven this rapid evolution. However, successfully constraining the orbital architecture and evolution of the outer solar system requires accurately comparing simulation results with observational datasets. This process is challenging because observed datasets are influenced by orbital discovery biases as well as TNO size and albedo distributions. Meanwhile, such influences are generally absent from numerical results. Here I will review recent work I and others have undertaken using numerical simulations in concert with catalogs of observed TNOs to constrain the outer solar system’s current orbital architecture and past evolution.

Real time optimal guidance of low-thrust spacecraft: an application of nonlinear model predictive control.

PubMed

Arrieta-Camacho, Juan José; Biegler, Lorenz T

2005-12-01

Real time optimal guidance is considered for a class of low thrust spacecraft. In particular, nonlinear model predictive control (NMPC) is utilized for computing the optimal control actions required to transfer a spacecraft from a low Earth orbit to a mission orbit. The NMPC methodology presented is able to cope with unmodeled disturbances. The dynamics of the transfer are modeled using a set of modified equinoctial elements because they do not exhibit singularities for zero inclination and zero eccentricity. The idea behind NMPC is the repeated solution of optimal control problems; at each time step, a new control action is computed. The optimal control problem is solved using a direct method-fully discretizing the equations of motion. The large scale nonlinear program resulting from the discretization procedure is solved using IPOPT--a primal-dual interior point algorithm. Stability and robustness characteristics of the NMPC algorithm are reviewed. A numerical example is presented that encourages further development of the proposed methodology: the transfer from low-Earth orbit to a molniya orbit.

An orbit determination algorithm for small satellites based on the magnitude of the earth magnetic field

NASA Astrophysics Data System (ADS)

Zagorski, P.; Gallina, A.; Rachucki, J.; Moczala, B.; Zietek, S.; Uhl, T.

2018-06-01

Autonomous attitude determination systems based on simple measurements of vector quantities such as magnetic field and the Sun direction are commonly used in very small satellites. However, those systems always require knowledge of the satellite position. This information can be either propagated from orbital elements periodically uplinked from the ground station or measured onboard by dedicated global positioning system (GPS) receiver. The former solution sacrifices satellite autonomy while the latter requires additional sensors which may represent a significant part of mass, volume, and power budget in case of pico- or nanosatellites. Hence, it is thought that a system for onboard satellite position determination without resorting to GPS receivers would be useful. In this paper, a novel algorithm for determining the satellite orbit semimajor-axis is presented. The methods exploit only the magnitude of the Earth magnetic field recorded onboard by magnetometers. This represents the first step toward an extended algorithm that can determine all orbital elements of the satellite. The method is validated by numerical analysis and real magnetic field measurements.

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.

Application of Semi-analytical Satellite Theory orbit propagator to orbit determination for space object catalog maintenance

NASA Astrophysics Data System (ADS)

Setty, Srinivas J.; Cefola, Paul J.; Montenbruck, Oliver; Fiedler, Hauke

2016-05-01

Catalog maintenance for Space Situational Awareness (SSA) demands an accurate and computationally lean orbit propagation and orbit determination technique to cope with the ever increasing number of observed space objects. As an alternative to established numerical and analytical methods, we investigate the accuracy and computational load of the Draper Semi-analytical Satellite Theory (DSST). The standalone version of the DSST was enhanced with additional perturbation models to improve its recovery of short periodic motion. The accuracy of DSST is, for the first time, compared to a numerical propagator with fidelity force models for a comprehensive grid of low, medium, and high altitude orbits with varying eccentricity and different inclinations. Furthermore, the run-time of both propagators is compared as a function of propagation arc, output step size and gravity field order to assess its performance for a full range of relevant use cases. For use in orbit determination, a robust performance of DSST is demonstrated even in the case of sparse observations, which is most sensitive to mismodeled short periodic perturbations. Overall, DSST is shown to exhibit adequate accuracy at favorable computational speed for the full set of orbits that need to be considered in space surveillance. Along with the inherent benefits of a semi-analytical orbit representation, DSST provides an attractive alternative to the more common numerical orbit propagation techniques.

Numerical modeling of on-orbit propellant motion resulting from an impulsive acceleration

NASA Technical Reports Server (NTRS)

Aydelott, John C.; Mjolsness, Raymond C.; Torrey, Martin D.; Hochstein, John I.

1987-01-01

In-space docking and separation maneuvers of spacecraft that have large fluid mass fractions may cause undesirable spacecraft motion in response to the impulsive-acceleration-induced fluid motion. An example of this potential low gravity fluid management problem arose during the development of the shuttle/Centaur vehicle. Experimentally verified numerical modeling techniques were developed to establish the propellant dynamics, and subsequent vehicle motion, associated with the separation of the Centaur vehicle from the shuttle orbiter cargo bay. Although the shuttle/Centaur development activity was suspended, the numerical modeling techniques are available to predict on-orbit liquid motion resulting from impulsive accelerations for other missions and spacecraft.

The Improvement of Efficiency in the Numerical Computation of Orbit Trajectories

NASA Technical Reports Server (NTRS)

Dyer, J.; Danchick, R.; Pierce, S.; Haney, R.

1972-01-01

An analysis, system design, programming, and evaluation of results are described for numerical computation of orbit trajectories. Evaluation of generalized methods, interaction of different formulations for satellite motion, transformation of equations of motion and integrator loads, and development of efficient integrators are also considered.

Application of Numerical Integration and Data Fusion in Unit Vector Method

NASA Astrophysics Data System (ADS)

Zhang, J.

2012-01-01

The Unit Vector Method (UVM) is a series of orbit determination methods which are designed by Purple Mountain Observatory (PMO) and have been applied extensively. It gets the conditional equations for different kinds of data by projecting the basic equation to different unit vectors, and it suits for weighted process for different kinds of data. The high-precision data can play a major role in orbit determination, and accuracy of orbit determination is improved obviously. The improved UVM (PUVM2) promoted the UVM from initial orbit determination to orbit improvement, and unified the initial orbit determination and orbit improvement dynamically. The precision and efficiency are improved further. In this thesis, further research work has been done based on the UVM: Firstly, for the improvement of methods and techniques for observation, the types and decision of the observational data are improved substantially, it is also asked to improve the decision of orbit determination. The analytical perturbation can not meet the requirement. So, the numerical integration for calculating the perturbation has been introduced into the UVM. The accuracy of dynamical model suits for the accuracy of the real data, and the condition equations of UVM are modified accordingly. The accuracy of orbit determination is improved further. Secondly, data fusion method has been introduced into the UVM. The convergence mechanism and the defect of weighted strategy have been made clear in original UVM. The problem has been solved in this method, the calculation of approximate state transition matrix is simplified and the weighted strategy has been improved for the data with different dimension and different precision. Results of orbit determination of simulation and real data show that the work of this thesis is effective: (1) After the numerical integration has been introduced into the UVM, the accuracy of orbit determination is improved obviously, and it suits for the high-accuracy data of available observation apparatus. Compare with the classical differential improvement with the numerical integration, its calculation speed is also improved obviously. (2) After data fusion method has been introduced into the UVM, weighted distribution accords rationally with the accuracy of different kinds of data, all data are fully used and the new method is also good at numerical stability and rational weighted distribution.

Analysis of close encounters with Ganymede and Callisto using a genetic n-body algorithm

NASA Astrophysics Data System (ADS)

Winter, Philip M.; Galiazzo, Mattia A.; Maindl, Thomas I.

2018-05-01

In this work we describe a genetic algorithm which is used in order to study orbits of minor bodies in the frames of close encounters. We find that the algorithm in combination with standard orbital numerical integrators can be used as a good proxy for finding typical orbits of minor bodies in close encounters with planets and even their moons, saving a lot of computational time compared t0 long-term orbital numerical integrations. Here, we study close encounters of Centaurs with Callisto and Ganymede in particular. We also perform n-body numerical simulations for comparison. We find typical impact velocities to be between v rel = 20[v esc ] and v rel = 30[v esc ] for Ganymede and between v rel = 25[v esc ] and v rel = 35[v esc ] for Callisto.

Solar Activity Forecasting for use in Orbit Prediction

NASA Technical Reports Server (NTRS)

Schatten, Kenneth

2001-01-01

Orbital prediction for satellites in low Earth orbit (LEO) or low planetary orbit depends strongly on exospheric densities. Solar activity forecasting is important in orbital prediction, as the solar UV and EUV inflate the upper atmospheric layers of the Earth and planets, forming the exosphere in which satellites orbit. Geomagnetic effects also relate to solar activity. Because of the complex and ephemeral nature of solar activity, with different cycles varying in strength by more than 100%, many different forecasting techniques have been utilized. The methods range from purely numerical techniques (essentially curve fitting) to numerous oddball schemes, as well as a small subset, called 'Precursor techniques.' The situation can be puzzling, owing to the numerous methodologies involved, somewhat akin to the numerous ether theories near the turn of the last century. Nevertheless, the Precursor techniques alone have a physical basis, namely dynamo theory, which provides a physical explanation for why this subset seems to work. I discuss this solar cycle's predictions, as well as the Sun's observed activity. I also discuss the SODA (Solar Dynamo Amplitude) index, which provides the user with the ability to track the Sun's hidden, interior dynamo magnetic fields. As a result, one may then update solar activity predictions continuously, by monitoring the solar magnetic fields as they change throughout the solar cycle. This paper ends by providing a glimpse into what the next solar cycle (#24) portends.

Outstanding performance of configuration interaction singles and doubles using exact exchange Kohn-Sham orbitals in real-space numerical grid method

NASA Astrophysics Data System (ADS)

Lim, Jaechang; Choi, Sunghwan; Kim, Jaewook; Kim, Woo Youn

2016-12-01

To assess the performance of multi-configuration methods using exact exchange Kohn-Sham (KS) orbitals, we implemented configuration interaction singles and doubles (CISD) in a real-space numerical grid code. We obtained KS orbitals with the exchange-only optimized effective potential under the Krieger-Li-Iafrate (KLI) approximation. Thanks to the distinctive features of KLI orbitals against Hartree-Fock (HF), such as bound virtual orbitals with compact shapes and orbital energy gaps similar to excitation energies; KLI-CISD for small molecules shows much faster convergence as a function of simulation box size and active space (i.e., the number of virtual orbitals) than HF-CISD. The former also gives more accurate excitation energies with a few dominant configurations than the latter, even with many more configurations. The systematic control of basis set errors is straightforward in grid bases. Therefore, grid-based multi-configuration methods using exact exchange KS orbitals provide a promising new way to make accurate electronic structure calculations.

The application of generalized, cyclic, and modified numerical integration algorithms to problems of satellite orbit computation

NASA Technical Reports Server (NTRS)

Chesler, L.; Pierce, S.

1971-01-01

Generalized, cyclic, and modified multistep numerical integration methods are developed and evaluated for application to problems of satellite orbit computation. Generalized methods are compared with the presently utilized Cowell methods; new cyclic methods are developed for special second-order differential equations; and several modified methods are developed and applied to orbit computation problems. Special computer programs were written to generate coefficients for these methods, and subroutines were written which allow use of these methods with NASA's GEOSTAR computer program.

NASA Orbital Debris Engineering Model ORDEM2008 (Beta Version)

NASA Technical Reports Server (NTRS)

Stansbery, Eugene G.; Krisko, Paula H.

2009-01-01

This is an interim document intended to accompany the beta-release of the ORDEM2008 model. As such it provides the user with a guide for its use, a list of its capabilities, a brief summary of model development, and appendices included to educate the user as to typical runtimes for different orbit configurations. More detailed documentation will be delivered with the final product. ORDEM2008 supersedes NASA's previous model - ORDEM2000. The availability of new sensor and in situ data, the re-analysis of older data, and the development of new analytical techniques, has enabled the construction of this more comprehensive and sophisticated model. Integrated with the software is an upgraded graphical user interface (GUI), which uses project-oriented organization and provides the user with graphical representations of numerous output data products. These range from the conventional average debris size vs. flux magnitude for chosen analysis orbits, to the more complex color-contoured two-dimensional (2-D) directional flux diagrams in terms of local spacecraft pitch and yaw.

Conductance dips and spin precession in a nonuniform waveguide with spin–orbit coupling

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

Malyshev, A. I., E-mail: malyshev@phys.unn.ru; Kozulin, A. S.

An infinite waveguide with a nonuniformity, a segment of finite length with spin–orbit coupling, is considered in the case when the Rashba and Dresselhaus parameters are identical. Analytical expressions have been derived in the single-mode approximation for the conductance of the system for an arbitrary initial spin state. Based on numerical calculations with several size quantization modes, we have detected and described the conductance dips arising when the waves are localized in the nonuniformity due to the formation of an effective potential well in it. We show that allowance for the evanescent modes under carrier spin precession in an effectivemore » magnetic field does not lead to a change in the direction of the average spin vector at the output of the system.« less

Kohn-Sham potentials from electron densities using a matrix representation within finite atomic orbital basis sets

NASA Astrophysics Data System (ADS)

Zhang, Xing; Carter, Emily A.

2018-01-01

We revisit the static response function-based Kohn-Sham (KS) inversion procedure for determining the KS effective potential that corresponds to a given target electron density within finite atomic orbital basis sets. Instead of expanding the potential in an auxiliary basis set, we directly update the potential in its matrix representation. Through numerical examples, we show that the reconstructed density rapidly converges to the target density. Preliminary results are presented to illustrate the possibility of obtaining a local potential in real space from the optimized potential in its matrix representation. We have further applied this matrix-based KS inversion approach to density functional embedding theory. A proof-of-concept study of a solvated proton transfer reaction demonstrates the method's promise.

Detection of carbon monoxide and water absorption lines in an exoplanet atmosphere.

PubMed

Konopacky, Quinn M; Barman, Travis S; Macintosh, Bruce A; Marois, Christian

2013-03-22

Determining the atmospheric structure and chemical composition of an exoplanet remains a formidable goal. Fortunately, advancements in the study of exoplanets and their atmospheres have come in the form of direct imaging--spatially resolving the planet from its parent star--which enables high-resolution spectroscopy of self-luminous planets in jovian-like orbits. Here, we present a spectrum with numerous, well-resolved molecular lines from both water and carbon monoxide from a massive planet orbiting less than 40 astronomical units from the star HR 8799. These data reveal the planet's chemical composition, atmospheric structure, and surface gravity, confirming that it is indeed a young planet. The spectral lines suggest an atmospheric carbon-to-oxygen ratio that is greater than that of the host star, providing hints about the planet's formation.

Orbital and angular motion construction for low thrust interplanetary flight

NASA Astrophysics Data System (ADS)

Yelnikov, R. V.; Mashtakov, Y. V.; Ovchinnikov, M. Yu.; Tkachev, S. S.

2016-11-01

Low thrust interplanetary flight is considered. Firstly, the fuel-optimal control is found. Then the angular motion is synthesized. This motion provides the thruster tracking of the required by optimal control direction. And, finally, reaction wheel control law for tracking this angular motion is proposed and implemented. The numerical example is given and total operation time for thrusters is found. Disturbances from solar pressure, thrust eccentricity, inaccuracy of reaction wheels installation and errors of inertia tensor are taken into account.

Compensator-based 6-DOF control for probe asteroid-orbital-frame hovering with actuator limitations

NASA Astrophysics Data System (ADS)

Liu, Xiaosong; Zhang, Peng; Liu, Keping; Li, Yuanchun

2016-05-01

This paper is concerned with 6-DOF control of a probe hovering in the orbital frame of an asteroid. Considering the requirements of the scientific instruments pointing direction and orbital position in practical missions, the coordinate control of relative attitude and orbit between the probe and target asteroid is imperative. A 6-DOF dynamic equation describing the relative translational and rotational motion of a probe in the asteroid's orbital frame is derived, taking the irregular gravitation, model and parameter uncertainties and external disturbances into account. An adaptive sliding mode controller is employed to guarantee the convergence of the state error, where the adaptation law is used to estimate the unknown upper bound of system uncertainty. Then the controller is improved to deal with the practical problem of actuator limitations by introducing a RBF neural network compensator, which is used to approximate the difference between the actual control with magnitude constraint and the designed nominal control law. The closed-loop system is proved to be asymptotically stable through the Lyapunov stability analysis. Numerical simulations are performed to compare the performances of the preceding designed control laws. Simulation results demonstrate the validity of the control scheme using the compensator-based adaptive sliding mode control law in the presence of actuator limitations, system uncertainty and external disturbance.

The long-term dynamical behavior of short-period comets

NASA Technical Reports Server (NTRS)

Levison, Harold F.; Duncan, Martin J.

1993-01-01

The orbits of the known short-period comets under the influence of the Sun and all the planets except Mercury and Pluto are numerically integrated. The calculation was undertaken in order to determine the dynamical lifetimes for these objects as well as explaining the current orbital element distribution. It is found that a comet can move between Jupiter-family and Halley-family comets several times in its dynamical lifetime. The median lifetime of the known short-period comets from the time they are first injected into a short-period comet orbit to ultimate ejection is approximately 50,000 years. The very flat inclination distribution of Jupiter-family comets is observed to become more distended as it ages. The only possible explanation for the observed flat distribution is that the comets become extinct before their inclination distribution can change significantly. It is shown that the anomalous concentration of the argument of perihelion of Jupiter-family comets near 0 and 180 deg is a direct result of their aphelion distance being close to 5.2AU and the comet being recently perturbed onto a Jupiter-family orbit. Also the concentration of their aphelion near Jupiter's orbit is a result of the conservation of the Tisserand invariant during the capture process.

K- and L-edge X-ray absorption spectroscopy (XAS) and resonant inelastic X-ray scattering (RIXS) determination of differential orbital covalency (DOC) of transition metal sites

DOE PAGES

Baker, Michael L.; Mara, Michael W.; Yan, James J.; ...

2017-02-09

Continual advancements in the development of synchrotron radiation sources have resulted in X-ray based spectroscopic techniques capable of probing the electronic and structural properties of numerous systems. This review gives an overview of the application of metal K-edge and L-edge X-ray absorption spectroscopy (XAS), as well as Kα resonant inelastic X-ray scattering (RIXS), to the study of electronic structure in transition metal sites with emphasis on experimentally quantifying 3d orbital covalency. The specific sensitivities of K-edge XAS, L-edge XAS, and RIXS are discussed emphasizing the complementary nature of the methods. L-edge XAS and RIXS are sensitive to mixing between 3dmore » orbitals and ligand valence orbitals, and to the differential orbital covalency (DOC), that is, the difference in the covalencies for different symmetry sets of the d orbitals. Both L-edge XAS and RIXS are highly sensitive to and enable separation of σ and π donor bonding and π back bonding contributions to bonding. Applying ligand field multiplet simulations, including charge transfer via valence bond configuration interactions, DOC can be obtained for direct comparison with density functional theory calculations and to understand chemical trends. Here, the application of RIXS as a probe of frontier molecular orbitals in a heme enzyme demonstrates the potential of this method for the study of metal sites in highly covalent coordination sites in bioinorganic chemistry.« less

K- and L-edge X-ray absorption spectroscopy (XAS) and resonant inelastic X-ray scattering (RIXS) determination of differential orbital covalency (DOC) of transition metal sites

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

Baker, Michael L.; Mara, Michael W.; Yan, James J.

Continual advancements in the development of synchrotron radiation sources have resulted in X-ray based spectroscopic techniques capable of probing the electronic and structural properties of numerous systems. This review gives an overview of the application of metal K-edge and L-edge X-ray absorption spectroscopy (XAS), as well as Kα resonant inelastic X-ray scattering (RIXS), to the study of electronic structure in transition metal sites with emphasis on experimentally quantifying 3d orbital covalency. The specific sensitivities of K-edge XAS, L-edge XAS, and RIXS are discussed emphasizing the complementary nature of the methods. L-edge XAS and RIXS are sensitive to mixing between 3dmore » orbitals and ligand valence orbitals, and to the differential orbital covalency (DOC), that is, the difference in the covalencies for different symmetry sets of the d orbitals. Both L-edge XAS and RIXS are highly sensitive to and enable separation of σ and π donor bonding and π back bonding contributions to bonding. Applying ligand field multiplet simulations, including charge transfer via valence bond configuration interactions, DOC can be obtained for direct comparison with density functional theory calculations and to understand chemical trends. Here, the application of RIXS as a probe of frontier molecular orbitals in a heme enzyme demonstrates the potential of this method for the study of metal sites in highly covalent coordination sites in bioinorganic chemistry.« less

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

Kikuchi, Akihiro; Higuchi, Arika; Ida, Shigeru, E-mail: kikuchi.a@geo.titech.ac.jp, E-mail: higuchia@geo.titech.ac.jp, E-mail: ida@elsi.jp

Recently, gas giant planets in nearly circular orbits with large semimajor axes (a ∼ 30-1000 AU) have been detected by direct imaging. We have investigated orbital evolution in a formation scenario for such planets, based on a core accretion model. (1) Icy cores accrete from planetesimals at ≲ 30 AU, (2) they are scattered outward by an emerging nearby gas giant to acquire highly eccentric orbits, and (3) their orbits are circularized through the accretion of disk gas in outer regions, where they spend most of their time. We analytically derived equations to describe the orbital circularization through gas accretion.more » Numerical integrations of these equations show that the eccentricity decreases by a factor of more than 5 while the planetary mass increases by a factor of 10. Because runaway gas accretion increases planetary mass by ∼10-300, the orbits are sufficiently circularized. On the other hand, a is reduced at most only by a factor of two, leaving the planets in the outer regions. If the relative velocity damping by shock is considered, the circularization slows down, but is still efficient enough. Therefore, this scenario potentially accounts for the formation of observed distant jupiters in nearly circular orbits. If the apocenter distances of the scattered cores are larger than the disk sizes, their a shrink to a quarter of the disk sizes; the a-distribution of distant giants could reflect the outer edges of the disks in a similar way that those of hot jupiters may reflect inner edges.« less

[Interactions of fibroblasts, adipocytes and immunocompeent cells in the pathogenesis of endocrine ophthalmopathy].

PubMed

Heufelder, A E

2001-01-01

Graves' ophthalmopathy is thought to result from a complex interplay of genetic and environmental factors. Various genes including those coding for HLA may determine a patient's susceptibility to the disease and its severity, but in addition numerous and often unknown environmental factors may determine its course. The orbital immune process is thought to be initiated, on the background of a permissive immunogenetic milieu, by circulating T cells directed against certain antigens on thyroid follicular cells that also recognize antigenic epitopes which are shared by tissues contained in the orbital space. Analysis of variable region genes of T cell antigen receptors in orbital T cells of patients with active Graves' ophthalmopathy has revealed limited variability of TcR V gene usage, suggesting that antigen-driven selection and/or expansion of specific T cells may occur during the early stages of Graves' ophthalmopathy. T cell recruitment into the orbital tissues is facilitated by certain chemokines and cytokines, which attract T cells by stimulating the expression of several adhesion molecules (e.g. ICAM-1, VCAM-1, CD44) in vascular endothelium and connective tissue cells. Adhesion molecules are known to be important for a variety of interactions between immunocompetent cells, preadipocyte fibroblasts and adipocytes. In addition, these molecules play a central role in lymphocyte activation and localization, facilitating antigen recognition, T cell costimulation, and various effector-target cell functions at the inflammatory sites, which result in amplification of the cellular immune process in active Graves' ophthalmopathy. T cells and macrophages populate the orbital space and release a number of cytokines (most likely a Th-1-type spectrum) into the surrounding tissues. Cytokines, oxygen free radicals and fibrogenic growth factors, released both from infiltrating inflammatory and residential cells, act upon orbital preadipocytes in a paracrine and autocrine manner to stimulate adipogenesis, fibroblast proliferation, glycosaminoglycan synthesis, and the expression of immunomodulatory molecules. Smoking, a well-known aggravating factor in Graves' ophthalmopathy, may aggravate tissue hypoxia and exert important immunomodulatory and pro-oxidant effects. Differentiation of orbital preadipocyte fibroblasts into mature adipocytes expressing increased levels of TSHR may also be driven by stimulation with circulating or locally produced cytokines or effectors. TSHR-directed autoantibodies or T cells may thus play a direct role promoting adipogenesis, glycosaminoglycan synthesis and expression of immunomodulatory proteins within the orbits. Once the net effect of these changes has come to increase the volume of the fatty connective tissues within the orbit, then proptosis, extraocular muscle dysfunction, and periorbital congestion will ensue.

On the accuracy of ERS-1 orbit predictions

NASA Technical Reports Server (NTRS)

Koenig, Rolf; Li, H.; Massmann, Franz-Heinrich; Raimondo, J. C.; Rajasenan, C.; Reigber, C.

1993-01-01

Since the launch of ERS-1, the D-PAF (German Processing and Archiving Facility) provides regularly orbit predictions for the worldwide SLR (Satellite Laser Ranging) tracking network. The weekly distributed orbital elements are so called tuned IRV's and tuned SAO-elements. The tuning procedure, designed to improve the accuracy of the recovery of the orbit at the stations, is discussed based on numerical results. This shows that tuning of elements is essential for ERS-1 with the currently applied tracking procedures. The orbital elements are updated by daily distributed time bias functions. The generation of the time bias function is explained. Problems and numerical results are presented. The time bias function increases the prediction accuracy considerably. Finally, the quality assessment of ERS-1 orbit predictions is described. The accuracy is compiled for about 250 days since launch. The average accuracy lies in the range of 50-100 ms and has considerably improved.

The orbital evolution of NEA 30825 1900 TG1

NASA Astrophysics Data System (ADS)

Timoshkova, E. I.

2008-02-01

The orbital evolution of the near-Earth asteroid (NEA) 30825 1990 TG1 has been studied by numerical integration of the equations of its motion over the 100 000-year time interval with allowance for perturbations from eight major planets and Pluto, and the variations in its osculating orbit over this time interval were determined. The numerical integrations were performed using two methods: the Bulirsch-Stoer method and the Everhart method. The comparative analysis of the two resulting orbital evolutions of motion is presented for the time interval examined. The evolution of the asteroid motion is qualitatively the same for both variants, but the rate of evolution of the orbital elements is different. Our research confirms the known fact that the application of different integrators to the study of the long-term evolution of the NEA orbit may lead to different evolution tracks.

Nonlinear dynamics behavior analysis of the spatial configuration of a tendril-bearing plant

NASA Astrophysics Data System (ADS)

Feng, Jingjing; Zhang, Qichang; Wang, Wei; Hao, Shuying

2017-03-01

Tendril-bearing plants appear to have a spiraling shape when tendrils climb along a support during growth. The growth characteristics of a tendril-bearer can be simplified to a model of a thin elastic rod with a cylindrical constraint. In this paper, the connection between some typical configuration characteristics of tendrils and complex nonlinear dynamic behavior are qualitatively analyzed. The space configuration problem of tendrils can be explained through the study of the nonlinear dynamic behavior of the thin elastic rod system equation. In this study, the complex non-Z2 symmetric critical orbits in the system equation under critical parameters were presented. A new function transformation method that can effectively maintain the critical orbit properties was proposed, and a new nonlinear differential equations system containing complex nonlinear terms can been obtained to describe the cross section position and direction of a rod during climbing. Numerical simulation revealed that the new system can describe the configuration of a rod with reasonable accuracy. To adequately explain the growing regulation of the rod shape, the critical orbit and configuration of rod are connected in a direct way. The high precision analytical expressions of these complex non-Z2 symmetric critical orbits are obtained by introducing a suitable analytical method, and then these expressions are used to draw the corresponding three-dimensional configuration figures of an elastic thin rod. Combined with actual tendrils on a live plant, the space configuration of the winding knots of tendril is explained by the concept of heteroclinic orbit from the perspective of nonlinear dynamics, and correctness of the theoretical analysis was verified. This theoretical analysis method could also be effectively applied to other similar slender structures.

Angles-only, ground-based, initial orbit determination

NASA Astrophysics Data System (ADS)

Taff, L. G.; Randall, P. M. S.; Stansfield, S. A.

1984-05-01

Over the past few years, passive, ground-based, angles-only initial orbit determination has had a thorough analytical, numerical, experimental, and creative re-examination. This report presents the numerical culmination of this effort and contains specific recommendations for which of several techniques one should use on the different subsets of high altitude artificial satellites and minor planets.

Dynamical lifetimes of asteroids in retrograde orbits

NASA Astrophysics Data System (ADS)

Kankiewicz, Paweł; Włodarczyk, Ireneusz

2017-07-01

The population of known minor bodies in retrograde orbits (I > 90°) that are classified as asteroids is still growing. The aim of our study was to estimate the dynamical lifetimes of these bodies using the latest observational data, including astrometry and physical properties. We selected 25 asteroids with the best-determined orbital elements. We studied their dynamical evolution in the past and future for ±100 Myr (±1 Gyr for three particular cases). We first used orbit determination and cloning to produce swarms of test particles. These swarms were then input into long-term numerical integrations, and the orbital elements were averaged. Next, we collected the available thermal properties of our objects and we used them in an enhanced dynamical model with Yarkovsky forces. We also used a gravitational model for comparison. Finally, we estimated the median lifetimes of 25 asteroids. We found three objects whose retrograde orbits were stable with a dynamical lifetime τ ˜ 10-100 Myr. A large portion of the objects studied displayed smaller values of τ (τ ˜ 1 Myr). In addition, we studied the possible influence of the Yarkovsky effect on our results. We found that the Yarkovsky effect can have a significant influence on the lifetimes of asteroids in retrograde orbits. Because of the presence of this effect, it is possible that the median lifetimes of these objects are extended. Additionally, the changes in orbital elements, caused by Yarkovsky forces, appear to depend on the integration direction. To explain this more precisely, the same model based on new physical parameters, determined from future observations, will be required.

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

Ball, J.B. Jr.

Direct oblique sagittal CT was used to evaluate trauma to 77 orbits. Sixty-seven orbital wall fractures with intact orbital rims (36 floor, 22 medial wall, nine roof) were identified in 47 orbits. Since persistent diplopia and/or enophthalmos may warrant surgical repair of orbital floor fractures, optimal imaging should include an evaluation of extraocular muscle status, the nature and amount of displaced orbital contents, and an accurate definition of fracture margins. For orbital floor fractures, a combination of the direct oblique sagittal and direct coronal projections optimally displayed all fracture margins, the fracture's relationship to the inferior orbital rim and medialmore » orbital wall, and the amount of displacement into the maxillary sinus. Inferior rectus muscle status with 36 floor fractures was best seen on the direct oblique sagittal projection in 30 fractures (83.3%) and was equally well seen on sagittal and coronal projections in two fractures (5.5%). Floor fractures were missed on 100% of axial, 5.5% of sagittal, and 0% of coronal projections. Since the direct oblique sagittal projection complements the direct coronal projection in evaluating orbital floor fractures, it should not be performed alone. A technical approach to the CT evaluation or orbital wall fractures is presented.« less

Chaotic orbits obeying one isolating integral in a four-dimensional map

NASA Astrophysics Data System (ADS)

Muzzio, J. C.

2018-02-01

We have recently presented strong evidence that chaotic orbits that obey one isolating integral besides energy exist in a toy Hamiltonian model with three degrees of freedom and are bounded by regular orbits that isolate them from the Arnold web. The interval covered by those numerical experiments was equivalent to about one million Hubble times in a galactic context. Here, we use a four-dimensional map to confirm our previous results and to extend that interval 50 times. We show that, at least within that interval, features found in lower dimension Hamiltonian systems and maps are also present in our study, e.g. within the phase space occupied by a chaotic orbit that obeys one integral there are subspaces where that orbit does not enter and are, instead, occupied by regular orbits that, if tori, bound other chaotic orbits obeying one integral and, if cantori, produce stickiness. We argue that the validity of our results might exceed the time intervals covered by the numerical experiments.

Approximate analytic method for high-apogee twelve-hour orbits of artificial Earth's satellites

NASA Astrophysics Data System (ADS)

Vashkovyaka, M. A.; Zaslavskii, G. S.

2016-09-01

We propose an approach to the study of the evolution of high-apogee twelve-hour orbits of artificial Earth's satellites. We describe parameters of the motion model used for the artificial Earth's satellite such that the principal gravitational perturbations of the Moon and Sun, nonsphericity of the Earth, and perturbations from the light pressure force are approximately taken into account. To solve the system of averaged equations describing the evolution of the orbit parameters of an artificial satellite, we use both numeric and analytic methods. To select initial parameters of the twelve-hour orbit, we assume that the path of the satellite along the surface of the Earth is stable. Results obtained by the analytic method and by the numerical integration of the evolving system are compared. For intervals of several years, we obtain estimates of oscillation periods and amplitudes for orbital elements. To verify the results and estimate the precision of the method, we use the numerical integration of rigorous (not averaged) equations of motion of the artificial satellite: they take into account forces acting on the satellite substantially more completely and precisely. The described method can be applied not only to the investigation of orbit evolutions of artificial satellites of the Earth; it can be applied to the investigation of the orbit evolution for other planets of the Solar system provided that the corresponding research problem will arise in the future and the considered special class of resonance orbits of satellites will be used for that purpose.

Dynamics of vortex dipoles in anisotropic Bose-Einstein condensates

DOE PAGES

Goodman, Roy H.; Kevrekidis, P. G.; Carretero-González, R.

2015-04-14

We study the motion of a vortex dipole in a Bose-Einstein condensate confined to an anisotropic trap. We focus on a system of ODEs describing the vortices' motion, which is in turn a reduced model of the Gross-Pitaevskii equation describing the condensate's motion. Using a sequence of canonical changes of variables, we reduce the dimension and simplify the equations of motion. In this study, we uncover two interesting regimes. Near a family of periodic orbits known as guiding centers, we find that the dynamics is essentially that of a pendulum coupled to a linear oscillator, leading to stochastic reversals inmore » the overall direction of rotation of the dipole. Near the separatrix orbit in the isotropic system, we find other families of periodic, quasi-periodic, and chaotic trajectories. In a neighborhood of the guiding center orbits, we derive an explicit iterated map that simplifies the problem further. Numerical calculations are used to illustrate the phenomena discovered through the analysis. Using the results from the reduced system, we are able to construct complex periodic orbits in the original, PDE, mean-field model for Bose-Einstein condensates, which corroborates the phenomenology observed in the reduced dynamical equations.« less

Dynamics of vortex dipoles in anisotropic Bose-Einstein condensates

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

Goodman, Roy H.; Kevrekidis, P. G.; Carretero-González, R.

We study the motion of a vortex dipole in a Bose-Einstein condensate confined to an anisotropic trap. We focus on a system of ODEs describing the vortices' motion, which is in turn a reduced model of the Gross-Pitaevskii equation describing the condensate's motion. Using a sequence of canonical changes of variables, we reduce the dimension and simplify the equations of motion. In this study, we uncover two interesting regimes. Near a family of periodic orbits known as guiding centers, we find that the dynamics is essentially that of a pendulum coupled to a linear oscillator, leading to stochastic reversals inmore » the overall direction of rotation of the dipole. Near the separatrix orbit in the isotropic system, we find other families of periodic, quasi-periodic, and chaotic trajectories. In a neighborhood of the guiding center orbits, we derive an explicit iterated map that simplifies the problem further. Numerical calculations are used to illustrate the phenomena discovered through the analysis. Using the results from the reduced system, we are able to construct complex periodic orbits in the original, PDE, mean-field model for Bose-Einstein condensates, which corroborates the phenomenology observed in the reduced dynamical equations.« less

Communication: xDH double hybrid functionals can be qualitatively incorrect for non-equilibrium geometries: Dipole moment inversion and barriers to radical-radical association using XYG3 and XYGJ-OS

NASA Astrophysics Data System (ADS)

Hait, Diptarka; Head-Gordon, Martin

2018-05-01

Double hybrid (DH) density functionals are amongst the most accurate density functional approximations developed so far, largely due to the incorporation of correlation effects from unoccupied orbitals via second order perturbation theory (PT2). The xDH family of DH functionals calculate energy directly from orbitals optimized by a lower level approach like B3LYP, without self-consistent optimization. XYG3 and XYGJ-OS are two widely used xDH functionals that are known to be quite accurate at equilibrium geometries. Here, we show that the XYG3 and XYGJ-OS functionals can be ill behaved for stretched bonds well beyond the Coulson-Fischer point, predicting unphysical dipole moments and humps in potential energy curves for some simple systems like the hydrogen fluoride molecule. Numerical experiments and analysis show that these failures are not due to PT2. Instead, a large mismatch at stretched bond-lengths between the reference B3LYP orbitals and the optimized orbitals associated with the non-PT2 part of XYG3 leads to an unphysically large non-Hellman-Feynman contribution to first order properties like forces and electron densities.

The role of global cloud climatologies in validating numerical models

NASA Technical Reports Server (NTRS)

HARSHVARDHAN

1993-01-01

The purpose of this work is to estimate sampling errors of area-time averaged rain rate due to temporal samplings by satellites. In particular, the sampling errors of the proposed low inclination orbit satellite of the Tropical Rainfall Measuring Mission (TRMM) (35 deg inclination and 350 km altitude), one of the sun synchronous polar orbiting satellites of NOAA series (98.89 deg inclination and 833 km altitude), and two simultaneous sun synchronous polar orbiting satellites--assumed to carry a perfect passive microwave sensor for direct rainfall measurements--will be estimated. This estimate is done by performing a study of the satellite orbits and the autocovariance function of the area-averaged rain rate time series. A model based on an exponential fit of the autocovariance function is used for actual calculations. Varying visiting intervals and total coverage of averaging area on each visit by the satellites are taken into account in the model. The data are generated by a General Circulation Model (GCM). The model has a diurnal cycle and parameterized convective processes. A special run of the GCM was made at NASA/GSFC in which the rainfall and precipitable water fields were retained globally for every hour of the run for the whole year.

Development and evaluation of a hybrid averaged orbit generator

NASA Technical Reports Server (NTRS)

Mcclain, W. D.; Long, A. C.; Early, L. W.

1978-01-01

A rapid orbit generator based on a first-order application of the Generalized Method of Averaging has been developed for the Research and Development (R&D) version of the Goddard Trajectory Determination System (GTDS). The evaluation of the averaged equations of motion can use both numerically averaged and recursively evaluated, analytically averaged perturbation models. These equations are numerically integrated to obtain the secular and long-period motion. Factors affecting efficient orbit prediction are discussed and guidelines are presented for treatment of each major perturbation. Guidelines for obtaining initial mean elements compatible with the theory are presented. An overview of the orbit generator is presented and comparisons with high precision methods are given.

A globally nonsingular quaternion-based formulation for all-electric satellite trajectory optimization

NASA Astrophysics Data System (ADS)

Libraro, Paola

The general electric propulsion orbit-raising maneuver of a spacecraft must contend with four main limiting factors: the longer time of flight, multiple eclipses prohibiting continuous thrusting, long exposure to radiation from the Van Allen belt and high power requirement of the electric engines. In order to optimize a low-thrust transfer with respect to these challenges, the choice of coordinates and corresponding equations of motion used to describe the kinematical and dynamical behavior of the satellite is of critical importance. This choice can potentially affect the numerical optimization process as well as limit the set of mission scenarios that can be investigated. To increase the ability to determine the feasible set of mission scenarios able to address the challenges of an all-electric orbit-raising, a set of equations free of any singularities is required to consider a completely arbitrary injection orbit. For this purpose a new quaternion-based formulation of a spacecraft translational dynamics that is globally nonsingular has been developed. The minimum-time low-thrust problem has been solved using the new set of equations of motion inside a direct optimization scheme in order to investigate optimal low-thrust trajectories over the full range of injection orbit inclinations between 0 and 90 degrees with particular focus on high-inclinations. The numerical results consider a specific mission scenario in order to analyze three key aspects of the problem: the effect of the initial guess on the shape and duration of the transfer, the effect of Earth oblateness on transfer time and the role played by, radiation damage and power degradation in all-electric minimum-time transfers. Finally trade-offs between mass and cost savings are introduced through a test case.

Translation and integration of numerical atomic orbitals in linear molecules

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

Heinäsmäki, Sami, E-mail: sami.heinasmaki@gmail.com

2014-02-14

We present algorithms for translation and integration of atomic orbitals for LCAO calculations in linear molecules. The method applies to arbitrary radial functions given on a numerical mesh. The algorithms are based on pseudospectral differentiation matrices in two dimensions and the corresponding two-dimensional Gaussian quadratures. As a result, multicenter overlap and Coulomb integrals can be evaluated effectively.

Nature of magnetization and lateral spin-orbit interaction in gated semiconductor nanowires.

PubMed

Karlsson, H; Yakimenko, I I; Berggren, K-F

2018-05-31

Semiconductor nanowires are interesting candidates for realization of spintronics devices. In this paper we study electronic states and effects of lateral spin-orbit coupling (LSOC) in a one-dimensional asymmetrically biased nanowire using the Hartree-Fock method with Dirac interaction. We have shown that spin polarization can be triggered by LSOC at finite source-drain bias,as a result of numerical noise representing a random magnetic field due to wiring or a random background magnetic field by Earth magnetic field, for instance. The electrons spontaneously arrange into spin rows in the wire due to electron interactions leading to a finite spin polarization. The direction of polarization is, however, random at zero source-drain bias. We have found that LSOC has an effect on orientation of spin rows only in the case when source-drain bias is applied.

Nature of magnetization and lateral spin–orbit interaction in gated semiconductor nanowires

NASA Astrophysics Data System (ADS)

Karlsson, H.; Yakimenko, I. I.; Berggren, K.-F.

2018-05-01

Semiconductor nanowires are interesting candidates for realization of spintronics devices. In this paper we study electronic states and effects of lateral spin–orbit coupling (LSOC) in a one-dimensional asymmetrically biased nanowire using the Hartree–Fock method with Dirac interaction. We have shown that spin polarization can be triggered by LSOC at finite source-drain bias,as a result of numerical noise representing a random magnetic field due to wiring or a random background magnetic field by Earth magnetic field, for instance. The electrons spontaneously arrange into spin rows in the wire due to electron interactions leading to a finite spin polarization. The direction of polarization is, however, random at zero source-drain bias. We have found that LSOC has an effect on orientation of spin rows only in the case when source-drain bias is applied.

On the alleged collisional origin of the Kirkwood Gaps. [in asteroid belt

NASA Technical Reports Server (NTRS)

Heppenheimer, T. A.

1975-01-01

This paper examines two proposed mechanisms whereby asteroidal collisions and close approaches may have given rise to the Kirkwood Gaps. The first hypothesis is that asteroids in near-resonant orbits have markedly increased collision probabilities and so are preferentially destroyed, or suffer decay in population density, within the resonance zones. A simple order-of-magnitude analysis shows that this hypothesis is untenable since it leads to conclusions which are either unrealistic or not in accord with present understanding of asteroidal physics. The second hypothesis is the Brouwer-Jefferys theory that collisions would smooth an asteroidal distribution function, as a function of Jacobi constant, thus forming resonance gaps. This hypothesis is examined by direct numerical integration of 50 asteroid orbits near the 2:1 resonance, with collisions simulated by random variables. No tendency to form a gap was observed.

Exoplanetary Photometry

NASA Astrophysics Data System (ADS)

Harrington, Joseph

2008-09-01

The Spitzer Space Telescope measured the first photons from exoplanets (Charbonneau et al. 2005, Deming et al. 2005). These secondary eclipses (planet passing behind star) revealed the planet's emitted infrared flux, and under a blackbody assumption provide a brightness temperature in each measured bandpass. Since the initial direct detections, Spitzer has made numerous measurements in the four Infrared Array Camera bandpasses at 3.6, 4.5, 5.7, and 8.0 microns; the Infrared Spectrograph's Blue Peakup Array at 16 microns; and the Multiband Imaging Photometer for Spitzer's 24-micron array. Initial measurements of orbital variation and further photometric study (Harrington et al. 2006, 2007) revealed the extreme day-night variability of some exoplanets, but full orbital phase curves of different planets (Knutson et al. 2007, 2008) demonstrated that not all planets are so variable. This talk will review progress and prospects in exoplanetary photometry.

Periastron advance in spinning black hole binaries: Gravitational self-force from numerical relativity

NASA Astrophysics Data System (ADS)

Le Tiec, Alexandre; Buonanno, Alessandra; Mroué, Abdul H.; Pfeiffer, Harald P.; Hemberger, Daniel A.; Lovelace, Geoffrey; Kidder, Lawrence E.; Scheel, Mark A.; Szilágyi, Bela; Taylor, Nicholas W.; Teukolsky, Saul A.

2013-12-01

We study the general relativistic periastron advance in spinning black hole binaries on quasicircular orbits, with spins aligned or antialigned with the orbital angular momentum, using numerical-relativity simulations, the post-Newtonian approximation, and black hole perturbation theory. By imposing a symmetry by exchange of the bodies’ labels, we devise an improved version of the perturbative result and use it as the leading term of a new type of expansion in powers of the symmetric mass ratio. This allows us to measure, for the first time, the gravitational self-force effect on the periastron advance of a nonspinning particle orbiting a Kerr black hole of mass M and spin S=-0.5M2, down to separations of order 9M. Comparing the predictions of our improved perturbative expansion with the exact results from numerical simulations of equal-mass and equal-spin binaries, we find a remarkable agreement over a wide range of spins and orbital separations.

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.

Numerical black hole initial data with low eccentricity based on post-Newtonian orbital parameters

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

Walther, Benny; Bruegmann, Bernd; Mueller, Doreen

2009-06-15

Black hole binaries on noneccentric orbits form an important subclass of gravitational wave sources, but it is a nontrivial issue to construct numerical initial data with minimal initial eccentricity for numerical simulations. We compute post-Newtonian orbital parameters for quasispherical orbits using the method of Buonanno, Chen and Damour, (2006) and examine the resulting eccentricity in numerical simulations. Four different methods are studied resulting from the choice of Taylor-expanded or effective-one-body Hamiltonians, and from two choices for the energy flux. For equal-mass, nonspinning binaries the approach succeeds in obtaining low-eccentricity numerical initial data with an eccentricity of about e=0.002 for rathermore » small initial separations of D > or approx. 10M. The eccentricity increases for unequal masses and for spinning black holes, but remains smaller than that obtained from previous post-Newtonian approaches. The effective-one-body Hamiltonian offers advantages for decreasing initial separation as expected, but in the context of this study also performs significantly better than the Taylor-expanded Hamiltonian for binaries with spin. For mass ratio 4 ratio 1 and vanishing spin, the eccentricity reaches e=0.004. For mass ratio 1 ratio 1 and aligned spins of size 0.85M{sup 2} the eccentricity is about e=0.07 for the Taylor method and e=0.014 for the effective-one-body method.« less

High altitude chemically reacting gas particle mixtures. Volume 1: A theoretical analysis and development of the numerical solution. [rocket nozzle and orbital plume flow fields

NASA Technical Reports Server (NTRS)

Smith, S. D.

1984-01-01

The overall contractual effort and the theory and numerical solution for the Reacting and Multi-Phase (RAMP2) computer code are described. The code can be used to model the dominant phenomena which affect the prediction of liquid and solid rocket nozzle and orbital plume flow fields. Fundamental equations for steady flow of reacting gas-particle mixtures, method of characteristics, mesh point construction, and numerical integration of the conservation equations are considered herein.

The dynamics of post-main sequence planetary systems

NASA Astrophysics Data System (ADS)

Mustill, Alexander James

2017-06-01

The study of planetary systems after their host stars have left the main sequence is of fundamental importance for exoplanet science, as the most direct determination of the compositions of extra-Solar planets, asteroids and comets is in fact made by an analysis of the elemental abundances of the remnants of these bodies accreted into the atmospheres of white dwarfs.To understand how the accreted bodies relate to the source populations in the planetary system, and to model their dynamical delivery to the white dwarf, it is necessary to understand the effects of stellar evolution on bodies' orbits. On the red giant branch (RGB) and asymptotic giant branch (AGB) prior to becoming a white dwarf, stars expand to a large size (>1 au) and are easily deformed by orbiting planets, leading to tidal energy dissipation and orbital decay. They also lose half or more of their mass, causing the expansion of bodies' orbits. This mass loss increases the planet:star mass ratio, so planetary systems orbiting white dwarfs can be much less stable than those orbiting their main-sequence progenitors. Finally, small bodies in the system experience strong non-gravitational forces during the RGB and AGB: aerodynamic drag from the mass shed by the star, and strong radiation forces as the stellar luminosity reaches several thousand Solar luminosities.I will review these effects, focusing on planet--star tidal interactions and planet--asteroid interactions, and I will discuss some of the numerical challenges in modelling systems over their entire lifetimes of multiple Gyr.

Application of artificial intelligence to impulsive orbital transfers

NASA Technical Reports Server (NTRS)

Burns, Rowland E.

1987-01-01

A generalized technique for the numerical solution of any given class of problems is presented. The technique requires the analytic (or numerical) solution of every applicable equation for all variables that appear in the problem. Conditional blocks are employed to rapidly expand the set of known variables from a minimum of input. The method is illustrated via the use of the Hohmann transfer problem from orbital mechanics.

The absence of intraband scattering in a consistent theory of Gilbert damping in pure metallic ferromagnets.

PubMed

Edwards, D M

2016-03-02

Damping of magnetization dynamics in a ferromagnetic metal, arising from spin-orbit coupling, is usually characterised by the Gilbert parameter α. Recent calculations of this quantity, using a formula due to Kambersky, find that it is infinite for a perfect crystal owing to an intraband scattering term which is of third order in the spin-orbit parameter ξ. This surprising result conflicts with recent work by Costa and Muniz who study damping numerically by direct calculation of the dynamical transverse susceptibility in the presence of spin-orbit coupling. We resolve this inconsistency by following the approach of Costa and Muniz for a slightly simplified model where it is possible to calculate α analytically. We show that to second order in ξ one retrieves the Kambersky result for α, but to higher order one does not obtain any divergent intraband terms. The present work goes beyond that of Costa and Muniz by pointing out the necessity of including the effect of long-range Coulomb interaction in calculating damping for large ξ. A direct derivation of the Kambersky formula is given which shows clearly the restriction of its validity to second order in ξ so that no intraband scattering terms appear. This restriction has an important effect on the damping over a substantial range of impurity content and temperature. The experimental situation is discussed.

Orbital evolution of 95/P Chiron, 39P/Oterma, 29P/Shwassmann-Wachmann 1, and of 33 Centaurs

NASA Astrophysics Data System (ADS)

Kovalenko, N. S.; Churyumov, K. I.; Babenko, Yu. G.

2011-12-01

The paper is devoted to numerical modeling of orbital evolution of 34 Centaurs, and 2 distant Jupiter-family comets - 39P/Oterma and 29P/Shwassmann-Wachmann 1. As a result the evolutionary tracks of orbital elements of 33 Centaurs and 3 comets (95/P Chiron (2060), 39P/Oterma and 29P/Shwassmann-Wachmann 1) are obtained. The integrations were produced for 1 Myr back and forth in time starting at epoch and using the implicit single sequence Everhart methods. The statistical analysis of numerical integrations results was done, trends in changes of Centaurs' orbital elements in the past and in the future are revealed. The part of Centaurs that are potential comets is defined by the values of perihelia distributions for modeled orbits. It is shown that Centaurs may transits into orbits typical for Jupiter-family comets, and vice versa. Centaurs represent one of possible sources for replenishment of JFCs population, but other sources are also necessary.

Evaluation of Temperature Gradient in Advanced Automated Directional Solidification Furnace (AADSF) by Numerical Simulation

NASA Technical Reports Server (NTRS)

Bune, Andris V.; Gillies, Donald C.; Lehoczky, Sandor L.

1996-01-01

A numerical model of heat transfer using combined conduction, radiation and convection in AADSF was used to evaluate temperature gradients in the vicinity of the crystal/melt interface for variety of hot and cold zone set point temperatures specifically for the growth of mercury cadmium telluride (MCT). Reverse usage of hot and cold zones was simulated to aid the choice of proper orientation of crystal/melt interface regarding residual acceleration vector without actual change of furnace location on board the orbiter. It appears that an additional booster heater will be extremely helpful to ensure desired temperature gradient when hot and cold zones are reversed. Further efforts are required to investigate advantages/disadvantages of symmetrical furnace design (i.e. with similar length of hot and cold zones).

Recent advances in analytical satellite theory

NASA Technical Reports Server (NTRS)

Gaposchkin, E. M.

1978-01-01

Recent work on analytical satellite perturbation theory has involved the completion of a revision to 4th order for zonal harmonics, the addition of a treatment for ocean tides, an extension of the treatment for the noninertial reference system, and the completion of a theory for direct solar-radiation pressure and earth-albedo pressure. Combined with a theory for tesseral-harmonics, lunisolar, and body-tide perturbations, these formulations provide a comprehensive orbit-computation program. Detailed comparisons with numerical integration and observations are presented to assess the accuracy of each theoretical development.

Fine-Branched Ridges

NASA Image and Video Library

2015-10-14

This image from NASA Mars Reconnaissance Orbiter spacecraft shows numerous branching ridges with various degrees of sinuosity. These branching forms resemble tributaries funneling and draining into larger channel trunks towards the upper portion of the scene. The raised relief of these branching ridges suggests that these are ancient channels are inverted due to lithification and cementation of the riverbed sediment, which made it more resistant to erosion than the surrounding material. Wind-blown bedforms are abundant and resemble small ridges that are aligned in an approximately north-south direction. http://photojournal.jpl.nasa.gov/catalog/PIA20006

Bifurcation Analysis and Chaos Control in a Modified Finance System with Delayed Feedback

NASA Astrophysics Data System (ADS)

Yang, Jihua; Zhang, Erli; Liu, Mei

2016-06-01

We investigate the effect of delayed feedback on the finance system, which describes the time variation of the interest rate, for establishing the fiscal policy. By local stability analysis, we theoretically prove the existences of Hopf bifurcation and Hopf-zero bifurcation. By using the normal form method and center manifold theory, we determine the stability and direction of a bifurcating periodic solution. Finally, we give some numerical solutions, which indicate that when the delay passes through certain critical values, chaotic oscillation is converted into a stable equilibrium or periodic orbit.

Modeling Multi-wavelength Stellar Astrometry. III. Determination of the Absolute Masses of Exoplanets and Their Host Stars

NASA Astrophysics Data System (ADS)

Coughlin, J. L.; López-Morales, Mercedes

2012-05-01

Astrometric measurements of stellar systems are becoming significantly more precise and common, with many ground- and space-based instruments and missions approaching 1 μas precision. We examine the multi-wavelength astrometric orbits of exoplanetary systems via both analytical formulae and numerical modeling. Exoplanets have a combination of reflected and thermally emitted light that causes the photocenter of the system to shift increasingly farther away from the host star with increasing wavelength. We find that, if observed at long enough wavelengths, the planet can dominate the astrometric motion of the system, and thus it is possible to directly measure the orbits of both the planet and star, and thus directly determine the physical masses of the star and planet, using multi-wavelength astrometry. In general, this technique works best for, though is certainly not limited to, systems that have large, high-mass stars and large, low-mass planets, which is a unique parameter space not covered by other exoplanet characterization techniques. Exoplanets that happen to transit their host star present unique cases where the physical radii of the planet and star can be directly determined via astrometry alone. Planetary albedos and day-night contrast ratios may also be probed via this technique due to the unique signature they impart on the observed astrometric orbits. We develop a tool to examine the prospects for near-term detection of this effect, and give examples of some exoplanets that appear to be good targets for detection in the K to N infrared observing bands, if the required precision can be achieved.

Rotation of a spheroid in a Couette flow at moderate Reynolds numbers.

PubMed

Yu, Zhaosheng; Phan-Thien, Nhan; Tanner, Roger I

2007-08-01

The rotation of a single spheroid in a planar Couette flow as a model for simple shear flow is numerically simulated with the distributed Lagrangian multiplier based fictitious domain method. The study is focused on the effects of inertia on the orbital behavior of prolate and oblate spheroids. The numerical orbits are found to be well described by a simple empirical model, which states that the rate of the spheroid rotation about the vorticity axis is a sinusoidal function of the corresponding projection angle in the flow-gradient plane, and that the exponential growth rate of the orbit function is a constant. The following transitions in the steady state with increasing Reynolds number are identified: Jeffery orbit, tumbling, quasi-Jeffery orbit, log rolling, and inclined rolling for a prolate spheroid; and Jeffery orbit, log rolling, inclined rolling, and motionless state for an oblate spheroid. In addition, it is shown that the orbit behavior is sensitive to the initial orientation in the case of strong inertia and there exist different steady states for certain shear Reynolds number regimes.

High-order moments of spin-orbit energy in a multielectron configuration

NASA Astrophysics Data System (ADS)

Na, Xieyu; Poirier, M.

2016-07-01

In order to analyze the energy-level distribution in complex ions such as those found in warm dense plasmas, this paper provides values for high-order moments of the spin-orbit energy in a multielectron configuration. Using second-quantization results and standard angular algebra or fully analytical expressions, explicit values are given for moments up to 10th order for the spin-orbit energy. Two analytical methods are proposed, using the uncoupled or coupled orbital and spin angular momenta. The case of multiple open subshells is considered with the help of cumulants. The proposed expressions for spin-orbit energy moments are compared to numerical computations from Cowan's code and agree with them. The convergence of the Gram-Charlier expansion involving these spin-orbit moments is analyzed. While a spectrum with infinitely thin components cannot be adequately represented by such an expansion, a suitable convolution procedure ensures the convergence of the Gram-Charlier series provided high-order terms are accounted for. A corrected analytical formula for the third-order moment involving both spin-orbit and electron-electron interactions turns out to be in fair agreement with Cowan's numerical computations.

Detection of symmetric homoclinic orbits to saddle-centres in reversible systems

NASA Astrophysics Data System (ADS)

Yagasaki, Kazuyuki; Wagenknecht, Thomas

2006-02-01

We present a perturbation technique for the detection of symmetric homoclinic orbits to saddle-centre equilibria in reversible systems of ordinary differential equations. We assume that the unperturbed system has primary, symmetric homoclinic orbits, which may be either isolated or appear in a family, and use an idea similar to that of Melnikov’s method to detect homoclinic orbits in their neighbourhood. This technique also allows us to identify bifurcations of unperturbed or perturbed, symmetric homoclinic orbits. Our technique is of importance in applications such as nonlinear optics and water waves since homoclinic orbits to saddle-centre equilibria describe embedded solitons (ESs) in systems of partial differential equations representing physical models, and except for special cases their existence has been previously studied only numerically using shooting methods and continuation techniques. We apply the general theory to two examples, a four-dimensional system describing ESs in nonlinear optical media and a six-dimensional system which can possess a one-parameter family of symmetric homoclinic orbits in the unperturbed case. For these examples, the analysis is compared with numerical computations and an excellent agreement between both results is found.

Three-axis attitude control by two-step rotations using only magnetic torquers in a low Earth orbit near the magnetic equator

NASA Astrophysics Data System (ADS)

Inamori, Takaya; Otsuki, Kensuke; Sugawara, Yoshiki; Saisutjarit, Phongsatorn; Nakasuka, Shinichi

2016-11-01

This study proposes a novel method for three-axis attitude control using only magnetic torquers (MTQs). Previously, MTQs have been utilized for attitude control in many low Earth orbit satellites. Although MTQs are useful for achieving attitude control at low cost and high reliability without the need for propellant, these electromagnetic coils cannot be used to generate an attitude control torque about the geomagnetic field vector. Thus, conventional attitude control methods using MTQs assume the magnetic field changes in an orbital period so that the satellite can generate a required attitude control torque after waiting for a change in the magnetic field direction. However, in a near magnetic equatorial orbit, the magnetic field does not change in an inertial reference frame. Thus, satellites cannot generate a required attitude control torque in a single orbital period with only MTQs. This study proposes a method for achieving a rotation about the geomagnetic field vector by generating a torque that is perpendicular to it. First, this study shows that the three-axis attitude control using only MTQs is feasible with a two-step rotation. Then, the study proposes a method for controlling the attitude with the two-step rotation using a PD controller. Finally, the proposed method is assessed by examining the results of numerical simulations.

Numerical simulations of particle orbits around 2060 Chiron

NASA Technical Reports Server (NTRS)

Stern, S. A.; Jackson, A. A.; Boice, D. C.

1994-01-01

Scattered light from orbiting or coorbiting dust is a primary signature by which Earth-based observers study the activity and atmosphere of the unusual outer solar system object 2060 Chiron. Therefore, it is important to understand the lifetime, dynamics, and loss rates of dust in its coma. We report here dynamical simulations of particles in Chiron's collisionless coma. The orbits of 17,920 dust particles were numerically integrated under the gravitational influence of Chiron, the Sun, and solar radiation pressure. These simulations show that particles ejected from Chiron are more likely to follow suborbital trajectories, or to escape altogether, than to enter quasistable orbits. Significant orbital lifetimes can only be achieved for very specific launch conditions. These results call into question models of a long-term, bound coma generated by discrete outbursts, and instead suggest that Chiron's coma state is closely coupled to the nearly instantaneous level of Chiron's surface activity.

Efficient Trajectory Propagation for Orbit Determination Problems

NASA Technical Reports Server (NTRS)

Roa, Javier; Pelaez, Jesus

2015-01-01

Regularized formulations of orbital motion apply a series of techniques to improve the numerical integration of the orbit. Despite their advantages and potential applications little attention has been paid to the propagation of the partial derivatives of the corresponding set of elements or coordinates, required in many orbit-determination scenarios and optimization problems. This paper fills this gap by presenting the general procedure for integrating the state-transition matrix of the system together with the nominal trajectory using regularized formulations and different sets of elements. The main difficulty comes from introducing an independent variable different from time, because the solution needs to be synchronized. The correction of the time delay is treated from a generic perspective not focused on any particular formulation. The synchronization using time-elements is also discussed. Numerical examples include strongly-perturbed orbits in the Pluto system, motivated by the recent flyby of the New Horizons spacecraft, together with a geocentric flyby of the NEAR spacecraft.

Linear-scaling method for calculating nuclear magnetic resonance chemical shifts using gauge-including atomic orbitals within Hartree-Fock and density-functional theory.

PubMed

Kussmann, Jörg; Ochsenfeld, Christian

2007-08-07

Details of a new density matrix-based formulation for calculating nuclear magnetic resonance chemical shifts at both Hartree-Fock and density functional theory levels are presented. For systems with a nonvanishing highest occupied molecular orbital-lowest unoccupied molecular orbital gap, the method allows us to reduce the asymptotic scaling order of the computational effort from cubic to linear, so that molecular systems with 1000 and more atoms can be tackled with today's computers. The key feature is a reformulation of the coupled-perturbed self-consistent field (CPSCF) theory in terms of the one-particle density matrix (D-CPSCF), which avoids entirely the use of canonical MOs. By means of a direct solution for the required perturbed density matrices and the adaptation of linear-scaling integral contraction schemes, the overall scaling of the computational effort is reduced to linear. A particular focus of our formulation is to ensure numerical stability when sparse-algebra routines are used to obtain an overall linear-scaling behavior.

A numerical comparison of discrete Kalman filtering algorithms: An orbit determination case study

NASA Technical Reports Server (NTRS)

Thornton, C. L.; Bierman, G. J.

1976-01-01

The numerical stability and accuracy of various Kalman filter algorithms are thoroughly studied. Numerical results and conclusions are based on a realistic planetary approach orbit determination study. The case study results of this report highlight the numerical instability of the conventional and stabilized Kalman algorithms. Numerical errors associated with these algorithms can be so large as to obscure important mismodeling effects and thus give misleading estimates of filter accuracy. The positive result of this study is that the Bierman-Thornton U-D covariance factorization algorithm is computationally efficient, with CPU costs that differ negligibly from the conventional Kalman costs. In addition, accuracy of the U-D filter using single-precision arithmetic consistently matches the double-precision reference results. Numerical stability of the U-D filter is further demonstrated by its insensitivity of variations in the a priori statistics.

Trajectory Optimization for Spacecraft Collision Avoidance

DTIC Science & Technology

2013-09-01

Modified Set of Equinoctial Orbit Elements . AAS/AIAA 91-524," in Astrodynamics Specialist Conference, Durango, CO, 1991. [18] D. E. Kirk...these singularities, the COE are not necessarily the best set of states for numerical analysis. 2.3.3 Equinoctial Orbital Elements A third method of...completely defining an orbit is by the use of the Equinoctial Orbital Elements . This element set maintains the

Improving multi-GNSS ultra-rapid orbit determination for real-time precise point positioning

NASA Astrophysics Data System (ADS)

Li, Xingxing; Chen, Xinghan; Ge, Maorong; Schuh, Harald

2018-03-01

Currently, with the rapid development of multi-constellation Global Navigation Satellite Systems (GNSS), the real-time positioning and navigation are undergoing dramatic changes with potential for a better performance. To provide more precise and reliable ultra-rapid orbits is critical for multi-GNSS real-time positioning, especially for the three merging constellations Beidou, Galileo and QZSS which are still under construction. In this contribution, we present a five-system precise orbit determination (POD) strategy to fully exploit the GPS + GLONASS + BDS + Galileo + QZSS observations from CDDIS + IGN + BKG archives for the realization of hourly five-constellation ultra-rapid orbit update. After adopting the optimized 2-day POD solution (updated every hour), the predicted orbit accuracy can be obviously improved for all the five satellite systems in comparison to the conventional 1-day POD solution (updated every 3 h). The orbit accuracy for the BDS IGSO satellites can be improved by about 80, 45 and 50% in the radial, cross and along directions, respectively, while the corresponding accuracy improvement for the BDS MEO satellites reaches about 50, 20 and 50% in the three directions, respectively. Furthermore, the multi-GNSS real-time precise point positioning (PPP) ambiguity resolution has been performed by using the improved precise satellite orbits. Numerous results indicate that combined GPS + BDS + GLONASS + Galileo (GCRE) kinematic PPP ambiguity resolution (AR) solutions can achieve the shortest time to first fix (TTFF) and highest positioning accuracy in all coordinate components. With the addition of the BDS, GLONASS and Galileo observations to the GPS-only processing, the GCRE PPP AR solution achieves the shortest average TTFF of 11 min with 7{°} cutoff elevation, while the TTFF of GPS-only, GR, GE and GC PPP AR solution is 28, 15, 20 and 17 min, respectively. As the cutoff elevation increases, the reliability and accuracy of GPS-only PPP AR solutions decrease dramatically, but there is no evident decrease for the accuracy of GCRE fixed solutions which can still achieve an accuracy of a few centimeters in the east and north components.

Numerical proof for chemostat chaos of Shilnikov's type.

PubMed

Deng, Bo; Han, Maoan; Hsu, Sze-Bi

2017-03-01

A classical chemostat model is considered that models the cycling of one essential abiotic element or nutrient through a food chain of three trophic levels. The long-time behavior of the model was known to exhibit complex dynamics more than 20 years ago. It is still an open problem to prove the existence of chaos analytically. In this paper, we aim to solve the problem numerically. In our approach, we introduce an artificial singular parameter to the model and construct singular homoclinic orbits of the saddle-focus type which is known for chaos generation. From the configuration of the nullclines of the equations that generates the singular homoclinic orbits, a shooting algorithm is devised to find such Shilnikov saddle-focus homoclinic orbits numerically which in turn imply the existence of chaotic dynamics for the original chemostat model.

Advances in Black-Hole Mergers: Spins and Unequal Masses

NASA Technical Reports Server (NTRS)

Kelly, Bernard

2007-01-01

The last two years have seen incredible development in numerical relativity: from fractions of an orbit, evolutions of an equal-mass binary have reached multiple orbits, and convergent gravitational waveforms have been produced from several research groups and numerical codes. We are now able to move our attention from pure numerics to astrophysics, and address scenarios relevant to current and future gravitational-wave detectors.Over the last 12 months at NASA Goddard, we have extended the accuracy of our Hahn-Dol code, and used it to move toward these goals. We have achieved high-accuracy simulations of black-hole binaries of low initial eccentricity, with enough orbits of inspiral before merger to allow us to produce hybrid waveforms that reflect accurately the entire lifetime of the BH binary. We are extending this work, looking at the effects of unequal masses and spins.

Regularization in Orbital Mechanics; Theory and Practice

NASA Astrophysics Data System (ADS)

Roa, Javier

2017-09-01

Regularized equations of motion can improve numerical integration for the propagation of orbits, and simplify the treatment of mission design problems. This monograph discusses standard techniques and recent research in the area. While each scheme is derived analytically, its accuracy is investigated numerically. Algebraic and topological aspects of the formulations are studied, as well as their application to practical scenarios such as spacecraft relative motion and new low-thrust trajectories.

On the Unreasonable Effectiveness of post-Newtonian Theory in Gravitational-Wave Physics

ScienceCinema

Will, Clifford M.

2017-12-22

The first indirect detection of gravitational waves involved a binary system of neutron stars.  In the future, the first direct detection may also involve binary systems -- inspiralling and merging binary neutron stars or black holes. This means that it is essential to understand in full detail the two-body system in general relativity, a notoriously difficult problem with a long history. Post-Newtonian approximation methods are thought to work only under slow motion and weak field conditions, while numerical solutions of Einstein's equations are thought to be limited to the final merger phase.  Recent results have shown that post-Newtonian approximations seem to remain unreasonably valid well into the relativistic regime, while advances in numerical relativity now permit solutions for numerous orbits before merger.  It is now possible to envision linking post-Newtonian theory and numerical relativity to obtain a complete "solution" of the general relativistic two-body problem.  These solutions will play a central role in detecting and understanding gravitational wave signals received by interferometric observatories on Earth and in space.

Scalar self-force for highly eccentric equatorial orbits in Kerr spacetime

NASA Astrophysics Data System (ADS)

Thornburg, Jonathan; Wardell, Barry

2017-04-01

If a small "particle" of mass μ M (with μ ≪1 ) orbits a black hole of mass M , the leading-order radiation-reaction effect is an O (μ2) "self-force" acting on the particle, with a corresponding O (μ ) "self-acceleration" of the particle away from a geodesic. Such "extreme-mass-ratio inspiral" systems are likely to be important gravitational-wave sources for future space-based gravitational-wave detectors. Here we consider the "toy model" problem of computing the self-force for a scalar-field particle on a bound eccentric orbit in Kerr spacetime. We use the Barack-Golbourn-Vega-Detweiler effective-source regularization with a 4th-order puncture field, followed by an ei m ϕ ("m -mode") Fourier decomposition and a separate time-domain numerical evolution in 2 +1 dimensions for each m . We introduce a finite worldtube that surrounds the particle worldline and define our evolution equations in a piecewise manner so that the effective source is only used within the worldtube. Viewed as a spatial region, the worldtube moves to follow the particle's orbital motion. We use slices of constant Boyer-Lindquist time in the region of the particle's motion, deformed to be asymptotically hyperboloidal and compactified near the horizon and J+ . Our numerical evolution uses Berger-Oliger mesh refinement with 4th-order finite differencing in space and time. Our computational scheme allows computation for highly eccentric orbits and should be generalizable to orbital evolution in the future. Our present implementation is restricted to equatorial geodesic orbits, but this restriction is not fundamental. We present numerical results for a number of test cases with orbital eccentricities as high as 0.98. In some cases we find large oscillations ("wiggles") in the self-force on the outgoing leg of the orbit shortly after periastron passage; these appear to be caused by the passage of the orbit through the strong-field region close to the background Kerr black hole.

Streamwise-Localized Solutions with natural 1-fold symmetry

NASA Astrophysics Data System (ADS)

Altmeyer, Sebastian; Willis, Ashley; Hof, Björn

2014-11-01

It has been proposed in recent years that turbulence is organized around unstable invariant solutions, which provide the building blocks of the chaotic dynamics. In direct numerical simulations of pipe flow we show that when imposing a minimal symmetry constraint (reflection in an axial plane only) the formation of turbulence can indeed be explained by dynamical systems concepts. The hypersurface separating laminar from turbulent motion, the edge of turbulence, is spanned by the stable manifolds of an exact invariant solution, a periodic orbit of a spatially localized structure. The turbulent states themselves (turbulent puffs in this case) are shown to arise in a bifurcation sequence from a related localized solution (the upper branch orbit). The rather complex bifurcation sequence involves secondary Hopf bifurcations, frequency locking and a period doubling cascade until eventually turbulent puffs arise. In addition we report preliminary results of the transition sequence for pipe flow without symmetry constraints.

Retarding potential analyzer for the Pioneer-Venus Orbiter Mission

NASA Technical Reports Server (NTRS)

Knudsen, W. C.; Bakke, J.; Spenner, K.; Novak, V.

1979-01-01

The retarding potential analyzer on the Pioneer-Venus Orbiter Mission has been designed to measure most of the thermal plasma parameters within and near the Venusian ionosphere. Parameters include total ion concentration, concentrations of the more abundant ions, ion temperatures, ion drift velocity, electron temperature, and low-energy (0-50 eV) electron distribution function. To accomplish these measurements on a spinning vehicle with a small telemetry bit rate, several functions, including decision functions not previously used in RPA's, have been developed and incorporated into this instrument. The more significant functions include automatic electrometer ranging with background current compensation; digital, quadratic retarding potential step generation for the ion and low-energy electron scans; a current sampling interval of 2 ms throughout all scans; digital logic inflection point detection and data selection; and automatic ram direction detection. Extensive numerical simulation and plasma chamber tests have been conducted to verify adequacy of the design for the Pioneer Mission.

Neoclassical orbit calculations with a full-f code for tokamak edge plasmas

NASA Astrophysics Data System (ADS)

Rognlien, T. D.; Cohen, R. H.; Dorr, M.; Hittinger, J.; Xu, X. Q.; Collela, P.; Martin, D.

2008-11-01

Ion distribution function modifications are considered for the case of neoclassical orbit widths comparable to plasma radial-gradient scale-lengths. Implementation of proper boundary conditions at divertor plates in the continuum TEMPEST code, including the effect of drifts in determining the direction of total flow, enables such calculations in single-null divertor geometry, with and without an electrostatic potential. The resultant poloidal asymmetries in densities, temperatures, and flows are discussed. For long-time simulations, a slow numerical instability develops, even in simplified (circular) geometry with no endloss, which aids identification of the mixed treatment of parallel and radial convection terms as the cause. The new Edge Simulation Laboratory code, expected to be operational, has algorithmic refinements that should address the instability. We will present any available results from the new code on this problem as well as geodesic acoustic mode tests.

Magnus-induced ratchet effects for skyrmions interacting with asymmetric substrates

NASA Astrophysics Data System (ADS)

Reichhardt, C.; Ray, D.; Olson Reichhardt, C. J.

2015-07-01

We show using numerical simulations that pronounced ratchet effects can occur for ac driven skyrmions moving over asymmetric quasi-one-dimensional substrates. We find a new type of ratchet effect called a Magnus-induced transverse ratchet that arises when the ac driving force is applied perpendicular rather than parallel to the asymmetry direction of the substrate. This transverse ratchet effect only occurs when the Magnus term is finite, and the threshold ac amplitude needed to induce it decreases as the Magnus term becomes more prominent. Ratcheting skyrmions follow ordered orbits in which the net displacement parallel to the substrate asymmetry direction is quantized. Skyrmion ratchets represent a new ac current-based method for controlling skyrmion positions and motion for spintronic applications.

Commensurability resonances in two-dimensional magnetoelectric lateral superlattices

NASA Astrophysics Data System (ADS)

Schluck, J.; Fasbender, S.; Heinzel, T.; Pierz, K.; Schumacher, H. W.; Kazazis, D.; Gennser, U.

2015-05-01

Hybrid lateral superlattices composed of a square array of antidots and a periodic one-dimensional magnetic modulation are prepared in Ga [Al ]As heterostructures. The two-dimensional electron gases exposed to these superlattices are characterized by magnetotransport experiments in vanishing average perpendicular magnetic fields. Despite the absence of closed orbits, the diagonal magnetoresistivity in the direction perpendicular to the magnetic modulation shows pronounced classical resonances. They are located at magnetic fields where snake trajectories exist which are quasicommensurate with the antidot lattice. The diagonal magnetoresistivity in the direction of the magnetic modulation increases sharply above a threshold magnetic field and shows no fine structure. The experimental results are interpreted with the help of numerical simulations based on the semiclassical Kubo model.

Self-Consistent Chaotic Transport in a High-Dimensional Mean-Field Hamiltonian Map Model

DOE PAGES

Martínez-del-Río, D.; del-Castillo-Negrete, D.; Olvera, A.; ...

2015-10-30

We studied the self-consistent chaotic transport in a Hamiltonian mean-field model. This model provides a simplified description of transport in marginally stable systems including vorticity mixing in strong shear flows and electron dynamics in plasmas. Self-consistency is incorporated through a mean-field that couples all the degrees-of-freedom. The model is formulated as a large set of N coupled standard-like area-preserving twist maps in which the amplitude and phase of the perturbation, rather than being constant like in the standard map, are dynamical variables. Of particular interest is the study of the impact of periodic orbits on the chaotic transport and coherentmore » structures. Furthermore, numerical simulations show that self-consistency leads to the formation of a coherent macro-particle trapped around the elliptic fixed point of the system that appears together with an asymptotic periodic behavior of the mean field. To model this asymptotic state, we introduced a non-autonomous map that allows a detailed study of the onset of global transport. A turnstile-type transport mechanism that allows transport across instantaneous KAM invariant circles in non-autonomous systems is discussed. As a first step to understand transport, we study a special type of orbits referred to as sequential periodic orbits. Using symmetry properties we show that, through replication, high-dimensional sequential periodic orbits can be generated starting from low-dimensional periodic orbits. We show that sequential periodic orbits in the self-consistent map can be continued from trivial (uncoupled) periodic orbits of standard-like maps using numerical and asymptotic methods. Normal forms are used to describe these orbits and to find the values of the map parameters that guarantee their existence. Numerical simulations are used to verify the prediction from the asymptotic methods.« less

Signatures Of A Putative Planetary Mass Solar Companion On The Orbital Distribution Of Tno's And Centaurs

NASA Astrophysics Data System (ADS)

Gomes, Rodney S.; Soares, J. S.

2012-05-01

Gomes et al. 2006 (Icarus 184, 589) show that a planetary mass solar companion (PMSC) can produce orbits in an inner Oort cloud that can account for Sedna's orbit. On the other hand, one should expect that this faraway planet would also produce some peculiar orbital distribution for distant TNO's and Centaurs. A pair of interesting orbits in this respect are those of 2006 SQ372 and 2000 OO67. These objects have very large semimajor axes and perihelion between Uranus and Neptune orbits. It has been claimed that a likely source for 2006 SQ372 is the Oort cloud. Yet a PMSC has an important effect on objects at inner Oort cloud distances, say between 300 AU and 2000 AU, to make their perihelion distances to continually oscillate with a large enough amplitude to account for objects both inside and outside Neptune's orbit. This naturally produces an extra amount of TNO's with semimajor axes between 300 and 2000 AU and perihelion inside Neptune's orbit, like 2006 SQ372 and 2000 OO67. This signature should be found in present observations. To deal with this problem we construct a numerical simulator and apply it to populations of distant TNO's produced by numerical integration of planetesimals and planets according to the Nice model, either including or not a PMSC. With the results from the numerical simulator we compare the model with and without the PMSC with observations. We conclude that a PMSC is compatible with the existence of 2006 SQ372 and 2000 OO67 and, in fact, although not conclusively, we can also claim that the observations of 2006 SQ372 and 2000 OO67, compared to all other scattered objects, would be lucky events if no PMSC exists.

Self-Consistent Chaotic Transport in a High-Dimensional Mean-Field Hamiltonian Map Model

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

Martínez-del-Río, D.; del-Castillo-Negrete, D.; Olvera, A.

We studied the self-consistent chaotic transport in a Hamiltonian mean-field model. This model provides a simplified description of transport in marginally stable systems including vorticity mixing in strong shear flows and electron dynamics in plasmas. Self-consistency is incorporated through a mean-field that couples all the degrees-of-freedom. The model is formulated as a large set of N coupled standard-like area-preserving twist maps in which the amplitude and phase of the perturbation, rather than being constant like in the standard map, are dynamical variables. Of particular interest is the study of the impact of periodic orbits on the chaotic transport and coherentmore » structures. Furthermore, numerical simulations show that self-consistency leads to the formation of a coherent macro-particle trapped around the elliptic fixed point of the system that appears together with an asymptotic periodic behavior of the mean field. To model this asymptotic state, we introduced a non-autonomous map that allows a detailed study of the onset of global transport. A turnstile-type transport mechanism that allows transport across instantaneous KAM invariant circles in non-autonomous systems is discussed. As a first step to understand transport, we study a special type of orbits referred to as sequential periodic orbits. Using symmetry properties we show that, through replication, high-dimensional sequential periodic orbits can be generated starting from low-dimensional periodic orbits. We show that sequential periodic orbits in the self-consistent map can be continued from trivial (uncoupled) periodic orbits of standard-like maps using numerical and asymptotic methods. Normal forms are used to describe these orbits and to find the values of the map parameters that guarantee their existence. Numerical simulations are used to verify the prediction from the asymptotic methods.« less

On M31's Double Nucleus

NASA Technical Reports Server (NTRS)

Miller, R. H.; Smith, B. F.; Cuzzi, Jeffrey (Technical Monitor)

1995-01-01

The recent HST discovery of a double nucleus in M31 brings into prominence the question how long, a second core can survive within the nuclear regions of a galaxy. Physical conditions in the nuclear regions of a typical galaxy help a second core survive, so it can orbit for a long time. possibly for thousands of orbits. Given the nearly uniform mass density in a core, tidal forces within a core radius are compressive in all directions and help the core survive the buffeting it takes as it orbits near the center of the galaxy. We use numerical experiments to illustrate these physical principles. Our method allows the full power of the experiments to be concentrated on the nuclear regions. Spatial resolution of about 0.2 pc comfortably resolves detail within the 1.4 parsec core radius of the second, but brighter core (P1) in M31. We use these physical principles to discuss M31's double nucleus, but they apply to other galaxies as well. and in other astronomical situations such as dumbbell galaxies. galaxies orbiting near the center of a galaxy cluster, and subclustering in galaxy clusters. The experiments also illustrate that galaxy encounters and merging are quite sensitive to external tidal forces, such as those produced by the gravitational potential in a group or cluster of galaxies.

Multiple Core Galaxies: Implications for M31

NASA Technical Reports Server (NTRS)

Smith, B. F.; Miller, R. H.; Cuzzi, Jeffrey N. (Technical Monitor)

1994-01-01

It is generally perceived that two cores cannot survive very long within the nuclear regions of a galaxy. The recent HST discovery of a double nucleus in M31 brings this question into prominence. Physical conditions in the nuclear regions of a typical galaxy help a second core survive so it can orbit for a long time, possibly for thousands of orbits. Given the nearly uniform mass density in a core, tidal forces within a core radius are compressive in all directions and help the core survive the buffeting it takes as it orbits near the center of the galaxy. We use numerical experiments to illustrate these physical principles. Modifications to the experimental method allow the full power of the experiments to be concentrated on the nuclear regions. Spatial resolution of about 0.2 parsec comfortably resolves detail within the 1.4 parsec core radius of the second, but brighter, core (P1) in M31. The same physical principles apply in other astronomical situations, such as dumbbell galaxies, galaxies orbiting near the center of a galaxy cluster, and subclustering in galaxy clusters. The experiments also illustrate that galaxy encounters and merging are quite sensitive to external tidal forces, such as those produced by the gravitational potential in a group or cluster of galaxies.

Massive black hole and gas dynamics in galaxy nuclei mergers - I. Numerical implementation

NASA Astrophysics Data System (ADS)

Lupi, Alessandro; Haardt, Francesco; Dotti, Massimo

2015-01-01

Numerical effects are known to plague adaptive mesh refinement (AMR) codes when treating massive particles, e.g. representing massive black holes (MBHs). In an evolving background, they can experience strong, spurious perturbations and then follow unphysical orbits. We study by means of numerical simulations the dynamical evolution of a pair MBHs in the rapidly and violently evolving gaseous and stellar background that follows a galaxy major merger. We confirm that spurious numerical effects alter the MBH orbits in AMR simulations, and show that numerical issues are ultimately due to a drop in the spatial resolution during the simulation, drastically reducing the accuracy in the gravitational force computation. We therefore propose a new refinement criterion suited for massive particles, able to solve in a fast and precise way for their orbits in highly dynamical backgrounds. The new refinement criterion we designed enforces the region around each massive particle to remain at the maximum resolution allowed, independently upon the local gas density. Such maximally resolved regions then follow the MBHs along their orbits, and effectively avoids all spurious effects caused by resolution changes. Our suite of high-resolution, AMR hydrodynamic simulations, including different prescriptions for the sub-grid gas physics, shows that the new refinement implementation has the advantage of not altering the physical evolution of the MBHs, accounting for all the non-trivial physical processes taking place in violent dynamical scenarios, such as the final stages of a galaxy major merger.

Long-Term Evolution of Orbits About a Precessing Oblate Planet: 3. A Semianalytical and a Purely Numerical Approach

DTIC Science & Technology

2007-11-01

Keywords Orbital elements · Osculating elements · Mars · Natural satellites · Natural satellites’ orbits · Deimos · Equinoctial precession · The...theory of orbits about a precessing and nutating oblate planet, in terms of osculating elements defined in a frame associated with the equator of...solar-gravity-perturbed satellite orbiting an oblate planet subject to nonuniform equinoctial precession. This nonuniformity of precession is caused by

Numerical simulation of time delay Interferometry for LISA with one arm dysfunctional

NASA Astrophysics Data System (ADS)

Ni, Wei-Tou; Dhurandhar, Sanjeev V.; Nayak, K. Rajesh; Wang, Gang

In order to attain the requisite sensitivity for LISA, laser frequency noise must be suppressed below the secondary noises such as the optical path noise, acceleration noise etc. In a previous paper(a), we have found an infinite family of second generation analytic solutions of time delay interferometry and estimated the laser noise due to residual time delay semi-analytically from orbit perturbations due to earth. Since other planets and solar-system bodies also perturb the orbits of LISA spacecraft and affect the time delay interferometry, we simulate the time delay numerically in this paper. To conform to the actual LISA planning, we have worked out a set of 10-year optimized mission orbits of LISA spacecraft using CGC3 ephemeris framework(b). Here we use this numerical solution to calculate the residual errors in the second generation solutions upto n 3 of our previous paper, and compare with the semi-analytic error estimate. The accuracy of this calculation is better than 1 m (or 30 ns). (a) S. V. Dhurandhar, K. Rajesh Nayak and J.-Y. Vinet, time delay Interferometry for LISA with one arm dysfunctional (b) W.-T. Ni and G. Wang, Orbit optimization for 10-year LISA mission orbit starting at 21 June, 2021 using CGC3 ephemeris framework

Analytical formulation of lunar cratering asymmetries

NASA Astrophysics Data System (ADS)

Wang, Nan; Zhou, Ji-Lin

2016-10-01

Context. The cratering asymmetry of a bombarded satellite is related to both its orbit and impactors. The inner solar system impactor populations, that is, the main-belt asteroids (MBAs) and the near-Earth objects (NEOs), have dominated during the late heavy bombardment (LHB) and ever since, respectively. Aims: We formulate the lunar cratering distribution and verify the cratering asymmetries generated by the MBAs as well as the NEOs. Methods: Based on a planar model that excludes the terrestrial and lunar gravitations on the impactors and assuming the impactor encounter speed with Earth venc is higher than the lunar orbital speed vM, we rigorously integrated the lunar cratering distribution, and derived its approximation to the first order of vM/venc. Numerical simulations of lunar bombardment by the MBAs during the LHB were performed with an Earth-Moon distance aM = 20-60 Earth radii in five cases. Results: The analytical model directly proves the existence of a leading/trailing asymmetry and the absence of near/far asymmetry. The approximate form of the leading/trailing asymmetry is (1 + A1cosβ), which decreases as the apex distance β increases. The numerical simulations show evidence of a pole/equator asymmetry as well as the leading/trailing asymmetry, and the former is empirically described as (1 + A2cos2ϕ), which decreases as the latitude modulus | ϕ | increases. The amplitudes A1,2 are reliable measurements of asymmetries. Our analysis explicitly indicates the quantitative relations between cratering distribution and bombardment conditions (impactor properties and the lunar orbital status) like A1 ∝ vM/venc, resulting in a method for reproducing the bombardment conditions through measuring the asymmetry. Mutual confirmation between analytical model and numerical simulations is found in terms of the cratering distribution and its variation with aM. Estimates of A1 for crater density distributions generated by the MBAs and the NEOs are 0.101-0.159 and 0.117, respectively.

The gas drag in a circular binary system

NASA Astrophysics Data System (ADS)

Ciecielä G, P.; Ida, S.; Gawryszczak, A.; Burkert, A.

2007-07-01

We investigate the motion of massless particles orbiting the primary star in a close circular binary system with particular focus on the gas drag effects. These are the first calculations with particles ranging in size from 1 m to 10 km, which account for the presence of a tidally perturbed gaseous disk. We have found numerically that the radial mass transport by the tidal waves plays a crucial role in the orbital evolution of particles. In the outer region of the gaseous disk, where its perturbation is strongest, the migration rate of a particle for all considered sizes is enhanced by a factor of 3 with respect to the axisymmetric disk in radial equilibrium. Similar enhancement is observed in the damping rate of inclinations. We present a simple analytical argument proving that the migration rate of a particle in such a disk is enhanced due to the enhanced mass flux of gas colliding with the particle. Thus the enhancement factor does not depend on the sign of the radial gas velocity, and the migration is always directed inward. Within the framework of the perturbation theory, we derive more general, approximate formulae for short-term variations of the particle semi-major axis, eccentricity, and inclination in a disk out of radial equilibrium. The basic version of the formulae applies to the axisymmetric disk, but we present how to account for departures from axial symmetry by introducing effective components of the gas velocity. Comparison with numerical results proves that our formulae are correct within several percent. We have also found in numerical simulations that the tidal waves introduce coherence in periastron longitude and eccentricity for particles on neighboring orbits. The degree of the coherence depends on the particle size and on the distance from the primary star, being most prominent for particles with 10 m radius. The results are important mainly in the context of planetesimal formation and, to a lesser degree, during the early planetesimal accretion stage.

Comparison between numerical-relativity and post-Newtonian waveforms from spinning binaries: The orbital hang-up case

NASA Astrophysics Data System (ADS)

Hannam, Mark; Husa, Sascha; Brügmann, Bernd; Gopakumar, Achamveedu

2008-11-01

We compare results from numerical simulations of spinning binaries in the “orbital hang-up” case, where the binary completes at least nine orbits before merger, with post-Newtonian results using the approximants Taylor T1, T4, and Et. We find that, over the ten cycles before the gravitational-wave frequency reaches Mω=0.1, the accumulated phase disagreement between numerical relativity (NR) and 2.5 post-Newtonian (PN) results is less than three radians, and is less than 2.5 radians when using 3.5PN results. The amplitude disagreement between NR and restricted PN results increases with the black holes’ spin, from about 6% in the equal-mass case to 12% when the black holes’ spins are Si/Mi2=0.85. Finally, our results suggest that the merger waveform will play an important role in estimating the spin from such inspiral waveforms.

Numerical Algorithms for Precise and Efficient Orbit Propagation and Positioning

NASA Astrophysics Data System (ADS)

Bradley, Ben K.

Motivated by the growing space catalog and the demands for precise orbit determination with shorter latency for science and reconnaissance missions, this research improves the computational performance of orbit propagation through more efficient and precise numerical integration and frame transformation implementations. Propagation of satellite orbits is required for astrodynamics applications including mission design, orbit determination in support of operations and payload data analysis, and conjunction assessment. Each of these applications has somewhat different requirements in terms of accuracy, precision, latency, and computational load. This dissertation develops procedures to achieve various levels of accuracy while minimizing computational cost for diverse orbit determination applications. This is done by addressing two aspects of orbit determination: (1) numerical integration used for orbit propagation and (2) precise frame transformations necessary for force model evaluation and station coordinate rotations. This dissertation describes a recently developed method for numerical integration, dubbed Bandlimited Collocation Implicit Runge-Kutta (BLC-IRK), and compare its efficiency in propagating orbits to existing techniques commonly used in astrodynamics. The BLC-IRK scheme uses generalized Gaussian quadratures for bandlimited functions. It requires significantly fewer force function evaluations than explicit Runge-Kutta schemes and approaches the efficiency of the 8th-order Gauss-Jackson multistep method. Converting between the Geocentric Celestial Reference System (GCRS) and International Terrestrial Reference System (ITRS) is necessary for many applications in astrodynamics, such as orbit propagation, orbit determination, and analyzing geoscience data from satellite missions. This dissertation provides simplifications to the Celestial Intermediate Origin (CIO) transformation scheme and Earth orientation parameter (EOP) storage for use in positioning and orbit propagation, yielding savings in computation time and memory. Orbit propagation and position transformation simulations are analyzed to generate a complete set of recommendations for performing the ITRS/GCRS transformation for a wide range of needs, encompassing real-time on-board satellite operations and precise post-processing applications. In addition, a complete derivation of the ITRS/GCRS frame transformation time-derivative is detailed for use in velocity transformations between the GCRS and ITRS and is applied to orbit propagation in the rotating ITRS. EOP interpolation methods and ocean tide corrections are shown to impact the ITRS/GCRS transformation accuracy at the level of 5 cm and 20 cm on the surface of the Earth and at the Global Positioning System (GPS) altitude, respectively. The precession-nutation and EOP simplifications yield maximum propagation errors of approximately 2 cm and 1 m after 15 minutes and 6 hours in low-Earth orbit (LEO), respectively, while reducing computation time and memory usage. Finally, for orbit propagation in the ITRS, a simplified scheme is demonstrated that yields propagation errors under 5 cm after 15 minutes in LEO. This approach is beneficial for orbit determination based on GPS measurements. We conclude with a summary of recommendations on EOP usage and bias-precession-nutation implementations for achieving a wide range of transformation and propagation accuracies at several altitudes. This comprehensive set of recommendations allows satellite operators, astrodynamicists, and scientists to make informed decisions when choosing the best implementation for their application, balancing accuracy and computational complexity.

Numerical Analysis of Orbital Perturbation Effects on Inclined Geosynchronous SAR

PubMed Central

Dong, Xichao; Hu, Cheng; Long, Teng; Li, Yuanhao

2016-01-01

The geosynchronous synthetic aperture radar (GEO SAR) is susceptible to orbit perturbations, leading to orbit drifts and variations. The influences behave very differently from those in low Earth orbit (LEO) SAR. In this paper, the impacts of perturbations on GEO SAR orbital elements are modelled based on the perturbed dynamic equations, and then, the focusing is analyzed theoretically and numerically by using the Systems Tool Kit (STK) software. The accurate GEO SAR slant range histories can be calculated according to the perturbed orbit positions in STK. The perturbed slant range errors are mainly the first and second derivatives, leading to image drifts and defocusing. Simulations of the point target imaging are performed to validate the aforementioned analysis. In the GEO SAR with an inclination of 53° and an argument of perigee of 90°, the Doppler parameters and the integration time are different and dependent on the geometry configurations. Thus, the influences are varying at different orbit positions: at the equator, the first-order phase errors should be mainly considered; at the perigee and apogee, the second-order phase errors should be mainly considered; at other positions, first-order and second-order exist simultaneously. PMID:27598168

Study of a homotopy continuation method for early orbit determination with the Tracking and Data Relay Satellite System (TDRSS)

NASA Technical Reports Server (NTRS)

Smith, R. L.; Huang, C.

1986-01-01

A recent mathematical technique for solving systems of equations is applied in a very general way to the orbit determination problem. The study of this technique, the homotopy continuation method, was motivated by the possible need to perform early orbit determination with the Tracking and Data Relay Satellite System (TDRSS), using range and Doppler tracking alone. Basically, a set of six tracking observations is continuously transformed from a set with known solution to the given set of observations with unknown solutions, and the corresponding orbit state vector is followed from the a priori estimate to the solutions. A numerical algorithm for following the state vector is developed and described in detail. Numerical examples using both real and simulated TDRSS tracking are given. A prototype early orbit determination algorithm for possible use in TDRSS orbit operations was extensively tested, and the results are described. Preliminary studies of two extensions of the method are discussed: generalization to a least-squares formulation and generalization to an exhaustive global method.

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.

Orbital Debris Engineering Model (ORDEM) v.3

NASA Technical Reports Server (NTRS)

Matney, Mark; Krisko, Paula; Xu, Yu-Lin; Horstman, Matthew

2013-01-01

A model of the manmade orbital debris environment is required by spacecraft designers, mission planners, and others in order to understand and mitigate the effects of the environment on their spacecraft or systems. A manmade environment is dynamic, and can be altered significantly by intent (e.g., the Chinese anti-satellite weapon test of January 2007) or accident (e.g., the collision of Iridium 33 and Cosmos 2251 spacecraft in February 2009). Engineering models are used to portray the manmade debris environment in Earth orbit. The availability of new sensor and in situ data, the re-analysis of older data, and the development of new analytical and statistical techniques has enabled the construction of this more comprehensive and sophisticated model. The primary output of this model is the flux [#debris/area/time] as a function of debris size and year. ORDEM may be operated in spacecraft mode or telescope mode. In the former case, an analyst defines an orbit for a spacecraft and "flies" the spacecraft through the orbital debris environment. In the latter case, an analyst defines a ground-based sensor (telescope or radar) in terms of latitude, azimuth, and elevation, and the model provides the number of orbital debris traversing the sensor's field of view. An upgraded graphical user interface (GUI) is integrated with the software. This upgraded GUI uses project-oriented organization and provides the user with graphical representations of numerous output data products. These range from the conventional flux as a function of debris size for chosen analysis orbits (or views), for example, to the more complex color-contoured two-dimensional (2D) directional flux diagrams in local spacecraft elevation and azimuth.

Non-gravitational force modeling of Comet 81P/Wild 2. II. Rotational evolution

NASA Astrophysics Data System (ADS)

Gutiérrez, Pedro J.; Davidsson, Björn J. R.

2007-11-01

In this paper, we have studied both the dynamical and the rotational evolution of an 81P/Wild 2-like comet under the effects of the outgassing-induced force and torque. The main aim is to study if it is possible to reproduce the non-gravitational orbital changes observed in this comet, and to establish the likely evolution of both orbital and rotational parameters. To perform this study, a simple thermophysical model has been used to estimate the torque acting on the nucleus. Once the torque is calculated, Euler equations are solved numerically considering a nucleus mass directly estimated from the changes in the orbital elements (as determined from astrometry). According to these simulations, when the water production rate and changes in orbital parameters for 1997, as well as observational rotational parameters for 2004 are imposed as constraints, the change in the orbital period of 81P/Wild 2, ΔP=P˙, will decrease so that P¨=-5 to -1minorbit, which is similar to the actual tendency observed from 1988 up to 1997. This nearly constant decreasing can be explained as due to a slight drift of the spin axis orientation towards larger ecliptic longitudes. After studying the possible spin axis orientations proposed for 1997, simulations suggest that the spin obliquity and argument (I,Φ)=(56°,167°) is the most likely. As for rotational evolution, changes per orbit smaller than 10% of the actual spin velocity are probable, while the most likely value corresponds to a change between 2 and 7% of the spin velocity. Equally, net changes in the spin axis orientation of 4°-8° per orbit are highly expected.

Aerothermodynamics of Satellite During Atmospheric Reentry for the Whole Range of Gas Rarefaction: Influence of Inelastic Intermolecular Collisions

NASA Astrophysics Data System (ADS)

Kozak, Dalton Vinicius; Sharipov, Felix

2012-08-01

The aerothermodynamic characteristics of the Brazilian satellite Satélite de Reentrada Atmosférica were calculated for orbital-flight and atmospheric-reentry conditions with the direct simulation Monte Carlo method for a diatomic gas. The internal modes of molecule energy in the intermolecular interaction, such as the rotational energy, were taken into account. The numerical calculations cover a range of gas rarefactions wide enough to embrace the free-molecule and hydrodynamic regimes. Two Mach numbers were considered: 10 and 20. Numerical results include the drag force of the satellite, the energy flux, pressure coefficient, and skin friction coefficient over the satellite surface, the density and temperature distributions, and streamlines of the gas flow around the satellite. The influence of the satellite temperature upon these characteristics was evaluated at different satellite temperatures.

Solution of multi-center molecular integrals of Slater-type orbitals

NASA Technical Reports Server (NTRS)

Tai, H.

1989-01-01

The troublesome multi-center molecular integrals of Slater-type orbitals (STO) in molecular physics calculations can be evaluated by using the Fourier transform and proper coupling of the two center exchange integrals. A numerical integration procedure is then readily rendered to the final expression in which the integrand consists of well known special functions of arguments containing the geometrical arrangement of the nuclear centers and the exponents of the atomic orbitals. A practical procedure was devised for the calculation of a general multi-center molecular integrals coupling arbitrary Slater-type orbitals. Symmetry relations and asymptotic conditions are discussed. Explicit expressions of three-center one-electron nuclear-attraction integrals and four-center two-electron repulsion integrals for STO of principal quantum number n=2 are listed. A few numerical results are given for the purpose of comparison.

The use of tethers for payload orbital transfer. Continuation of investigation of electrodynamic stabilization and control of long orbiting tethers, volume 2

NASA Technical Reports Server (NTRS)

Colombo, G.; Martinez-Sanchez, M.; Arnold, D.

1982-01-01

The SKYHOOK program was used to do simulations of two cases of the use of the tether for payload orbital transfer. The transport of a payload along the tether from a heavy lower platform to an upper launching platform is considered. A numerical example of the Shuttle launching a payload using an orbital tether facility is described.

Effect of Numerical Error on Gravity Field Estimation for GRACE and Future Gravity Missions

NASA Astrophysics Data System (ADS)

McCullough, Christopher; Bettadpur, Srinivas

2015-04-01

In recent decades, gravity field determination from low Earth orbiting satellites, such as the Gravity Recovery and Climate Experiment (GRACE), has become increasingly more effective due to the incorporation of high accuracy measurement devices. Since instrumentation quality will only increase in the near future and the gravity field determination process is computationally and numerically intensive, numerical error from the use of double precision arithmetic will eventually become a prominent error source. While using double-extended or quadruple precision arithmetic will reduce these errors, the numerical limitations of current orbit determination algorithms and processes must be accurately identified and quantified in order to adequately inform the science data processing techniques of future gravity missions. The most obvious numerical limitation in the orbit determination process is evident in the comparison of measured observables with computed values, derived from mathematical models relating the satellites' numerically integrated state to the observable. Significant error in the computed trajectory will corrupt this comparison and induce error in the least squares solution of the gravitational field. In addition, errors in the numerically computed trajectory propagate into the evaluation of the mathematical measurement model's partial derivatives. These errors amalgamate in turn with numerical error from the computation of the state transition matrix, computed using the variational equations of motion, in the least squares mapping matrix. Finally, the solution of the linearized least squares system, computed using a QR factorization, is also susceptible to numerical error. Certain interesting combinations of each of these numerical errors are examined in the framework of GRACE gravity field determination to analyze and quantify their effects on gravity field recovery.

A Christmas comet falling onto a neutron star

NASA Astrophysics Data System (ADS)

Campana, S.

The Sun and the planets are the main, but not the only, bodies of the Solar System. There are thousands of asteroids and several tens of comets, many of which are still unknown. They are the remnants of the planetesimals that formed at the origin of our Solar System, and they are rocky objects of different dimensions and irregular shape. Sometimes these minor bodies fall onto the Sun or onto planets, like Jupiter. Less dramatic events occur when the infalling bodies do not directly impact onto the target but are tidally disrupted. The tidal disruption of solar mass stars around supermassive black holes has been extensively studied analytically and numerically. In these events the star, as it approaches the black hole, develops into an elongated banana-shaped structure, the most tightly bound debris being at the closer end to the compact object. After completing an (few) eccentric orbit(s), these bound debris fall onto the black hole, emitting energy. Orbital precession may lead to the crossing of the debris orbits producing an accretion disk. Observationally, these events will give rise to luminous events with different temporal decays in different energy bands. Tidal break-up events occur also in planetary systems around normal stars but these events are too faint to be detected. Things change when the star is a compact object. Indeed planets have been discovered around radio pulsars, making likely the existence also of orbiting minor bodies. The direct impact of minor bodies onto neutron stars has been studied in the past and it has been envisaged as a possible (local) explanation for Gamma-Ray Bursts (GRBs), producing short-duration (˜ seconds) events. To explain the peculiarities of GRB 101225A (Christmas burst) we propose that it resulted from the tidal disruption event of a minor body around a neutron star in our Galaxy.

Orbits in elementary, power-law galaxy bars - 1. Occurrence and role of single loops

NASA Astrophysics Data System (ADS)

Struck, Curtis

2018-05-01

Orbits in galaxy bars are generally complex, but simple closed loop orbits play an important role in our conceptual understanding of bars. Such orbits are found in some well-studied potentials, provide a simple model of the bar in themselves, and may generate complex orbit families. The precessing, power ellipse (p-ellipse) orbit approximation provides accurate analytic orbit fits in symmetric galaxy potentials. It remains useful for finding and fitting simple loop orbits in the frame of a rotating bar with bar-like and symmetric power-law potentials. Second-order perturbation theory yields two or fewer simple loop solutions in these potentials. Numerical integrations in the parameter space neighbourhood of perturbation solutions reveal zero or one actual loops in a range of such potentials with rising rotation curves. These loops are embedded in a small parameter region of similar, but librating orbits, which have a subharmonic frequency superimposed on the basic loop. These loops and their librating companions support annular bars. Solid bars can be produced in more complex potentials, as shown by an example with power-law indices varying with radius. The power-law potentials can be viewed as the elementary constituents of more complex potentials. Numerical integrations also reveal interesting classes of orbits with multiple loops. In two-dimensional, self-gravitating bars, with power-law potentials, single-loop orbits are very rare. This result suggests that gas bars or oval distortions are unlikely to be long-lived, and that complex orbits or three-dimensional structure must support self-gravitating stellar bars.

Tidal disruption of inclined or eccentric binaries by massive black holes

NASA Astrophysics Data System (ADS)

Brown, Harriet; Kobayashi, Shiho; Rossi, Elena M.; Sari, Re'em

2018-07-01

Binary stars that are on close orbits around massive black holes (MBHs) such as Sgr A* in the centre of the Milky Way are liable to undergo tidal disruption and eject a hypervelocity star. We study the interaction between such an MBH and circular binaries for general binary orientations and penetration depths (i.e. binaries penetrate into the tidal radius around the BH). We show that for very deep penetrators, almost all binaries are disrupted when the binary rotation axis is roughly oriented towards the BH or it is in the opposite direction. The surviving chance becomes significant when the angle between the binary rotation axis and the BH direction is between 0.15π and 0.85π. The surviving chance is as high as ˜20 per cent when the binary rotation axis is perpendicular to the BH direction. However, for shallow penetrators, the highest disruption chance is found in such a perpendicular case, especially in the prograde case. This is because the dynamics of shallow penetrators is more sensitive to the relative orientation of the binary and orbital angular momenta. We provide numerical fits to the disruption probability and energy gain at the BH encounter as a function of the penetration depth. The latter can be simply rescaled in terms of binary masses, their initial separation, and the binary-to-BH mass ratio to evaluate the ejection velocity of a binary members in various systems. We also investigate the disruption of coplanar, eccentric binaries by an MBH. It is shown that for highly eccentric binaries retrograde orbits have a significantly increased disruption probability and ejection velocities compared to the circular binaries.

Tidal Disruption of Inclined or Eccentric Binaries by Massive Black Holes

NASA Astrophysics Data System (ADS)

Brown, Harriet; Kobayashi, Shiho; Rossi, Elena M.; Sari, Re'em

2018-04-01

Binary stars that are on close orbits around massive black holes (MBH) such as Sgr A* in the centre of the Milky Way are liable to undergo tidal disruption and eject a hypervelocity star. We study the interaction between such a MBH and circular binaries for general binary orientations and penetration depths (i.e. binaries penetrate into the tidal radius around the BH). We show that for very deep penetrators, almost all binaries are disrupted when the binary rotation axis is roughly oriented toward the BH or it is in the opposite direction. The surviving chance becomes significant when the angle between the binary rotation axis and the BH direction is between 0.15π and 0.85π. The surviving chance is as high as ˜20% when the binary rotation axis is perpendicular to the BH direction. However, for shallow penetrators, the highest disruption chance is found in such a perpendicular case, especially in the prograde case. This is because the dynamics of shallow penetrators is more sensitive to the relative orientation of the binary and orbital angular momenta. We provide numerical fits to the disruption probability and energy gain at the the BH encounter as a function of the penetration depth. The latter can be simply rescaled in terms of binary masses, their initial separation and the binary-to-BH mass ratio to evaluate the ejection velocity of a binary members in various systems. We also investigate the disruption of coplanar, eccentric binaries by a MBH. It is shown that for highly eccentric binaries retrograde orbits have a significantly increased disruption probability and ejection velocities compared to the circular binaries.

Fuel-Optimal Altitude Maintenance of Low-Earth-Orbit Spacecrafts by Combined Direct/Indirect Optimization

NASA Astrophysics Data System (ADS)

Kim, Kyung-Ha; Park, Chandeok; Park, Sang-Young

2015-12-01

This work presents fuel-optimal altitude maintenance of Low-Earth-Orbit (LEO) spacecrafts experiencing non-negligible air drag and J2 perturbation. A pseudospectral (direct) method is first applied to roughly estimate an optimal fuel consumption strategy, which is employed as an initial guess to precisely determine itself. Based on the physical specifications of KOrea Multi-Purpose SATellite-2 (KOMPSAT-2), a Korean artificial satellite, numerical simulations show that a satellite ascends with full thrust at the early stage of the maneuver period and then descends with null thrust. While the thrust profile is presumably bang-off, it is difficult to precisely determine the switching time by using a pseudospectral method only. This is expected, since the optimal switching epoch does not coincide with one of the collocation points prescribed by the pseudospectral method, in general. As an attempt to precisely determine the switching time and the associated optimal thrust history, a shooting (indirect) method is then employed with the initial guess being obtained through the pseudospectral method. This hybrid process allows the determination of the optimal fuel consumption for LEO spacecrafts and their thrust profiles efficiently and precisely.

A single-electron picture based on the multiconfiguration time-dependent Hartree-Fock method: application to the anisotropic ionization and subsequent high-harmonic generation of the CO molecule

NASA Astrophysics Data System (ADS)

Ohmura, S.; Kato, T.; Oyamada, T.; Koseki, S.; Ohmura, H.; Kono, H.

2018-02-01

The mechanisms of anisotropic near-IR tunnel ionization and high-order harmonic generation (HHG) in a CO molecule are theoretically investigated by using the multiconfiguration time-dependent Hartree-Fock (MCTDHF) method developed for the simulation of multielectron dynamics of molecules. The multielectron dynamics obtained by numerically solving the equations of motion (EOMs) in the MCTDHF method is converted to a single orbital picture in the natural orbital representation where the first-order reduced density matrix is diagonalized. The ionization through each natural orbital is examined and the process of HHG is classified into different optical paths designated by a combinations of initial, intermediate and final natural orbitals. The EOMs for natural spin-orbitals are also derived within the framework of the MCTDHF, which maintains the first-order reduced density matrix to be a diagonal one throughout the time propagation of a many-electron wave function. The orbital dependent, time-dependent effective potentials that govern the dynamics of respective time-dependent natural orbitals are deduced from the derived EOMs, of which the temporal variation can be used to interpret the motion of the electron density associated with each natural spin-orbital. The roles of the orbital shape, multiorbital ionization, linear Stark effect and multielectron interaction in the ionization and HHG of a CO molecule are revealed by the effective potentials obtained. When the laser electric field points to the nucleus O from C, tunnel ionization from the C atom side is enhanced; a hump structure originating from multielectron interaction is then formed on the top of the field-induced distorted barrier of the HOMO effective potential. This hump formation, responsible for the directional anisotropy of tunnel ionization, restrains the influence of the linear Stark effect on the energy shifts of bound states.

NEA impactors: what direction to they come from?

NASA Astrophysics Data System (ADS)

Harris, Alan

2018-04-01

One might expect, if Earth-crossing NEAs are "thermalized" by prior close scattering encounters with the Earth, that final impact trajectories would be isotropic in direction. But orbital perturbations and other sources of entry and exit to the Earth-crossing zone are faster acting that thermalization, so the actual distribution of impacting orbits is quite anisotropic. I have studied impactor directions by adjusting the orbits of known Earth-crossing PHAs slightly to put them on intersecting orbits and then computed the direction of approach to the Earth. This arguably suffers from "looking under the lamp post", since NEAs are mostly discovered close to the opposition direction, so I also took the distribution of NEA orbits recently derived by Granvik and others and extracted, from a set of 100,000 synthetic orbits they provided, a subset of Earth-crossing PHAs and similarly adjusted them to be intersecting orbits. This should represent an unbiased set of orbits. I then weighted the impact directions by the individual Opik impact probability to obtain a distribution of impact directions weighted by actual impact probabilities. The result was that more than 40% of incoming trajectories clustered within 60 degrees of the opposition direction, and a similar fraction come from within 60 degrees of the solar direction. Thus ~80% of impactors come from only about 1/3 of the sky area, with almost none coming from 60-120 degrees solar elongation. The message is that existing ground-based surveys can hardly be improved upon by greater sky coverage with respect to detecting "death plunge" objects, and even space-based instruments offer very little improvement due to the very low solar elongation of most objects approaching from the solar direction.

A satellite constellation optimization for a regional GNSS remote sensing mission

NASA Astrophysics Data System (ADS)

Gavili Kilaneh, Narin; Mashhadi Hossainali, Masoud

2017-04-01

Due to the recent advances in the Global Navigation Satellite System Remote sensing (GNSS¬R) applications, optimization of a satellite orbit to investigate the Earth's properties seems significant. The comparison of the GNSS direct and reflected signals received by a Low Earth Orbit (LEO) satellite introduces a new technique to remotely sense the Earth. Several GNSS¬R missions including Cyclone Global Navigation Satellite System (CYGNSS) have been proposed for different applications such as the ocean wind speed and height monitoring. The geometric optimization of the satellite orbit before starting the mission is a key step for every space mission. Since satellite constellation design varies depending on the application, we have focused on the required geometric criteria for oceanography applications in a specified region. Here, the total number of specular points, their spatial distribution and the accuracy of their position are assumed to be sufficient for oceanography applications. Gleason's method is used to determine the position of specular points. We considered the 2-D lattice and 3-D lattice theory of flower constellation to survey whether a circular orbit or an elliptical one is suitable to improve the solution. Genetic algorithm is implemented to solve the problem. To check the visibility condition between the LEO and GPS satellites, the satellite initial state is propagated by a variable step size numerical integration method. Constellation orbit parameters achieved by optimization provide a better resolution and precession for the specular points in the study area of this research.

Propagation effects in the generation process of high-order vortex harmonics.

PubMed

Zhang, Chaojin; Wu, Erheng; Gu, Mingliang; Liu, Chengpu

2017-09-04

We numerically study the propagation of a Laguerre-Gaussian beam through polar molecular media via the exact solution of full-wave Maxwell-Bloch equations where the rotating-wave and slowly-varying-envelope approximations are not included. It is found that beyond the coexistence of odd-order and even-order vortex harmonics due to inversion asymmetry of the system, the light propagation effect results in the intensity enhancement of a high-order vortex harmonics. Moreover, the orbital momentum successfully transfers from the fundamental laser driver to the vortex harmonics which topological charger number is directly proportional to its order.

Verified solutions for the gravitational attraction to an oblate spheroid: Implications for planet mass and satellite orbits

NASA Astrophysics Data System (ADS)

Hofmeister, Anne M.; Criss, Robert E.; Criss, Everett M.

2018-03-01

Forces external to the oblate spheroid shape, observed from planetary to galactic scales, are demonstrably non-central, which has important ramifications for planetary science. We simplify historic formulae and derive new analytical solutions for the gravitational potential and force outside a constant density oblate. Numerical calculations that sum point mass contributions in a >109 element mesh confirm our equations. We show that contours of constant force and potential about oblate bodies are closely approximated by two confocal families whose foci (f) respectively are (9/10)½ae and (3/5)½ae for a body with f = ae. This leads to useful approximations that address internal density variations. We demonstrate that the force on a general point is not directed towards the oblate's center, nor are forces simply proportional to the inverse square of that distance, despite forces in the equatorial and axial directions pointing towards the center. Our results explain complex dynamics of galactic systems. Because most planets and stars have an aspect ratio >0.9, the spherical approximation is reasonable except for orbits within ∼2 body radii. We show that applying the "generalized" potential, which assumes central forces, yields J2 values half those expected for oblate bodies, and probably underestimates masses of Uranus and Neptune by ∼0.2%. We show that the inner Saturnian moons are subject to non-central forces, which may affect calculations of their orbital precession. Our new series should improve interpretation of flyby data.

Magnetic anisotropy in the Kitaev model systems Na2IrO3 and RuCl3

NASA Astrophysics Data System (ADS)

Chaloupka, Jiří; Khaliullin, Giniyat

2016-08-01

We study the ordered moment direction in the extended Kitaev-Heisenberg model relevant to honeycomb lattice magnets with strong spin-orbit coupling. We utilize numerical diagonalization and analyze the exact cluster ground states using a particular set of spin-coherent states, obtaining thereby quantum corrections to the magnetic anisotropy beyond conventional perturbative methods. It is found that the quantum fluctuations strongly modify the moment direction obtained at a classical level and are thus crucial for a precise quantification of the interactions. The results show that the moment direction is a sensitive probe of the model parameters in real materials. Focusing on the experimentally relevant zigzag phases of the model, we analyze the currently available neutron-diffraction and resonant x-ray-diffraction data on Na2IrO3 and RuCl3 and discuss the parameter regimes plausible in these Kitaev-Heisenberg model systems.

Tables Of Gaussian-Type Orbital Basis Functions

NASA Technical Reports Server (NTRS)

Partridge, Harry

1992-01-01

NASA technical memorandum contains tables of estimated Hartree-Fock wave functions for atoms lithium through neon and potassium through krypton. Sets contain optimized Gaussian-type orbital exponents and coefficients, and near Hartree-Fock quality. Orbital exponents optimized by minimizing restricted Hartree-Fock energy via scaled Newton-Raphson scheme in which Hessian evaluated numerically by use of analytically determined gradients.

Orbiter/Space lab momentum management for POP orientations

NASA Technical Reports Server (NTRS)

Cox, J. W.

1974-01-01

An angular momentum management scheme applicable to the orbiter/spacelab is described. The basis of the scheme is to periodically maneuver the vehicle through a small angle thereby using the gravity gradient torque to dump momentum from the control moment gyro (CMG) control system. The orbiter is operated with its principal vehicle axis perpendicular to the orbital plane. Numerous case runs were conducted on the hybrid simulation and representative cases are included.

Orbital theory in terms of KS elements with luni-solar perturbations

NASA Astrophysics Data System (ADS)

Sellamuthu, Harishkumar; Sharma, Ram

2016-07-01

Precise orbit computation of Earth orbiting satellites is essential for efficient mission planning of planetary exploration, navigation and satellite geodesy. The third-body perturbations of the Sun and the Moon predominantly affect the satellite motion in the high altitude and elliptical orbits, where the effect of atmospheric drag is negligible. The physics of the luni-solar gravity effect on Earth satellites have been studied extensively over the years. The combined luni-solar gravitational attraction will induce a cumulative effect on the dynamics of satellite orbits, which mainly oscillates the perigee altitude. Though accurate orbital parameters are computed by numerical integration with respect to complex force models, analytical theories are highly valued for the manifold of solutions restricted to relatively simple force models. During close approach, the classical equations of motion in celestial mechanics are almost singular and they are unstable for long-term orbit propagation. A new singularity-free analytical theory in terms of KS (Kustaanheimo and Stiefel) regular elements with respect to luni-solar perturbation is developed. These equations are regular everywhere and eccentric anomaly is the independent variable. Plataforma Solar de Almería (PSA) algorithm and a Fourier series algorithm are used to compute the accurate positions of the Sun and the Moon, respectively. Numerical studies are carried out for wide range of initial parameters and the analytical solutions are found to be satisfactory when compared with numerically integrated values. The symmetrical nature of the equations allows only two of the nine equations to be solved for computing the state vectors and the time. Only a change in the initial conditions is required to solve the other equations. This theory will find multiple applications including on-board software packages and for mission analysis purposes.

Preliminary Experimental Results for Charge Drag in a Simulated Low Earth Orbit Environment

NASA Astrophysics Data System (ADS)

Azema-Rovira, Monica

Interest in the Low Earth Orbit (LEO) environment is growing in the science community as well as in the private sector. The number of spacecraft launched in these altitudes (150 - 700 km) keeps growing, and this region is accumulating space debris. In this scenario, the precise location of all LEO objects is a key factor to avoid catastrophic collisions and to safely perform station-keeping maneuvers. The detailed study of the atmospheric models in LEO can enhance the disturbances forces calculation of an orbiting object. Recent numerical studies indicate that one of the biggest non-conservative forces on a spacecraft is underestimated, the charge drag phenomenon. Validating these numerical models experimentally, will help to improve the numerical models for future spacecraft mission design. For this reason, the motivation of this thesis is to characterize a plasma source to later be used for charged drag measurements. The characterization has been done at the University of Colorado Colorado Springs in the Chamber for Atmospheric and Orbital Space Simulation. In the characterization process, a nano-Newton Thrust Stand has been characterized as a plasma diagnosis tool and compared with Langmuir Probe data.

Relative motion of orbiting satellites

NASA Technical Reports Server (NTRS)

Eades, J. B., Jr.

1972-01-01

The relative motion problem is analyzed, as a linearized case, and as a numerically determined solution to provide a time history of the geometries representing the motion state. The displacement history and the hodographs for families of solutions are provided, analytically and graphically, to serve as an aid to understanding this problem area. Linearized solutions to relative motion problems of orbiting particles are presented for the impulsive and fixed thrust cases. Second order solutions are described to enhance the accuracy of prediction. A method was developed to obtain accurate, numerical solutions to the intercept and rendezvous problem; and, special situations are examined. A particular problem related to relative motions, where the motion traces develop a cusp, is examined in detail. This phenomenon is found to be dependent on a particular relationship between orbital eccentricity and the inclination between orbital planes. These conditions are determined, and, example situations are presented and discussed.

New meteoroid model predictions for directional impacts on LDEF

NASA Technical Reports Server (NTRS)

Divine, Neil; Agueero, Rene C.

1993-01-01

An extensive body of data, from meteors, zodiacal light, spacecraft-borne impact detectors (Helios, Pioneer, Galileo, Ulysses), and other sources, forms the basis of a new numerical model for the distributions of interplanetary meteoroids. For each of the five populations in this model it is possible to evaluate meteoroid concentration and flux for oriented surfaces or detectors having arbitrary position and velocity in interplanetary space. For a spacecraft in geocentric orbit the effects of gravitational focussing and shielding by the Earth have been newly derived with full attention to the directionality of the particles, both on approach (i.e., relative to a massless Earth) and at the target. This modeling approach was exercised to provide an estimate of meteoroid fluence for each of several oriented surfaces on LDEF.

Magnus-induced ratchet effects for skyrmions interacting with asymmetric substrates

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

Reichhardt, C.; Ray, D.; Reichhardt, C. J. Olson

2015-07-31

We show using numerical simulations that pronounced ratchet effects can occur for ac driven skyrmions moving over asymmetric quasi-one-dimensional substrates. We find a new type of ratchet effect called a Magnus-induced transverse ratchet that arises when the ac driving force is applied perpendicular rather than parallel to the asymmetry direction of the substrate. This transverse ratchet effect only occurs when the Magnus term is finite, and the threshold ac amplitude needed to induce it decreases as the Magnus term becomes more prominent. Ratcheting skyrmions follow ordered orbits in which the net displacement parallel to the substrate asymmetry direction is quantized.more » As a result, skyrmion ratchets represent a new ac current-based method for controlling skyrmion positions and motion for spintronic applications.« less

Numerical estimates of secular effects in the translational-rotational motion of an orbital station with 'Martian' gravity on board

NASA Astrophysics Data System (ADS)

Koenov, D. Z.

Attention is given to an orbital station consisting of two identical cylindrical spacecraft with symmetrical wings (solar arrays); connected by a long tether, the two craft rotate about an axis that passes through their common center of mass. It is assumed that a Martian type of gravity has been created on board. Numerical estimates show that, in the course of a single mean solar day, the station performs more than 15.5 revolutions around the earth.

Rarefied flow past a flat plate at incidence

NASA Technical Reports Server (NTRS)

Dogra, Virendra K.; Moss, James N.; Price, Joseph M.

1988-01-01

Results of a numerical study using the direct simulation Monte Carlo (DSMC) method are presented for the transitional flow about a flat plate at 40 deg incidence. The plate has zero thickness and a length of 1.0 m. The flow conditions simulated are those experienced by the Shuttle Orbiter during reentry at 7.5 km/s. The range of freestream conditions are such that the freestream Knudsen number values are between 0.02 and 8.4, i.e., conditions that encompass most of the transitional flow regime. The DSMC simulations show that transitional effects are evident when compared with free molecule results for all cases considered. The calculated results demonstrate clearly the necessity of having a means of identifying the effects of transitional flow when making aerodynamic flight measurements as are currently being made with the Space Shuttle Orbiter vehicles. Previous flight data analyses have relied exclusively on adjustments in the gas-surface interaction models without accounting for the transitional effect which can be comparable in magnitude. The present calculations show that the transitional effect at 175 km would increase the Space Shuttle Orbiter lift-drag ratio by 90 percent over the free molecule value.

Pathology of orbital bones. The XXXII Edward Jackson Memorial Lecture.

PubMed

Blodi, F C

1976-01-01

The orbital bones may show nearly all the pathologic changes observed in the skull and in the face. The congenital anomalies in this area are numerous and involve various forms of craniostenoses. Among the benign osseous tumors the osteoma is most frequently encountered in the orbit. Fibrous dysplasia is a tumefaction of indeterminate behavior that often involves the orbit. Osteosarcoma or other malignant neoplasms are rarely seen in this area. Eosinophilic granuloma and Hand-Schüller-Christian disease are tumor-like lesions that may involve the orbit.

Correlation of nonorthogonality of best hybrid bond orbitals with bond strength of orthogonal orbitals

PubMed Central

Pauling, Linus

1976-01-01

An expression is derived for the bond length of two spd orbitals with maximum values in two directions forming a given bond angle by consideration of the nonorthogonality integral of two best orbitals in these directions. This equation is equivalent to the expression derived by formulating the pair of orthogonal orbitals. Similar expressions are derived for spdf orbitals. Applications are made to icosahedral and cuboctahedral bonds and to the packing of nucleons in atomic nuclei. PMID:16578736

Correlation of nonorthogonality of best hybrid bond orbitals with bond strength of orthogonal orbitals.

PubMed

Pauling, L

1976-02-01

An expression is derived for the bond length of two spd orbitals with maximum values in two directions forming a given bond angle by consideration of the nonorthogonality integral of two best orbitals in these directions. This equation is equivalent to the expression derived by formulating the pair of orthogonal orbitals. Similar expressions are derived for spdf orbitals. Applications are made to icosahedral and cuboctahedral bonds and to the packing of nucleons in atomic nuclei.

Orbital dynamics in the post-Newtonian planar circular restricted Sun-Jupiter system

NASA Astrophysics Data System (ADS)

Zotos, Euaggelos E.; Dubeibe, F. L.

The theory of the post-Newtonian (PN) planar circular restricted three-body problem is used for numerically investigating the orbital dynamics of a test particle (e.g. a comet, asteroid, meteor or spacecraft) in the planar Sun-Jupiter system with a scattering region around Jupiter. For determining the orbital properties of the test particle, we classify large sets of initial conditions of orbits for several values of the Jacobi constant in all possible Hill region configurations. The initial conditions are classified into three main categories: (i) bounded, (ii) escaping and (iii) collisional. Using the smaller alignment index (SALI) chaos indicator, we further classify bounded orbits into regular, sticky or chaotic. In order to get a spherical view of the dynamics of the system, the grids of the initial conditions of the orbits are defined on different types of two-dimensional planes. We locate the different types of basins and we also relate them with the corresponding spatial distributions of the escape and collision time. Our thorough analysis exposes the high complexity of the orbital dynamics and exhibits an appreciable difference between the final states of the orbits in the classical and PN approaches. Furthermore, our numerical results reveal a strong dependence of the properties of the considered basins with the Jacobi constant, along with a remarkable presence of fractal basin boundaries. Our outcomes are compared with the earlier ones regarding other planetary systems.

Formation and Migration of Trans-Neptunian Objects

NASA Technical Reports Server (NTRS)

Ipatov, S. I.; Oegerle, William (Technical Monitor)

2002-01-01

We consider that trans-Neptunian objects (TNOs) with diameter d greater than 100 kilometers moving now in not very eccentric orbits could be formed directly by the compression of large rarefied dust condensations (with a greater than 30 AU), but not by the accretion of smaller solid planetesimals. Probably, some planetesimals with d approximately 100- 1000 kilometers in the feeding zone of the giant planets and even large main-belt asteroids also could be formed directly by such compression. Some smaller objects (TNOs, planetesimals, asteroids) could be debris of larger objects, and other such objects could be formed directly by compression of condensations. A small portion of planetesimals from the feeding zone of the giant planets that entered into the trans-Neptunian region could left in eccentrical orbits beyond Neptune and became so called "scattered objects". Our computer runs in which gravitational interactions of bodies were taken into account with the use of the spheres method, showed that the embryos of Uranus and Neptune could increase their semimajor axes from less than 10 AU to their present values, moving permanently in orbits with small eccentricities, due to gravitational interactions with the migrating planetesimals. Later on, Thommes et al. considered a similar model using direct numerical integration. The total amount of water delivered to the Earth during the formation of the giant, planets was about the mass of water in the Earth oceans. The end of such bombardment could be caused mainly by the planetesimals that became scattered objects. For the present mass of the trans-Neptunian belt, the collisional lifetime of 1-kilometer TNO is about the age of the Solar system, but only a small portion (less than 1%) of 100-km TNOs could be destroyed during this age. The probability of destruction of a typical TNO (with 30 less than a,less than 50 AU) by scattered objects can be of the same order of magnitude as that by typical TNOs. TNOs could be even more often destroyed during planet formation than during last 4 Gyr. The analysis of the results of the orbital evolution of Jupiter-crossing objects (JCOs) and TNOs showed that, in principle, the trans-Neptunian belt can provide up to 100% of Earth-crossing objects, but, of course, some of them came from the main asteroid belt. Most of the collisions of former JCOs with the Earth were from orbits with aphelia inside Jupiter's orbit and belonged to a small portion of objects which moved in such orbits for a long time. About 1 of 300 JCOs collided with the Sun. The ratio of the total mass of icy planetesimals that migrated from the feeding zone of the giant planets and collided with the planet to the mass of this planet was greater (by a factor of 3 in our runs) for Mars than that for Earth and Venus.

Orbits of Two-Body Problem From the Lenz Vector

ERIC Educational Resources Information Center

Caplan, S.; And Others

1978-01-01

Obtains the orbits with reference to the center of mass of two bodies under mutual universe square law interaction by use of the eccentricity vector which is equivalent to the Lenz vector within a numerical factor. (Author/SL)

The dynamics and control of large flexible space structures. Part B: Development of continuum model and computer simulation

NASA Technical Reports Server (NTRS)

Bainum, P. M.; Kumar, V. K.; James, P. K.

1978-01-01

The equations of motion of an arbitrary flexible body in orbit were derived. The model includes the effects of gravity with all its higher harmonics. As a specific example, the motion of a long, slender, uniform beam in circular orbit was modelled. The example considers both the inplane and three dimensional motion of the beam in orbit. In the case of planar motion with only flexible vibrations, the pitch motion is not influenced by the elastic motion of the beam. For large values of the square of the ratio of the structural modal frequency to the orbital angular rate the elastic motion was decoupled from the pitch motion. However, for small values of the ratio and small amplitude pitch motion, the elastic motion was governed by a Hill's 3 term equation. Numerical simulation of the equation indicates the possibilities of instability for very low values of the square of the ratio of the modal frequency to the orbit angular rate. Also numerical simulations of the first order nonlinear equations of motion for a long flexible beam in orbit were performed. The effect of varying the initial conditions and the number of modes was demonstrated.

Spin-orbit coupling for tidally evolving super-Earths

NASA Astrophysics Data System (ADS)

Rodríguez, A.; Callegari, N.; Michtchenko, T. A.; Hussmann, H.

2012-12-01

We investigate the spin behaviour of close-in rocky planets and the implications for their orbital evolution. Considering that the planet rotation evolves under simultaneous actions of the torque due to the equatorial deformation and the tidal torque, both raised by the central star, we analyse the possibility of temporary captures in spin-orbit resonances. The results of the numerical simulations of the exact equations of motions indicate that, whenever the planet rotation is trapped in a resonant motion, the orbital decay and the eccentricity damping are faster than the ones in which the rotation follows the so-called pseudo-synchronization. Analytical results obtained through the averaged equations of the spin-orbit problem show a good agreement with the numerical simulations. We apply the analysis to the cases of the recently discovered hot super-Earths Kepler-10 b, GJ 3634 b and 55 Cnc e. The simulated dynamical history of these systems indicates the possibility of capture in several spin-orbit resonances; particularly, GJ 3634 b and 55 Cnc e can currently evolve under a non-synchronous resonant motion for suitable values of the parameters. Moreover, 55 Cnc e may avoid a chaotic rotation behaviour by evolving towards synchronization through successive temporary resonant trappings.

Numerical model of the evolution of asteroid orbits at the 2:5 resonance

NASA Astrophysics Data System (ADS)

Ipatov, S. I.

1992-12-01

The interrelations of the variations in the orbital elements of asteroids at the 2:5 resonance and in its vicinity are investigated.. These investigations are based on the numerical integration of the complete equations of motion of the three-body problem (sun-Jupiter-asteroid) for 500 model asteroids. The time interval under consideration for most versions of the calculations equaled 10(4) orbital periods of Jupiter. The limits of the variations in the orbital elements and the regions of initial data corresponding to different types of interrelations of the variations in the eccentricity and longitude of perihelion are examined. It is shown that thr 2:5 gap may play a larger role than other gaps in the replenishment of the Apollo and Amor groups. The time over which the argument of perihelion changed by 360 degrees was usually equal to two periods of variation in the orbital inclination. When this interrelation was not found, the time over which the longitude of the ascending node changed by 360 degrees was equal, as a rule, to one period of variation in this inclination. For some asteroids moving along orbits of small eccentricity and inclination, interrelations were found between the periods of variation in four orbital elements: eccentricity, inclination, argument of perihelion, and longitude of the ascending node. For initial inclinations i° = 40° of asteroid orbits, the maximum values of inclinations of some model asteroids reached 160 degrees. Such asteroids could reach the sun or nearly parabolic orbits.

How does the Structure of Spherical Dark Matter Halos Affect the Types of Orbits in Disk Galaxies?

NASA Astrophysics Data System (ADS)

Zotos, Euaggelos E.

The main objective of this work is to determine the character of orbits of stars moving in the meridional (R,z) plane of an axially symmetric time-independent disk galaxy model with a central massive nucleus and an additional spherical dark matter halo component. In particular, we try to reveal the influence of the scale length of the dark matter halo on the different families of orbits of stars, by monitoring how the percentage of chaotic orbits, as well as the percentages of orbits of the main regular resonant families evolve when this parameter varies. The smaller alignment index (SALI) was computed by numerically integrating the equations of motion as well as the variational equations to extensive samples of orbits in order to distinguish safely bet ween ordered and chaotic motion. In addition, a method based on the concept of spectral dynamics that utilizes the Fourier transform of the time series of each coordinate is used to identify the various families of regular orbits and also to recognize the secondary resonances that bifurcate from them. Our numerical computations reveal that when the dark matter halo is highly concentrated, that is when the scale length has low values the vast majority of star orbits move in regular orbits, while on the oth er hand in less concentrated dark matter halos the percentage of chaos increases significantly. We also compared our results with early related work.

The bar-halo interaction - I. From fundamental dynamics to revised N-body requirements

NASA Astrophysics Data System (ADS)

Weinberg, Martin D.; Katz, Neal

2007-02-01

A galaxy remains near equilibrium for most of its history. Only through resonances can non-axisymmetric features, such as spiral arms and bars, exert torques over large scales and change the overall structure of the galaxy. In this paper, we describe the resonant interaction mechanism in detail, derive explicit criteria for the particle number required to simulate these dynamical processes accurately using N-body simulations, and illustrate them with numerical experiments. To do this, we perform a direct numerical solution of perturbation theory, in short, by solving for each orbit in an ensemble and make detailed comparisons with N-body simulations. The criteria include: sufficient particle coverage in phase space near the resonance and enough particles to minimize gravitational potential fluctuations that will change the dynamics of the resonant encounter. These criteria are general in concept and can be applied to any dynamical interaction. We use the bar-halo interaction as our primary example owing to its technical simplicity and astronomical ubiquity. Some of our more surprising findings are as follows. First, the inner Lindblad like resonance, responsible for coupling the bar to the central halo cusp, requires more than equal-mass particles within the virial radius or inside the bar radius for a Milky Way like bar in a Navarro, Frenk & White profile. Secondly, orbits that linger near the resonance receive more angular momentum than orbits that move through the resonance quickly. Small-scale fluctuations present in state-of-the-art particle-particle simulations can knock orbits out of resonance, preventing them from lingering and, thereby, decrease the torque per orbit. This can be offset by the larger number of orbits affected by the resonance due to the diffusion. However, noise from orbiting substructure remains at least an order of magnitude too small to be of consequence. Applied to N-body simulations, the required particle numbers are sufficiently high for scenarios of interest that apparent convergence in particle number is misleading: the convergence with N may still be in the noise-dominated regime. State-of-the-art simulations are not adequate to follow all aspects of secular evolution driven by the bar-halo interaction. It is not possible to derive particle number requirements that apply to all situations, for example, more subtle interactions may be even more difficult to simulate. Therefore, we present a procedure to test the requirements for individual N-body codes to the actual problem of interest.

Three-dimensional vortex-bright solitons in a spin-orbit-coupled spin-1 condensate

NASA Astrophysics Data System (ADS)

Gautam, Sandeep; Adhikari, S. K.

2018-01-01

We demonstrate stable and metastable vortex-bright solitons in a three-dimensional spin-orbit-coupled three-component hyperfine spin-1 Bose-Einstein condensate (BEC) using numerical solution and variational approximation of a mean-field model. The spin-orbit coupling provides attraction to form vortex-bright solitons in both attractive and repulsive spinor BECs. The ground state of these vortex-bright solitons is axially symmetric for weak polar interaction. For a sufficiently strong ferromagnetic interaction, we observe the emergence of a fully asymmetric vortex-bright soliton as the ground state. We also numerically investigate moving solitons. The present mean-field model is not Galilean invariant, and we use a Galilean-transformed mean-field model for generating the moving solitons.

Helical vortices: Quasiequilibrium states and their time evolution

NASA Astrophysics Data System (ADS)

Selçuk, Can; Delbende, Ivan; Rossi, Maurice

2017-08-01

The time evolution of a viscous helical vortex is investigated by direct numerical simulations of the Navier-Stokes equations where helical symmetry is enforced. Using conservation laws in the framework of helical symmetry, we elaborate an initial condition consisting in a finite core vortex, the time evolution of which leads to a generic quasiequilibrium state independent of the initial core size. Numerical results at different helical pitch values provide an accurate characterization in time for such helical states, for which specific techniques have been introduced: helix radius, angular velocity, stream function-velocity-vorticity relationships, and core properties (size, self-similarity, and ellipticity). Viscosity is shown to be at the origin of a small helical velocity component, which we relate to the helical vorticity component. Finally, changes in time of the flow topology are studied using the helical stream function and three-dimensional Lagrangian orbits.

Trojans in habitable zones.

PubMed

Schwarz, Richard; Pilat-Lohinger, Elke; Dvorak, Rudolf; Erdi, Balint; Sándor, Zsolt

2005-10-01

With the aid of numerical experiments we examined the dynamical stability of fictitious terrestrial planets in 1:1 mean motion resonance with Jovian-like planets of extrasolar planetary systems. In our stability study of the so-called "Trojan" planets in the habitable zone, we used the restricted three-body problem with different mass ratios of the primary bodies. The application of the three-body problem showed that even massive Trojan planets can be stable in the 1:1 mean motion resonance. From the 117 extrasolar planetary systems only 11 systems were found with one giant planet in the habitable zone. Out of this sample set we chose four planetary systems--HD17051, HD27442, HD28185, and HD108874--for further investigation. To study the orbital behavior of the stable zone in the different systems, we used direct numerical computations (Lie Integration Method) that allowed us to determine the escape times and the maximum eccentricity of the fictitious "Trojan planets."

Lattice properties of the Phase I BNL x-ray lithography source obtained from fits to magnetic measurement data

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

Blumberg, L.N.; Murphy, J.B.; Reusch, M.F.

1991-01-01

The orbit, tune, chromaticity and {beta} values for the Phase 1 XLS ring were computed by numerical integration of equations of motion using fields obtained from the coefficients of the 3-dimensional solution of Laplace's Equation evaluated by fits to magnetic measurements. The results are in good agreement with available data. The method has been extended to higher order fits of TOSCA generated fields in planes normal to the reference axis using the coil configuration proposed for the Superconducting X-Ray Lithography Source. Agreement with results from numerical integration through fields given directly by TOSCA is excellent. The formulation of the normalmore » multipole expansion presented by Brown and Servranckx has been extended to include skew multipole terms. The method appears appropriate for analysis of magnetic measurements of the SXLS. 8 refs. , 2 figs., 2 tabs.« less

Control-based continuation: Bifurcation and stability analysis for physical experiments

NASA Astrophysics Data System (ADS)

Barton, David A. W.

2017-02-01

Control-based continuation is technique for tracking the solutions and bifurcations of nonlinear experiments. The idea is to apply the method of numerical continuation to a feedback-controlled physical experiment such that the control becomes non-invasive. Since in an experiment it is not (generally) possible to set the state of the system directly, the control target becomes a proxy for the state. Control-based continuation enables the systematic investigation of the bifurcation structure of a physical system, much like if it was numerical model. However, stability information (and hence bifurcation detection and classification) is not readily available due to the presence of stabilising feedback control. This paper uses a periodic auto-regressive model with exogenous inputs (ARX) to approximate the time-varying linearisation of the experiment around a particular periodic orbit, thus providing the missing stability information. This method is demonstrated using a physical nonlinear tuned mass damper.

CONORBIT: constrained optimization by radial basis function interpolation in trust regions

DOE PAGES

Regis, Rommel G.; Wild, Stefan M.

2016-09-26

Here, this paper presents CONORBIT (CONstrained Optimization by Radial Basis function Interpolation in Trust regions), a derivative-free algorithm for constrained black-box optimization where the objective and constraint functions are computationally expensive. CONORBIT employs a trust-region framework that uses interpolating radial basis function (RBF) models for the objective and constraint functions, and is an extension of the ORBIT algorithm. It uses a small margin for the RBF constraint models to facilitate the generation of feasible iterates, and extensive numerical tests confirm that such a margin is helpful in improving performance. CONORBIT is compared with other algorithms on 27 test problems, amore » chemical process optimization problem, and an automotive application. Numerical results show that CONORBIT performs better than COBYLA, a sequential penalty derivative-free method, an augmented Lagrangian method, a direct search method, and another RBF-based algorithm on the test problems and on the automotive application.« less

Orbit determination based on meteor observations using numerical integration of equations of motion

NASA Astrophysics Data System (ADS)

Dmitriev, V.; Lupovka, V.; Gritsevich, M.

2014-07-01

We review the definitions and approaches to orbital-characteristics analysis applied to photographic or video ground-based observations of meteors. A number of camera networks dedicated to meteors registration were established all over the word, including USA, Canada, Central Europe, Australia, Spain, Finland and Poland. Many of these networks are currently operational. The meteor observations are conducted from different locations hosting the network stations. Each station is equipped with at least one camera for continuous monitoring of the firmament (except possible weather restrictions). For registered multi-station meteors, it is possible to accurately determine the direction and absolute value for the meteor velocity and thus obtain the topocentric radiant. Based on topocentric radiant one further determines the heliocentric meteor orbit. We aim to reduce total uncertainty in our orbit-determination technique, keeping it even less than the accuracy of observations. The additional corrections for the zenith attraction are widely in use and are implemented, for example, here [1]. We propose a technique for meteor-orbit determination with higher accuracy. We transform the topocentric radiant in inertial (J2000) coordinate system using the model recommended by IAU [2]. The main difference if compared to the existing orbit-determination techniques is integration of ordinary differential equations of motion instead of addition correction in visible velocity for zenith attraction. The attraction of the central body (the Sun), the perturbations by Earth, Moon and other planets of the Solar System, the Earth's flattening (important in the initial moment of integration, i.e. at the moment when a meteoroid enters the atmosphere), atmospheric drag may be optionally included in the equations. In addition, reverse integration of the same equations can be performed to analyze orbital evolution preceding to meteoroid's collision with Earth. To demonstrate the developed technique, we provide calculated orbits for several cases, including well-known meteorite-producing fireballs. A comparison of our estimates with previously published ones is also provided.

The Dynamical Challenges of the Polaris Multiple System

NASA Astrophysics Data System (ADS)

Turner, David G.; Usenko, I. A.; Miroshnichenko, A. S.; Klochkova, V. G.; Panchuk, V. E.; Yang, S. L.

2006-06-01

The hierarchal triple system formed by the bright, nearby Cepheid Polaris, its visual companion (ADS 1477B), and recently resolved spectroscopic companion (ADS 1477Ab) at first sight seems well understood in terms of its astrometric properties: a parallax implying a distance of 132 +-8 pc (Hipparcos), and residuals implying an orbital inclination of 50 degrees (Wielen et al. 2000). But the recent optical detection of ADS 1477Ab by Evans et al. (2005) with the Hubble Space Telescope can be used to place independent constraints on the orbital properties of the system, once it is combined with the parameters of the spectroscopic orbit. To that end, existing radial velocity data for Polaris over the past 120 years, including previously-unpublished and recent observations obtained over the past two decades, have been collected, reanalyzed, and examined in order to improve the orbital parameters for the spectroscopic binary. There are small discrepancies in the data that may be linked to different sets of spectral lines and wavelength coverage used to infer the photospheric motion of the Cepheid, or to the inevitable problems of establishing reliable systemic velocities for a pulsating star. But the primary discrepancies lie in the implied properties of the Polaris system from the orbital solution, which seem to confirm the parallax of Polaris but not the orbital inclination, which may be edge-on. The results also conflict directly with other features of Polaris that are inferred from its other Cepheid characteristics: decreasing light amplitude, rapid period increase, location near the center of the instability strip, and possible membership in the Pleiades moving group. Such discrepancies are numerous enough to raise suspicions that there may be a fourth star in the system, although its detection may defy observers.

DASTCOM5: A Portable and Current Database of Asteroid and Comet Orbit Solutions

NASA Astrophysics Data System (ADS)

Giorgini, Jon D.; Chamberlin, Alan B.

2014-11-01

A portable direct-access database containing all NASA/JPL asteroid and comet orbit solutions, with the software to access it, is available for download (ftp://ssd.jpl.nasa.gov/pub/xfr/dastcom5.zip; unzip -ao dastcom5.zip). DASTCOM5 contains the latest heliocentric IAU76/J2000 ecliptic osculating orbital elements for all known asteroids and comets as determined by a least-squares best-fit to ground-based optical, spacecraft, and radar astrometric measurements. Other physical, dynamical, and covariance parameters are included when known. A total of 142 parameters per object are supported within DASTCOM5. This information is suitable for initializing high-precision numerical integrations, assessing orbit geometry, computing trajectory uncertainties, visual magnitude, and summarizing physical characteristics of the body. The DASTCOM5 distribution is updated as often as hourly to include newly discovered objects or orbit solution updates. It includes an ASCII index of objects that supports look-ups based on name, current or past designation, SPK ID, MPC packed-designations, or record number. DASTCOM5 is the database used by the NASA/JPL Horizons ephemeris system. It is a subset exported from a larger MySQL-based relational Small-Body Database ("SBDB") maintained at JPL. The DASTCOM5 distribution is intended for programmers comfortable with UNIX/LINUX/MacOSX command-line usage who need to develop stand-alone applications. The goal of the implementation is to provide small, fast, portable, and flexibly programmatic access to JPL comet and asteroid orbit solutions. The supplied software library, examples, and application programs have been verified under gfortran, Lahey, Intel, and Sun 32/64-bit Linux/UNIX FORTRAN compilers. A command-line tool ("dxlook") is provided to enable database access from shell or script environments.

Transient ensemble dynamics in time-independent galactic potentials

NASA Astrophysics Data System (ADS)

Mahon, M. Elaine; Abernathy, Robert A.; Bradley, Brendan O.; Kandrup, Henry E.

1995-07-01

This paper summarizes a numerical investigation of the short-time, possibly transient, behaviour of ensembles of stochastic orbits evolving in fixed non-integrable potentials, with the aim of deriving insights into the structure and evolution of galaxies. The simulations involved three different two-dimensional potentials, quite different in appearance. However, despite these differences, ensembles in all three potentials exhibit similar behaviour. This suggests that the conclusions inferred from the simulations are robust, relying only on basic topological properties, e.g., the existence of KAM tori and cantori. Generic ensembles of initial conditions, corresponding to stochastic orbits, exhibit a rapid coarse-grained approach towards a near-invariant distribution on a time-scale <>t_H, although various irregularities associated with external and/or internal irregularities can drastically accelerate this process. A principal tool in the analysis is the notion of a local Liapounov exponent, which provides a statistical characterization of the overall instability of stochastic orbits over finite time intervals. In particular, there is a precise sense in which confined stochastic orbits are less unstable, with smaller local Liapounov exponents, than are unconfined stochastic orbits.

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

Spurzem, R.; Giersz, M.; Heggie, D. C.

At least 10%-15% of nearby Sunlike stars have known Jupiter-mass planets. In contrast, very few planets are found in mature open and globular clusters such as the Hyades and 47 Tuc. We explore here the possibility that this dichotomy is due to the postformation disruption of planetary systems associated with the stellar encounters in long-lived clusters. One supporting piece of evidence for this scenario is the discovery of freely floating low-mass objects in star forming regions. We use two independent numerical approaches, a hybrid Monte Carlo and a direct N-body method, to simulate the impact of the encounters. We showmore » that the results of numerical simulations are in reasonable agreement with analytical determinations in the adiabatic and impulsive limits. They indicate that distant stellar encounters generally do not significantly modify the compact and nearly circular orbits. However, moderately close stellar encounters, which are likely to occur in dense clusters, can excite planets' orbital eccentricity and induce dynamical instability in systems that are closely packed with multiple planets. The disruption of planetary systems occurs primarily through occasional nearly parabolic, nonadiabatic encounters, though eccentricity of the planets evolves through repeated hyperbolic adiabatic encounters that accumulate small-amplitude changes. The detached planets are generally retained by the potential of their host clusters as free floaters in young stellar clusters such as {sigma} Orionis. We compute effective cross sections for the dissolution of planetary systems and show that, for all initial eccentricities, dissolution occurs on timescales that are longer than the dispersion of small stellar associations, but shorter than the age of typical open and globular clusters. Although it is much more difficult to disrupt short-period planets, close encounters can excite modest eccentricity among them, such that subsequent tidal dissipation leads to orbital decay, tidal inflation, and even disruption of the close-in planets.« less

Mapping the stability region of the 3:2 Neptune-Pluto resonance

NASA Technical Reports Server (NTRS)

Levison, H. F.; Stern, S. A.

1993-01-01

Pluto and Charon are most likely the remnants of a large number of objects that existed in the Uranus-Neptune region at early epochs of the solar system. Numerical integrations have shown that, in general, such objects were ejected from the planetary region on timescales of approximately 10(exp 7) years after Neptune and Uranus reached their current masses. It is thought that the Pluto-Charon system survived to current times without being dynamically removed in this way because it is trapped in a set of secular and mean motion resonances with Neptune. The best-known Pluto-Neptune orbit coupling is the 3:2 mean motion resonance discovered almost 30 years ago by C. Cohen and E. Hubbard. These workers showed that the resonance angle, delta is equivalent to 3(lambda(sub P)) - 2(lambda(sub N)) - omega-bar(sub P) where omega-bar(sub P) is the longitude of perihelion of the Pluto-Charon system, and lambda(sub N) and lambda(sub P) are the mean longitude of Neptune and Pluto-Charon respectively, librates about 180 deg with an amplitude, A(sub delta), of 76 deg. A numerical simulation project to map out the stability region of the 3:2 resonance is reported. The results of these simulations are important to understanding whether Pluto's long-term heliocentric stability requires only the 3:2 resonance, or whether it instead requires one or more of the other Pluto-Neptune resonances. Our study also has another important application. By investigating stability timescales as a function of orbital elements, we gain insight into the fraction of orbital phase space which the stable 3:2 resonance occupies. This fraction is directly related to the probability that the Pluto-Charon system (and possibly other small bodies) could have been captured into this resonance.

The Spin-orbit resonance of Mercury: a Hamiltonian approach

NASA Astrophysics Data System (ADS)

D'Hoedt, S.; Lemaitre, A.

2005-04-01

One of the main characteristics of Mercury is its 3:2 spin-orbit resonance, combined with a 1:1 resonance between the orbital node of its orbit and the angle describing the precession of the rotation axis, both measured on the ecliptic plane. We build an analytical model, using Hamiltonian formalism, that takes into account this phenomenon thanks to the introduction of three resonant variables and conjugated momenta. We calculate the equilibria corresponding to four different configurations, which means four completely different values of the (ecliptic) obliquity; in particular, we focus on the present (stable) situation of Mercury, and thanks to several canonical transformations, we obtain, near the equilibrium, three pairs of angle-action variables, and consequently, three basic frequencies. Let us note that the model is as simple as possible: the gravitational potential is limited to the second degree terms (the only ones for which a value can be presently given), and the orbit of Mercury is Keplerian. The numerical values obtained by our simplified model are validated by the coherence with existing complete numerical models.

Design of multi-body Lambert type orbits with specified departure and arrival positions

NASA Astrophysics Data System (ADS)

Ishii, Nobuaki; Kawaguchi, Jun'ichiro; Matsuo, Hiroki

1991-10-01

A new procedure for designing a multi-body Lambert type orbit comprising a multiple swingby process is developed, aiming at relieving a numerical difficulty inherent to a highly nonlinear swingby mechanism. The proposed algorithm, Recursive Multi-Step Linearization, first divides a whole orbit into several trajectory segments. Then, with a maximum use of piecewised transition matrices, a segmentized orbit is repeatedly upgraded until an approximated orbit initially based on a patched conics method eventually converges. In application to the four body earth-moon system with sun's gravitation, one of the double lunar swingby orbits including 12 lunar swingbys is successfully designed without any velocity mismatch.

Topological classification of periodic orbits in the Kuramoto-Sivashinsky equation

NASA Astrophysics Data System (ADS)

Dong, Chengwei

2018-05-01

In this paper, we systematically research periodic orbits of the Kuramoto-Sivashinsky equation (KSe). In order to overcome the difficulties in the establishment of one-dimensional symbolic dynamics in the nonlinear system, two basic periodic orbits can be used as basic building blocks to initialize cycle searching, and we use the variational method to numerically determine all the periodic orbits under parameter ν = 0.02991. The symbolic dynamics based on trajectory topology are very successful for classifying all short periodic orbits in the KSe. The current research can be conveniently adapted to the identification and classification of periodic orbits in other chaotic systems.

Minimum fuel coplanar aeroassisted orbital transfer using collocation and nonlinear programming

NASA Technical Reports Server (NTRS)

Shi, Yun Yuan; Young, D. H.

1991-01-01

The fuel optimal control problem arising in coplanar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) without plane change. The basic approach here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the coplanar aeroassisted HEO to LEO orbit transfer consists of three phases. In the first phase, the transfer begins with a deorbit impulse at HEO which injects the vehicle into a elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and drag modulation to satisfy heating constraints and to exit the atmosphere with the desired flight path angle and velocity so that the apogee of the exit orbit is the altitude of the desired LEO. Finally, the second impulse is required to circularize the orbit at LEO. The performance index is maximum final mass. Simulation results show that the coplanar aerocapture is quite different from the case where orbital plane changes are made inside the atmosphere. In the latter case, the vehicle has to penetrate deeper into the atmosphere to perform the desired orbital plane change. For the coplanar case, the vehicle needs only to penetrate the atmosphere deep enough to reduce the exit velocity so the vehicle can be captured at the desired LEO. The peak heating rates are lower and the entry corridor is wider. From the thermal protection point of view, the coplanar transfer may be desirable. Parametric studies also show the maximum peak heating rates and the entry corridor width are functions of maximum lift coefficient. The problem is solved using a direct optimization technique which uses piecewise polynomial representation for the states and controls and collocation to represent the differential equations. This converts the optimal control problem into a nonlinear programming problem which is solved numerically by using a modified version of NPSOL. Solutions were obtained for the described problem for cases with and without heating constraints. The method appears to be more robust than other optimization methods. In addition, the method can handle complex dynamical constraints.

New variational principles for locating periodic orbits of differential equations.

PubMed

Boghosian, Bruce M; Fazendeiro, Luis M; Lätt, Jonas; Tang, Hui; Coveney, Peter V

2011-06-13

We present new methods for the determination of periodic orbits of general dynamical systems. Iterative algorithms for finding solutions by these methods, for both the exact continuum case, and for approximate discrete representations suitable for numerical implementation, are discussed. Finally, we describe our approach to the computation of unstable periodic orbits of the driven Navier-Stokes equations, simulated using the lattice Boltzmann equation.

Method and apparatus for relative navigation using reflected GPS signals

NASA Technical Reports Server (NTRS)

Cohen, Ian R. (Inventor); Boegner, Jr., Gregory J. (Inventor)

2010-01-01

A method and system to passively navigate an orbiting moving body towards an orbiting target using reflected GPS signals. A pair of antennas is employed to receive both direct signals from a plurality of GPS satellites and a second antenna to receive GPS signals reflected off an orbiting target. The direct and reflected signals are processed and compared to determine the relative distance and position of the orbiting moving body relative to the orbiting target.

Post-Newtonian equations of motion for LEO debris objects and space-based acquisition, pointing and tracking laser systems

NASA Astrophysics Data System (ADS)

Gambi, J. M.; García del Pino, M. L.; Gschwindl, J.; Weinmüller, E. B.

2017-12-01

This paper deals with the problem of throwing middle-sized low Earth orbit debris objects into the atmosphere via laser ablation. The post-Newtonian equations here provided allow (hypothetical) space-based acquisition, pointing and tracking systems endowed with very narrow laser beams to reach the pointing accuracy presently prescribed. In fact, whatever the orbital elements of these objects may be, these equations will allow the operators to account for the corrections needed to balance the deviations of the line of sight directions due to the curvature of the paths the laser beams are to travel along. To minimize the respective corrections, the systems will have to perform initial positioning manoeuvres, and the shooting point-ahead angles will have to be adapted in real time. The enclosed numerical experiments suggest that neglecting these measures will cause fatal errors, due to differences in the actual locations of the objects comparable to their size.

Atomic oxygen erosion considerations for spacecraft materials selection

NASA Technical Reports Server (NTRS)

Whitaker, Ann F.; Kamenetzky, Rachel R.

1993-01-01

The Long Duration Exposure Facility (LDEF) satellite carried 57 experiments that were designed to define the low-Earth orbit (LEO) space environment and to evaluate the impact of this environment on potential engineering materials and material processes. Deployed by the Shuttle Challenger in April of 1984, LDEF made over 32,000 orbits before being retrieved nearly 6 years later by the Shuttle Columbia in January of 1990. The Solar Array Passive LDEF Experiment (SAMPLE) AO171 contained approximately 300 specimens, representing numerous material classes and material processes. AO171 was located on LDEF in position A8 at a yaw of 38.1 degrees from the ram direction and was subjected to an atomic oxygen (AO) fluence of 6.93 x 10(exp 21) atoms/sq cm. LDEF AO171 data, as well as short-term shuttle data, will be discussed in this paper as it applies to engineering design applications of composites, bulk and thin film polymers, glassy ceramics, thermal control paints, and metals subjected to AO erosion.

On the chaotic diffusion in multidimensional Hamiltonian systems

NASA Astrophysics Data System (ADS)

Cincotta, P. M.; Giordano, C. M.; Martí, J. G.; Beaugé, C.

2018-01-01

We present numerical evidence that diffusion in the herein studied multidimensional near-integrable Hamiltonian systems departs from a normal process, at least for realistic timescales. Therefore, the derivation of a diffusion coefficient from a linear fit on the variance evolution of the unperturbed integrals fails. We review some topics on diffusion in the Arnold Hamiltonian and yield numerical and theoretical arguments to show that in the examples we considered, a standard coefficient would not provide a good estimation of the speed of diffusion. However, numerical experiments concerning diffusion would provide reliable information about the stability of the motion within chaotic regions of the phase space. In this direction, we present an extension of previous results concerning the dynamical structure of the Laplace resonance in Gliese-876 planetary system considering variations of the orbital parameters accordingly to the error introduced by the radial velocity determination. We found that a slight variation of the eccentricity of planet c would destabilize the inner region of the resonance that, though chaotic, shows stable when adopting the best fit values for the parameters.

Launch window analysis of satellites in high eccentricity or large circular orbits

NASA Technical Reports Server (NTRS)

Renard, M. L.; Bhate, S. K.; Sridharan, R.

1973-01-01

Numerical methods and computer programs for studying the stability and evolution of orbits of large eccentricity are presented. Methods for determining launch windows and target dates are developed. Mathematical models are prepared to analyze the characteristics of specific missions.

Preliminary orbit determination for lunar satellites.

NASA Technical Reports Server (NTRS)

Lancaster, E. R.

1973-01-01

Methods for the determination of orbits of artificial lunar satellites from earth-based range rate measurements developed by Koskela (1964) and Bateman et al. (1966) are simplified and extended to include range measurements along with range rate measurements. For illustration, a numerical example is presented.

A Numerical Method for Integrating Orbits

NASA Astrophysics Data System (ADS)

Sahakyan, Karen P.; Melkonyan, Anahit A.; Hayrapetyan, S. R.

2007-08-01

A numerical method based of trigonometric polynomials for integrating of ordinary differential equations of first and second order is suggested. This method is a trigonometric analogue of Everhart's method and can be especially useful for periodical trajectories.

Numerical computation of orbits and rigorous verification of existence of snapback repellers.

PubMed

Peng, Chen-Chang

2007-03-01

In this paper we show how analysis from numerical computation of orbits can be applied to prove the existence of snapback repellers in discrete dynamical systems. That is, we present a computer-assisted method to prove the existence of a snapback repeller of a specific map. The existence of a snapback repeller of a dynamical system implies that it has chaotic behavior [F. R. Marotto, J. Math. Anal. Appl. 63, 199 (1978)]. The method is applied to the logistic map and the discrete predator-prey system.

Methodology of Numerical Optimization for Orbital Parameters of Binary Systems

NASA Astrophysics Data System (ADS)

Araya, I.; Curé, M.

2010-02-01

The use of a numerical method of maximization (or minimization) in optimization processes allows us to obtain a great amount of solutions. Therefore, we can find a global maximum or minimum of the problem, but this is only possible if we used a suitable methodology. To obtain the global optimum values, we use the genetic algorithm called PIKAIA (P. Charbonneau) and other four algorithms implemented in Mathematica. We demonstrate that derived orbital parameters of binary systems published in some papers, based on radial velocity measurements, are local minimum instead of global ones.

Code Blue on Orbit: Treating Cardiac Arrest on the ISS

NASA Technical Reports Server (NTRS)

Bacal, Kira; Redmond, Melissa

2004-01-01

As a result of the Columbia tragedy on February 1,2003, the International Space Station (ISS) crew size has been temporarily reduced from three to two. This change forces adaptations in many operational procedures used by the crew, including medical protocols which were designed for scenarios involving one casualty and two caregivers. The Office of Space Medicine directed that the procedure for the resuscitation of a crewmember in cardiac arrest be rewritten for use by a single care provider. Methods: Adaptation of this procedure made use of current American Heart Association Advanced Cardiac Life Support (ACLS) procedures and reflects necessary compromises between the realities of the operational environment and prompt provision of medical care. Results: Numerous changes were incorporated due to the diminution in available personnel, including substitution of endotracheal rather than intravenous delivery of drugs, more rapid defibrillation, addition of a precordial thump, removal of transcutaneous pacing, streamlining of procedural steps, and clarification of termination criteria. Discussion: The on-orbit care available to the ISS crewmembers is constrained by numerous factors, including crew medical training, minimal medical assets, limited air/ground communication , and a single caregiver for the foreseeable future. All of these combine to make a successful resuscitation unlikely, however, this procedure must ultimately deal with not only the patient's welfare, but also that of the caregiver, the mission, and the program.

Study on galloping behavior of iced eight bundle conductor transmission lines

NASA Astrophysics Data System (ADS)

Zhou, Linshu; Yan, Bo; Zhang, Liang; Zhou, Song

2016-02-01

Wind tunnel test was carried out to obtain the aerodynamic coefficients of an eight bundle conductor accreted with crescent-shaped ice. A user-defined cable element with torsional degree of freedom is developed in ABAQUS software to capture the torsional deformation of the iced conductors during galloping. By means of the user-defined cable element, different damping ratios in in-plane, out-of-plane and torsional directions of the conductors can be defined and the aerodynamic forces varying with their motion status can be exerted on the conductors conveniently when ABAQUS is used to simulate galloping of transmission lines. A wind tunnel test to model galloping of an iced eight bundle conductor segment was carried out, and the validity of the numerical simulation method is demonstrated by the agreement of the galloping orbit of the bundle conductor segment model recorded in the test and that by the numerical simulation. Furthermore, galloping behavior, including dynamic responses, galloping orbits, frequencies, vibration modes and amplitudes, of typical iced eight bundle conductor transmission lines in the cases of different span lengths, initial tensions in sub-conductors, wind velocities, angles of wind attack and damping ratios is studied, and the galloping behavior of the lines with internal resonance conditions is discussed. The obtained results may provide a fundamental tool for the development of anti-galloping techniques of eight bundle conductor transmission lines.

Concurrent image-based visual servoing with adaptive zooming for non-cooperative rendezvous maneuvers

NASA Astrophysics Data System (ADS)

Pomares, Jorge; Felicetti, Leonard; Pérez, Javier; Emami, M. Reza

2018-02-01

An image-based servo controller for the guidance of a spacecraft during non-cooperative rendezvous is presented in this paper. The controller directly utilizes the visual features from image frames of a target spacecraft for computing both attitude and orbital maneuvers concurrently. The utilization of adaptive optics, such as zooming cameras, is also addressed through developing an invariant-image servo controller. The controller allows for performing rendezvous maneuvers independently from the adjustments of the camera focal length, improving the performance and versatility of maneuvers. The stability of the proposed control scheme is proven analytically in the invariant space, and its viability is explored through numerical simulations.

Apollo 10 Command/Service Modules seen from Lunar Module after separation

NASA Image and Video Library

1969-05-22

AS10-27-3873 (22 May 1969) --- The Apollo 10 Command and Service Modules (CSM) are photographed from the Lunar Module (LM) after CSM/LM separation in lunar orbit. The CSM was about 175 statute miles east of Smyth's Sea and was above the rough terrain which is typical of the lunar far side. The eastward oblique view of the lunar surface is centered near 105 degrees east longitude and 1 degree north latitude. The horizon is approximately 600 kilometers (374 statute miles) away. Numerous bright craters and the absence of shadows show that the sun was almost directly overhead when this photograph was taken.

Numerical calculation of ion polarization in the NICA collider

NASA Astrophysics Data System (ADS)

Kovalenko, A. D.; Butenko, A. V.; Kekelidze, V. D.; Mikhaylov, V. A.; Kondratenko, M. A.; Kondratenko, A. M.; Filatov, Yu N.

2016-02-01

The NICA Collider with two solenoid Siberian snakes is “transparent” to the spin. The collider transparent to the spin provides a unique capability to control any polarization direction of protons and deuterons using additional weak solenoids without affecting orbital parameters of the beam. The spin tune induced by the control solenoids must significantly exceed the strength of the zero-integer spin resonance, which contains a coherent part associated with errors in the collider's magnetic structure and an incoherent part associated with the beam emittances. We present calculations of the coherent part of the resonance strength in the NICA collider for proton and deuteron beams.

KSC-04pd1428

NASA Image and Video Library

2004-07-07

KENNEDY SPACE CENTER, FLA. - - Workers in the Orbiter Processing Facility complete the installation of the Reinforced Carbon-Carbon panel on Discovery. The chin panel is the smile-shaped section of RCC directly below the nose cap that provides a thermal barrier during re-entry. The nose cap, with chin panel, was removed from the vehicle in the summer of 2003 and returned to the vendor, where it underwent numerous forms of Non-Destructive Evaluation. These tests included X-ray, ultrasound and eddy current to ensure its structural integrity prior to reinstallation. Discovery is designated as the Return to Flight vehicle for mission STS-114, no earlier than March 2005.

KSC-04pd1424

NASA Image and Video Library

2004-07-07

KENNEDY SPACE CENTER, FLA. - Workers in the Orbiter Processing Facility lift the Reinforced Carbon-Carbon (RCC) chin panel to install on Discovery. The chin panel is the smile-shaped section of RCC directly below the nose cap that provides a thermal barrier during re-entry. The nose cap, with chin panel, was removed from the vehicle in the summer of 2003 and returned to the vendor, where it underwent numerous forms of Non-Destructive Evaluation. These tests included X-ray, ultrasound and eddy current to ensure its structural integrity prior to reinstallation. Discovery is designated as the Return to Flight vehicle for mission STS-114, no earlier than March 2005.

KSC-04pd1425

NASA Image and Video Library

2004-07-07

KENNEDY SPACE CENTER, FLA. - Workers in the Orbiter Processing Facility lift the Reinforced Carbon-Carbon (RCC) chin panel into place on Discovery. The chin panel is the smile-shaped section of RCC directly below the nose cap that provides a thermal barrier during re-entry. The nose cap, with chin panel, was removed from the vehicle in the summer of 2003 and returned to the vendor, where it underwent numerous forms of Non-Destructive Evaluation. These tests included X-ray, ultrasound and eddy current to ensure its structural integrity prior to reinstallation. Discovery is designated as the Return to Flight vehicle for mission STS-114, no earlier than March 2005.

KSC-04pd1423

NASA Image and Video Library

2004-07-07

KENNEDY SPACE CENTER, FLA. - Workers in the Orbiter Processing Facility prepare the Reinforced Carbon-Carbon (RCC) chin panel to install on Discovery. The chin panel is the smile-shaped section of RCC directly below the nose cap that provides a thermal barrier during re-entry. The nose cap, with chin panel, was removed from the vehicle in the summer of 2003 and returned to the vendor, where it underwent numerous forms of Non-Destructive Evaluation. These tests included X-ray, ultrasound and eddy current to ensure its structural integrity prior to reinstallation. Discovery is designated as the Return to Flight vehicle for mission STS-114, no earlier than March 2005.

KSC-04pd1427

NASA Image and Video Library

2004-07-07

KENNEDY SPACE CENTER, FLA. - - Workers in the Orbiter Processing Facility check the placement of the Reinforced Carbon-Carbon chin panel on Discovery. The chin panel is the smile-shaped section of RCC directly below the nose cap that provides a thermal barrier during re-entry. The nose cap, with chin panel, was removed from the vehicle in the summer of 2003 and returned to the vendor, where it underwent numerous forms of Non-Destructive Evaluation. These tests included X-ray, ultrasound and eddy current to ensure its structural integrity prior to reinstallation. Discovery is designated as the Return to Flight vehicle for mission STS-114, no earlier than March 2005.

KSC-04pd1426

NASA Image and Video Library

2004-07-07

KENNEDY SPACE CENTER, FLA. - Workers in the Orbiter Processing Facility check the placement of the Reinforced Carbon-Carbon (RCC) chin panel on Discovery. . The chin panel is the smile-shaped section of RCC directly below the nose cap that provides a thermal barrier during re-entry. The nose cap, with chin panel, was removed from the vehicle in the summer of 2003 and returned to the vendor, where it underwent numerous forms of Non-Destructive Evaluation. These tests included X-ray, ultrasound and eddy current to ensure its structural integrity prior to reinstallation. Discovery is designated as the Return to Flight vehicle for mission STS-114, no earlier than March 2005.

Spin-orbit coupling in quasiparticle studies of topological insulators

NASA Astrophysics Data System (ADS)

Aguilera, Irene; Friedrich, Christoph; Blügel, Stefan

2013-10-01

We present one-shot GW calculations of the bulk electronic structure of the topological insulators Bi2Se3 and Bi2Te3 within the all-electron full-potential linearized augmented-plane-wave formalism. We compare three different ways of treating the spin-orbit interaction in calculating the quasiparticle energies: (i) The spin-orbit coupling (SOC) is already incorporated in the noninteracting system that serves as starting point for the quasiparticle correction. (ii) The SOC is added in a second-variation approach only after the quasiparticle calculation has been performed in the absence of SOC. We found that the approximate treatment (ii) yields most quasiparticle bands with reasonable accuracy but does fail in the important band-gap region, where the SOC gives rise to a band inversion relevant for the topological properties of these materials. For example, Bi2Se3 is just on the brink of becoming a trivial semiconductor within this approximate approach, while it maintains its topological properties in the case of the consistent treatment (i). Finally, we consider another approach (iii), in which the SOC is included in the Green function G as in (i), but neglected in the calculation of the screened Coulomb potential W. This approach gives results in very good agreement with the full treatment (i), but with a smaller numerical effort. We conclude that, in the high-symmetry directions studied, bulk Bi2Se3 is a direct-gap and Bi2Te3 an indirect-gap semiconductor with band gaps of 0.20 and 0.19 eV, respectively.

Calculation of precision satellite orbits with nonsingular elements /VOP formulation/

NASA Technical Reports Server (NTRS)

Velez, C. E.; Cefola, P. J.; Long, A. C.; Nimitz, K. S.

1974-01-01

Review of some results obtained in an effort to develop efficient, high-precision trajectory computation processes for artificial satellites by optimum selection of the form of the equations of motion of the satellite and the numerical integration method. In particular, the matching of a Gaussian variation-of-parameter (VOP) formulation is considered which is expressed in terms of equinoctial orbital elements and partially decouples the motion of the orbital frame from motion within the orbital frame. The performance of the resulting orbit generators is then compared with the popular classical Cowell/Gauss-Jackson formulation/integrator pair for two distinctly different orbit types - namely, the orbit of the ATS satellite at near-geosynchronous conditions and the near-circular orbit of the GEOS-C satellite at 1000 km.

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.

Numerically Integrated Orbits of the Major Saturnian Satellites fit to Earthbased Observations

NASA Technical Reports Server (NTRS)

Jacobson, R. A.; Vaughan, R. M.

1993-01-01

We have fit numerically integrated orbits of the eight major satellites of Saturn to all available astrometric and meridian circle observations for the period of 1971 to 1992. The integration was carried out in cartesian coordinates in the J2000 system. The force model included the gravitational effects of the oblate primary, the mutual perturbations of the satellites, and perturbations due to Jupiter and the Sun. Values of the gravitational parameters of the Saturnian system, e.g. planet and satellite masses, were taken from Campbell, et. al., 1989, only the epoch state vectors of the satellites were adjusted to obtain orbits which fit the observations. All astrometric data was processed in the form of satellite relative positions which were weighted according to observer and opposition to reflect the varying data quality...

MALBEC: a new CUDA-C ray-tracer in general relativity

NASA Astrophysics Data System (ADS)

Quiroga, G. D.

2018-06-01

A new CUDA-C code for tracing orbits around non-charged black holes is presented. This code, named MALBEC, take advantage of the graphic processing units and the CUDA platform for tracking null and timelike test particles in Schwarzschild and Kerr. Also, a new general set of equations that describe the closed circular orbits of any timelike test particle in the equatorial plane is derived. These equations are extremely important in order to compare the analytical behavior of the orbits with the numerical results and verify the correct implementation of the Runge-Kutta algorithm in MALBEC. Finally, other numerical tests are performed, demonstrating that MALBEC is able to reproduce some well-known results in these metrics in a faster and more efficient way than a conventional CPU implementation.

Manipulator trajectories during orbital servicing mission: numerical simulations and experiments on microgravity simulator

NASA Astrophysics Data System (ADS)

Rybus, T.; Seweryn, K.

2018-06-01

It is considered to use a manipulator-equipped satellite for performing On-Orbit Servicing (OOS) or Active Debris Removal (ADR) missions. In this paper, several possible approaches are reviewed for end-effector (EE) trajectory planning in the Cartesian space, such as application of the Bézier curves for singularity avoidance and method for trajectory optimization. The results of numerical simulations for a satellite equipped with a 7 degree-of-freedom (DoF) manipulator and results of experiments performed on a planar air-bearing microgravity simulator for a simplified two-dimensional (2D) case with a 2-DoF manipulator are presented. Differences between the free-floating case and the case where Attitude and Orbit Control Systems (AOCS) keep constant position and orientation of the satellite are also shown.

Stern-Gerlach-like approach to electron orbital angular momentum measurement

DOE PAGES

Harvey, Tyler R.; Grillo, Vincenzo; McMorran, Benjamin J.

2017-02-28

Many methods now exist to prepare free electrons into orbital-angular-momentum states, and the predicted applications of these electron states as probes of materials and scattering processes are numerous. The development of electron orbital-angular-momentum measurement techniques has lagged behind. We show that coupling between electron orbital angular momentum and a spatially varying magnetic field produces an angular-momentum-dependent focusing effect. We propose a design for an orbital-angular-momentum measurement device built on this principle. As the method of measurement is noninterferometric, the device works equally well for mixed, superposed, and pure final orbital-angular-momentum states. The energy and orbital-angular-momentum distributions of inelastically scattered electronsmore » may be simultaneously measurable with this technique.« less

Stern-Gerlach-like approach to electron orbital angular momentum measurement

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

Harvey, Tyler R.; Grillo, Vincenzo; McMorran, Benjamin J.

Many methods now exist to prepare free electrons into orbital-angular-momentum states, and the predicted applications of these electron states as probes of materials and scattering processes are numerous. The development of electron orbital-angular-momentum measurement techniques has lagged behind. We show that coupling between electron orbital angular momentum and a spatially varying magnetic field produces an angular-momentum-dependent focusing effect. We propose a design for an orbital-angular-momentum measurement device built on this principle. As the method of measurement is noninterferometric, the device works equally well for mixed, superposed, and pure final orbital-angular-momentum states. The energy and orbital-angular-momentum distributions of inelastically scattered electronsmore » may be simultaneously measurable with this technique.« less

A Dynamical Systems Approach to the Design of the Science Orbit Around Europa

NASA Technical Reports Server (NTRS)

Gomez, Gerard; Lara, Martin; Russell, Ryan P.

2006-01-01

The science orbit for a future mission to Europa requires low eccentricity, low altitude, and high inclination. However, high inclination orbits around planetary satellites are unstable due to third-body perturbations. Without control, the orbiter impacts Europa after few weeks. To minimize control, a tour over the stable-unstable, averaged manifolds of unstable frozen orbits has been suggested. We proceed with the unaveraged equations and study the manifolds of unstable orbits that are periodic in a rotating frame attached to Europa. Massive numerical computation helps in understanding the unstable dynamics close to Europa, and, thus, in selecting long lifetime high inclination orbits. A final test of a selected set of initial conditions on a high fidelity, ephemeris model, validate the results.

New meteoroid model predictions for directional impacts on LDEF

NASA Technical Reports Server (NTRS)

Divine, Neil; Aguero, Rene C.

1992-01-01

An extensive body of data, from meteors, zodiacal light, spacecraft-borne impact detectors (helios, Pioneer, Galileo, and Ulysses), and other sources, forms the basis of a new numerical model for the distributions of interplanetary meteoroids. For each of the five populations in this model it is possible to evaluate meteoroid concentration and flux for oriented surfaces or detectors having arbitrary position and velocity in interplanetary space (Divine, 1992, in preparation). For a spacecraft in geocentric orbit, the effects of gravitational focusing and shielding by the Earth were derived with full attention to the directionality of the particles, both on approach (i.e., relative to a massless Earth) and at the target. This modeling approach was exercised to provide an estimate of meteoroid fluence for each of several oriented surfaces on the Long Duration Exposure Facility (LDEF).

Early Paleogene Orbital Variations in Atmospheric CO2 and New Astronomical Solutions

NASA Astrophysics Data System (ADS)

Zeebe, R. E.

2017-12-01

Geologic records across the globe show prominent variations on orbital time scales during numerous epochs going back hundreds of millions of years. The origin of the Milankovic cycles are variations in orbital parameters of the bodies of the Solar System. On long time scales, the orbital variations can not be computed analytically because of the chaotic nature of the Solar System. Thus, numerical solutions are used to estimate changes in, e.g., Earth's orbital parameters in the past. The orbital solutions represent the backbone of cyclostratigraphy and astrochronology, now widely used in geology and paleoclimatology. Hitherto only two solutions for Earth's eccentricity appear to be used in paleoclimate studies, provided by two different groups that integrated the full Solar System equations over the past >100 Myr. In this presentation, I will touch on the basic physics behind, and present new results of, accurate Solar System integrations for Earth's eccentricity over the past hundred million years. I will discuss various limitations within the framework of the present simulations and compare the results to existing solutions. Furthermore, I will present new results from practical applications of such orbital solutions, including effects of orbital forcing on coupled climate- and carbon cycle variations. For instance, we have recently revealed a mechanism for a large lag between changes in carbon isotope ratios and eccentricity at the 400-kyr period, which has been observed in Paleocene, Oligocene, and Miocene sections. Finally, I will present the first estimates of orbital-scale variations in atmospheric CO2 during the early Paleogene.

Warsaw Catalogue of cometary orbits: 119 near-parabolic comets

NASA Astrophysics Data System (ADS)

Królikowska, Małgorzata

2014-07-01

Context. The dynamical evolution of near-parabolic comets strongly depends on the starting values of the orbital elements derived from the positional observations. In addition, when drawing conclusions about the origin of these objects, it is crucial to control the uncertainties of orbital elements at each stage of the dynamical evolution. Aims: I apply a completely homogeneous approach to determine the cometary orbits and their uncertainties. The resulting catalogue is suitable for the investigation of the origin and future of near-parabolic comets. Methods: First, osculating orbits were determined on the basis of positional data. Second, the dynamical calculations were performed backwards and forwards up to 250 au from the Sun to derive original and future barycentric orbits for each comet. In the present investigation of dynamical evolution, the numerical calculations for a given object start from the swarm of virtual comets constructed using the previously determined osculating (nominal) orbit. In this way, the uncertainties of orbital elements were derived at the end of numerical calculations. Results: Homogeneous sets of orbital elements for osculating, original and future orbits are given. The catalogue of 119 cometary orbits constitutes about 70 per cent of all the first class so-called Oort spike comets discovered during the period 1801-2010 and about 90 per cent of those discovered in 1951-2010, for which observations were completed at the end of 2013. Non-gravitational (NG) orbits are derived for 45 comets, including asymmetric NG solution for six of them. Additionally, the new method for cometary orbit-quality assessment is applied for all these objects. The catalogue is available at http://ssdp.cbk.waw.pl/LPCs and also at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/567/A126

Analysis of orbital perturbations acting on objects in orbits near geosynchronous earth orbit

NASA Technical Reports Server (NTRS)

Friesen, Larry J.; Jackson, Albert A., IV; Zook, Herbert A.; Kessler, Donald J.

1992-01-01

The paper presents a numerical investigation of orbital evolution for objects started in GEO or in orbits near GEO in order to study potential orbital debris problems in this region. Perturbations simulated include nonspherical terms in the earth's geopotential field, lunar and solar gravity, and solar radiation pressure. Objects simulated include large satellites, for which solar radiation pressure is insignificant, and small particles, for which solar radiation pressure is an important force. Results for large satellites are largely in agreement with previous GEO studies that used classical perturbation techniques. The orbit plane of GEO satellites placed in a stable plane orbit inclined approximately 7.3 deg to the equator experience very little precession, remaining always within 1.2 percent of their initial orientation. Solar radiation pressure generates two major effects on small particles: an orbital eccentricity oscillation anticipated from previous research, and an oscillation in orbital inclination.

A Viking satellite orbit trim strategy

NASA Technical Reports Server (NTRS)

Hintz, G. R.

1971-01-01

One strategy is submitted for meeting the varied and stringent requirements of the Viking Project on the control of the satellite orbit to obtain reconnaissance and to prepare for lander release. To satisfy these requirements, different orbit trim maneuver strategies were developed for two typical Viking missions. In addition, a summary of recent numerical results is included to show that this strategy satisfies the mission requirements which have been identified.

General view of the flight deck of the Orbiter Discovery ...

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

General view of the flight deck of the Orbiter Discovery looking forward from behind the commander's seat looking towards the pilot's station. Note the numerous Velcro pads located throughout the crew compartment, used to secure frequently used items when in zero gravity. This image 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

Characteristics of Quasi-Terminator Orbits Near Primitive Bodies

NASA Technical Reports Server (NTRS)

Broschart, Stephen B.; Lantoine, Gregory; Grebow, Daniel J.

2013-01-01

Quasi-terminator orbits are introduced as a class of quasi-periodic trajectories in the solar radiation pressure (SRP) perturbed Hill dynamics. These orbits offer significant displacements along the Sun-direction without the need for station-keeping maneuvers. Thus, quasi-terminator orbits have application to primitive-body missions, where a variety of observation geometries relative to the Sun (or other directions) can be achieved. This paper describes the characteristics of these orbits as a function of normalized SRP strength and invariant torus frequency ratio and presents a discussion of mission design considerations for a global surface mapping orbit design.

Diagrammatic theory of transition of pendulum like systems. [orbit-orbit and spin-orbit gravitational resonance interactions

NASA Technical Reports Server (NTRS)

Yoder, C. F.

1979-01-01

Orbit-orbit and spin-orbit gravitational resonances are analyzed using the model of a rigid pendulum subject to both a time-dependent periodic torque and a constant applied torque. First, a descriptive model of passage through resonance is developed from an examination of the polynomial equation that determines the extremes of the momentum variable. From this study, a probability estimate for capture into libration is derived. Second, a lowest order solution is constructed and compared with the solution obtained from numerical integration. The steps necessary to systematically improve this solution are also discussed. Finally, the effect of a dissipative term in the pendulum equation is analyzed.

Orbital and Collisional Evolution of the Irregular Satellites

NASA Astrophysics Data System (ADS)

Nesvorný, David; Alvarellos, Jose L. A.; Dones, Luke; Levison, Harold F.

2003-07-01

The irregular moons of the Jovian planets are a puzzling part of the solar system inventory. Unlike regular satellites, the irregular moons revolve around planets at large distances in tilted and eccentric orbits. Their origin, which is intimately linked with the origin of the planets themselves, is yet to be explained. Here we report a study of the orbital and collisional evolution of the irregular satellites from times after their formation to the present epoch. The purpose of this study is to find out the features of the observed irregular moons that can be attributed to this evolution and separate them from signatures of the formation process. We numerically integrated ~60,000 test satellite orbits to map orbital locations that are stable on long time intervals. We found that the orbits highly inclined to the ecliptic are unstable due to the effect of the Kozai resonance, which radially stretches them so that satellites either escape from the Hill sphere, collide with massive inner moons, or impact the parent planet. We also found that prograde satellite orbits with large semimajor axes are unstable due to the effect of the evection resonance, which locks the orbit's apocenter to the apparent motion of the Sun around the parent planet. In such a resonance, the effect of solar tides on a resonant moon accumulates at each apocenter passage of the moon, which causes a radially outward drift of its orbital apocenter; once close to the Hill sphere, the moon escapes. By contrast, retrograde moons with large orbital semimajor axes are long-lived. We have developed an analytic model of the distant satellite orbits and used it to explain the results of our numerical experiments. In particular, we analytically studied the effect of the Kozai resonance. We numerically integrated the orbits of the 50 irregular moons (known by 2002 August 16) for 108 yr. All orbits were stable on this time interval and did not show any macroscopic variations that would indicate instabilities operating on longer time spans. The average orbits calculated from this experiment were then used to probe the collisional evolution of the irregular satellite systems. We found that (1) the large irregular moons must have collisionally eliminated many small irregular moons, thus shaping their population to the currently observed structures; (2) some dynamical families of satellites could have been formed by catastrophic collisions among the irregular moons; and (3) Phoebe's surface must have been heavily cratered by impacts from an extinct population of Saturnian irregular moons, much larger than the present one. We therefore suggest that the Cassini imaging of Phoebe in 2004 can be used to determine the primordial population of small irregular moons of Saturn. In such a case, we will also better understand the overall efficiency of the formation process of the irregular satellites and the physical conditions that existed during planetary formation. We discovered two dynamical families of tightly clustered orbits within the Jovian retrograde group. We believe that these two clusters may be the remnants of two collisionally disrupted bodies. We found that the entire Jovian retrograde group and the Saturnian inclination groups were not produced by single breakups, because the ejection velocities derived from the orbital structures of these groups greatly exceed values calculated by modern numerical models of collisional breakups. Taken together, the evidence presented here suggests that many properties of the irregular moons previously assigned to their formation process may have resulted from their later dynamical and collisional evolution. Finally, we have found that several irregular moons, namely, Pasiphae, Sinope, S/2001 J10, S/2000 S5, S/2000 S6, and S/2000 S3, have orbits characterized by secular resonances. The orbits of some of these moons apparently evolved by some slow dissipative process in the past and became captured in tiny resonant volumes.

Effective Power-Law Dependence of Lyapunov Exponents on the Central Mass in Galaxies

NASA Technical Reports Server (NTRS)

Delis, N.; Efthymiopoulos, C.; Kalapotharakos, C.

2015-01-01

Using both numerical and analytical approaches, we demonstrate the existence of an effective power-law relation L alpha m(sup p) between themean Lyapunov exponent L of stellar orbits chaotically scattered by a supermassive black hole (BH) in the centre of a galaxy and the mass parameter m, i.e. ratio of the mass of the BH over the mass of the galaxy. The exponent p is found numerically to obtain values in the range p approximately equals 0.3-0.5. We propose a theoretical interpretation of these exponents, based on estimates of local 'stretching numbers', i.e. local Lyapunov exponents at successive transits of the orbits through the BH's sphere of influence. We thus predict p = 2/3 - q with q approximately equaling 0.1-0.2. Our basic model refers to elliptical galaxy models with a central core. However, we find numerically that an effective power-law scaling of L with m holds also in models with central cusp, beyond a mass scale up to which chaos is dominated by the influence of the cusp itself. We finally show numerically that an analogous law exists also in disc galaxies with rotating bars. In the latter case, chaotic scattering by the BH affects mainly populations of thick tube-like orbits surrounding some low-order branches of the x(sub 1) family of periodic orbits, as well as its bifurcations at low-order resonances, mainly the inner Lindblad resonance and the 4/1 resonance. Implications of the correlations between L and m to determining the rate of secular evolution of galaxies are discussed.

Full particle orbit effects in regular and stochastic magnetic fields

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

Ogawa, Shun; Cambon, Benjamin P.; Leoncini, Xavier

Here we present a numerical study of charged particle motion in a time-independent magnetic field in cylindrical geometry. The magnetic field model consists of an unperturbed reversed-shear (non-monotonic q-profile) helical part and a perturbation consisting of a superposition of modes. Contrary to most of the previous studies, the particle trajectories are computed by directly solving the full Lorentz force equations of motion in a six-dimensional phase space using a sixth-order, implicit, symplectic Gauss-Legendre method. The level of stochasticity in the particle orbits is diagnosed using averaged, effective Poincare sections. It is shown that when only one mode is present, themore » particle orbits can be stochastic even though the magnetic field line orbits are not stochastic (i.e., fully integrable). The lack of integrability of the particle orbits in this case is related to separatrix crossing and the breakdown of the global conservation of the magnetic moment. Some perturbation consisting of two modes creates resonance overlapping, leading to Hamiltonian chaos in magnetic field lines. Then, the particle orbits exhibit a nontrivial dynamics depending on their energy and pitch angle. It is shown that the regions where the particle motion is stochastic decrease as the energy increases. The non-monotonicity of the q-profile implies the existence of magnetic ITBs (internal transport barriers) which correspond to shearless flux surfaces located in the vicinity of the q-profile minimum. It is shown that depending on the energy, these magnetic ITBs might or might not confine particles. That is, magnetic ITBs act as an energy-dependent particle confinement filter. Magnetic field lines in reversed-shear configurations exhibit topological bifurcations (from homoclinic to heteroclinic) due to separatrix reconnection. Finally, we show that a similar but more complex scenario appears in the case of particle orbits that depend in a non-trivial way on the energy and pitch angle of the particles.« less

Full particle orbit effects in regular and stochastic magnetic fields

DOE PAGES

Ogawa, Shun; Cambon, Benjamin P.; Leoncini, Xavier; ...

2016-07-18

Here we present a numerical study of charged particle motion in a time-independent magnetic field in cylindrical geometry. The magnetic field model consists of an unperturbed reversed-shear (non-monotonic q-profile) helical part and a perturbation consisting of a superposition of modes. Contrary to most of the previous studies, the particle trajectories are computed by directly solving the full Lorentz force equations of motion in a six-dimensional phase space using a sixth-order, implicit, symplectic Gauss-Legendre method. The level of stochasticity in the particle orbits is diagnosed using averaged, effective Poincare sections. It is shown that when only one mode is present, themore » particle orbits can be stochastic even though the magnetic field line orbits are not stochastic (i.e., fully integrable). The lack of integrability of the particle orbits in this case is related to separatrix crossing and the breakdown of the global conservation of the magnetic moment. Some perturbation consisting of two modes creates resonance overlapping, leading to Hamiltonian chaos in magnetic field lines. Then, the particle orbits exhibit a nontrivial dynamics depending on their energy and pitch angle. It is shown that the regions where the particle motion is stochastic decrease as the energy increases. The non-monotonicity of the q-profile implies the existence of magnetic ITBs (internal transport barriers) which correspond to shearless flux surfaces located in the vicinity of the q-profile minimum. It is shown that depending on the energy, these magnetic ITBs might or might not confine particles. That is, magnetic ITBs act as an energy-dependent particle confinement filter. Magnetic field lines in reversed-shear configurations exhibit topological bifurcations (from homoclinic to heteroclinic) due to separatrix reconnection. Finally, we show that a similar but more complex scenario appears in the case of particle orbits that depend in a non-trivial way on the energy and pitch angle of the particles.« less

Full particle orbit effects in regular and stochastic magnetic fields

NASA Astrophysics Data System (ADS)

Ogawa, Shun; Cambon, Benjamin; Leoncini, Xavier; Vittot, Michel; del Castillo-Negrete, Diego; Dif-Pradalier, Guilhem; Garbet, Xavier

2016-07-01

We present a numerical study of charged particle motion in a time-independent magnetic field in cylindrical geometry. The magnetic field model consists of an unperturbed reversed-shear (non-monotonic q-profile) helical part and a perturbation consisting of a superposition of modes. Contrary to most of the previous studies, the particle trajectories are computed by directly solving the full Lorentz force equations of motion in a six-dimensional phase space using a sixth-order, implicit, symplectic Gauss-Legendre method. The level of stochasticity in the particle orbits is diagnosed using averaged, effective Poincare sections. It is shown that when only one mode is present, the particle orbits can be stochastic even though the magnetic field line orbits are not stochastic (i.e., fully integrable). The lack of integrability of the particle orbits in this case is related to separatrix crossing and the breakdown of the global conservation of the magnetic moment. Some perturbation consisting of two modes creates resonance overlapping, leading to Hamiltonian chaos in magnetic field lines. Then, the particle orbits exhibit a nontrivial dynamics depending on their energy and pitch angle. It is shown that the regions where the particle motion is stochastic decrease as the energy increases. The non-monotonicity of the q-profile implies the existence of magnetic ITBs (internal transport barriers) which correspond to shearless flux surfaces located in the vicinity of the q-profile minimum. It is shown that depending on the energy, these magnetic ITBs might or might not confine particles. That is, magnetic ITBs act as an energy-dependent particle confinement filter. Magnetic field lines in reversed-shear configurations exhibit topological bifurcations (from homoclinic to heteroclinic) due to separatrix reconnection. We show that a similar but more complex scenario appears in the case of particle orbits that depend in a non-trivial way on the energy and pitch angle of the particles.

Intrinsic nonlinearity and method of disturbed observations in inverse problems of celestial mechanics

NASA Astrophysics Data System (ADS)

Avdyushev, Victor A.

2017-12-01

Orbit determination from a small sample of observations over a very short observed orbital arc is a strongly nonlinear inverse problem. In such problems an evaluation of orbital uncertainty due to random observation errors is greatly complicated, since linear estimations conventionally used are no longer acceptable for describing the uncertainty even as a rough approximation. Nevertheless, if an inverse problem is weakly intrinsically nonlinear, then one can resort to the so-called method of disturbed observations (aka observational Monte Carlo). Previously, we showed that the weaker the intrinsic nonlinearity, the more efficient the method, i.e. the more accurate it enables one to simulate stochastically the orbital uncertainty, while it is strictly exact only when the problem is intrinsically linear. However, as we ascertained experimentally, its efficiency was found to be higher than that of other stochastic methods widely applied in practice. In the present paper we investigate the intrinsic nonlinearity in complicated inverse problems of Celestial Mechanics when orbits are determined from little informative samples of observations, which typically occurs for recently discovered asteroids. To inquire into the question, we introduce an index of intrinsic nonlinearity. In asteroid problems it evinces that the intrinsic nonlinearity can be strong enough to affect appreciably probabilistic estimates, especially at the very short observed orbital arcs that the asteroids travel on for about a hundredth of their orbital periods and less. As it is known from regression analysis, the source of intrinsic nonlinearity is the nonflatness of the estimation subspace specified by a dynamical model in the observation space. Our numerical results indicate that when determining asteroid orbits it is actually very slight. However, in the parametric space the effect of intrinsic nonlinearity is exaggerated mainly by the ill-conditioning of the inverse problem. Even so, as for the method of disturbed observations, we conclude that it practically should be still entirely acceptable to adequately describe the orbital uncertainty since, from a geometrical point of view, the efficiency of the method directly depends only on the nonflatness of the estimation subspace and it gets higher as the nonflatness decreases.

Uncertainty of InSAR velocity fields for measuring long-wavelength displacement

NASA Astrophysics Data System (ADS)

Fattahi, H.; Amelung, F.

2014-12-01

Long-wavelength artifacts in InSAR data are the main limitation to measure long-wavelength displacement; they are traditionally attributed mainly to the inaccuracy of the satellite orbits (orbital errors). However, most satellites are precisely tracked resulting in uncertainties of orbits of 2-10 cm. Orbits of these satellites are thus precise enough to obtain precise velocity fields with uncertainties better than 1 mm/yr/100 km for older satellites (e.g. Envisat) and better than 0.2 mm/yr/100 km for modern satellites (e.g. TerraSAR-X and Sentinel-1) [Fattahi & Amelung, 2014]. Such accurate velocity fields are achievable if long-wavelength artifacts from sources other than orbital errors are identified and corrected for. We present a modified Small Baseline approach to measure long-wavelength deformation and evaluate the uncertainty of these measurements. We use a redundant network of interferograms for detection and correction of unwrapping errors to ensure the unbiased estimation of phase history. We distinguish between different sources of long-wavelength artifacts and correct those introduced by atmospheric delay, topographic residuals, timing errors, processing approximations and hardware issues. We evaluate the uncertainty of the velocity fields using a covariance matrix with the contributions from orbital errors and residual atmospheric delay. For contributions from the orbital errors we consider the standard deviation of velocity gradients in range and azimuth directions as a function of orbital uncertainty. For contributions from the residual atmospheric delay we use several approaches including the structure functions of InSAR time-series epochs, the predicted delay from numerical weather models and estimated wet delay from optical imagery. We validate this InSAR approach for measuring long-wavelength deformation by comparing InSAR velocity fields over ~500 km long swath across the southern San Andreas fault system with independent GPS velocities and examine the estimated uncertainties in several non-deforming areas. We show the efficiency of the approach to study the continental deformation across the Chaman fault system at the western Indian plate boundary. Ref: Fattahi, H., & Amelung, F., (2014), InSAR uncertainty due to orbital errors, Geophys, J. Int (in press).

Fast iterative solution of the Bethe-Salpeter eigenvalue problem using low-rank and QTT tensor approximation

NASA Astrophysics Data System (ADS)

Benner, Peter; Dolgov, Sergey; Khoromskaia, Venera; Khoromskij, Boris N.

2017-04-01

In this paper, we propose and study two approaches to approximate the solution of the Bethe-Salpeter equation (BSE) by using structured iterative eigenvalue solvers. Both approaches are based on the reduced basis method and low-rank factorizations of the generating matrices. We also propose to represent the static screen interaction part in the BSE matrix by a small active sub-block, with a size balancing the storage for rank-structured representations of other matrix blocks. We demonstrate by various numerical tests that the combination of the diagonal plus low-rank plus reduced-block approximation exhibits higher precision with low numerical cost, providing as well a distinct two-sided error estimate for the smallest eigenvalues of the Bethe-Salpeter operator. The complexity is reduced to O (Nb2) in the size of the atomic orbitals basis set, Nb, instead of the practically intractable O (Nb6) scaling for the direct diagonalization. In the second approach, we apply the quantized-TT (QTT) tensor representation to both, the long eigenvectors and the column vectors in the rank-structured BSE matrix blocks, and combine this with the ALS-type iteration in block QTT format. The QTT-rank of the matrix entities possesses almost the same magnitude as the number of occupied orbitals in the molecular systems, No

The 3D elliptic restricted three-body problem: periodic orbits which bifurcate from limiting restricted problems. Complex instability

NASA Astrophysics Data System (ADS)

Ollé, Mercè; Pacha, Joan R.

1999-11-01

In the present work we use certain isolated symmetric periodic orbits found in some limiting Restricted Three-Body Problems to obtain, by numerical continuation, families of symmetric periodic orbits of the more general Spatial Elliptic Restricted Three Body Problem. In particular, the Planar Isosceles Restricted Three Body Problem, the Sitnikov Problem and the MacMillan problem are considered. A stability study for the periodic orbits of the families obtained - specially focused to detect transitions to complex instability - is also made.

A parallel orbital-updating based plane-wave basis method for electronic structure calculations

NASA Astrophysics Data System (ADS)

Pan, Yan; Dai, Xiaoying; de Gironcoli, Stefano; Gong, Xin-Gao; Rignanese, Gian-Marco; Zhou, Aihui

2017-11-01

Motivated by the recently proposed parallel orbital-updating approach in real space method [1], we propose a parallel orbital-updating based plane-wave basis method for electronic structure calculations, for solving the corresponding eigenvalue problems. In addition, we propose two new modified parallel orbital-updating methods. Compared to the traditional plane-wave methods, our methods allow for two-level parallelization, which is particularly interesting for large scale parallelization. Numerical experiments show that these new methods are more reliable and efficient for large scale calculations on modern supercomputers.

Oort's cloud evolution under the influence of the galactic field.

NASA Astrophysics Data System (ADS)

Kiryushenkova, N. V.; Chepurova, V. M.; Shershkina, S. L.

By numerical integration (Everhart's method) of the differential equations of cometary movement in Oort's cloud an attempt was made to observe how the galactic gravitational field changes the orbital elements of these comets during three solar revolutions in the Galaxy. It is shown that the cometary orbits are more elongated, even the initially circular orbits become strongly elliptical, in the outer layers of Oort's cloud it is possible for comets to turn into hyperbolic orbits and to leave the solar system. The boundaries of the solar system have been precised.

Modeling of the Orbital Evolution of 2060 Chiron

NASA Astrophysics Data System (ADS)

Kovalenko, Nataliya S.; Babenko, Yury G.; Churyumov, Klim I.

2002-03-01

The origin of Centaurs is one of the most interesting problems of Solar system science, and it has not yet been solved. To shed light on this problem one can investigate Centaurs' past and future orbital evolution. In this paper we discuss the results of Chiron's orbital evolution modeling. It was the first discovered Centaur and is the brightest one. Numerical integration was produced for 1 Myr forward and backward from the present time. A program based on the Everhart single sequence method for integrating orbits was used.

Atomic orbitals in molecules: general electronegativity and improvement of Mulliken population analysis.

PubMed

Lu, Haigang; Dai, Dadi; Yang, Pin; Li, Lemin

2006-01-21

An approach of atomic orbitals in molecules (AOIM) has been developed to study the atomic properties in molecules, in which the molecular orbitals are expressed in terms of the optimized minimal atomic orbitals. The atomic electronegativities are calculated using Pauling's electronegativity of free atom and are employed to find the electronegativity equilibrium in molecules and to describe the amphoteric properties of the transition metals from the groups 4 to 10. AOIM can also improve the numerical stability and accuracy of the original Mulliken population analysis.

Regions of stability of asteroids

NASA Technical Reports Server (NTRS)

Szebehely, V.; Lundberg, J.; Vicente, R.

1983-01-01

Using Hill's modified stability criterion, regions of orbital elements are established for conditions of stability. The model of the three-dimensional restricted problem of three bodies is used with the sun and Jupiter as the primaries. Four different cases are studied: direct and retrograde, outside and inside asteroidal orbits. The directions of the asteroidal orbits refer to the synodical reference frame and the positions refer to Jupiter's orbit. The orbital parameters of the asteroids are the semi-major axis (a), the eccentricity (e), and the inclination from Jupiter's orbital plane (i). The argument of the perihelion and the longitude of the ascending node are fixed at Omega = omega = 90 deg and the time of perihelion passage is T = 0 for all orbits.

Orbital evolution of some Centaurs

NASA Astrophysics Data System (ADS)

Kovalenko, Nataliya; Babenko, Yuri; Churyumov, Klim

2002-11-01

In this work we investigated the dynamical evolution of Centaurs objects 2060 (Chiron), 5145 (Pholus), 7066 (Nessus), 8405 (Asbolus), 10199 (Chariklo), 10370 (Hylonome), and Scattered-Disk object 15874. We have carried out orbital integration of test particles with initial orbits similar to those of these objects. Calculations were produced for +/-600kyr-10Myr starting at epoch and using the implicit single sequence Everhart methods. 12 variational orbits for each of selected Centaurs also have been numerically integrated for +/-200 kyr toward the past and the future. The most probable paths were traced up to +/-1 Myr. The character of orbital elements changes and peculiarities of close approaches to giant planets are discussed.

The Spin-Orbit Resonant Rotation of Mercury: A Two Degree of Freedom Hamiltonian Model

NASA Astrophysics Data System (ADS)

D'Hoedt, Sandrine; Lemaitre, Anne

2004-04-01

The paper develops a hamiltonian formulation describing the coupled orbital and spin motions of a rigid Mercury rotation about its axis of maximum moment of inertia in the frame of a 3:2 spin orbit resonance; the (ecliptic) obliquity is not constant, the gravitational potential of mercury is developed up to the second degree terms (the only ones for which an approximate numerical value can be given) and is reduced to a two degree of freedom model in the absence of planetary perturbations. Four equilibria can be calculated, corresponding to four different values of the (ecliptic) obliquity. The present situation of Mercury corresponds to one of them, which is proved to be stable. We introduce action-angle variables in the neighborhood of this stable equilibrium, by several successive canonical transformations, so to get two constant frequencies, the first one for the free spin-orbit libration, the other one for the 1:1 resonant precession of both nodes (orbital and rotational) on the ecliptic plane. The numerical values obtained by this simplified model are in perfect agreement with those obtained by Rambaux and Bois [Astron. Astrophys. 413, 381 393].

Impact of Orbit Position Errors on Future Satellite Gravity Models

NASA Astrophysics Data System (ADS)

Encarnacao, J.; Ditmar, P.; Klees, R.

2015-12-01

We present the results of a study of the impact of orbit positioning noise (OPN) caused by incomplete knowledge of the Earth's gravity field on gravity models estimated from satellite gravity data. The OPN is simulated as the difference between two sets of orbits integrated on the basis of different static gravity field models. The OPN is propagated into ll-SST data, here computed as averaged inter-satellite accelerations projected onto the Line of Sight (LoS) vector between the two satellites. We consider the cartwheel formation (CF), pendulum formation (PF), and trailing formation (TF) as they produce a different dominant orientation of the LoS vector. Given the polar orbits of the formations, the LoS vector is mainly aligned with the North-South direction in the TF, with the East-West direction in the PF (i.e. no along-track offset), and contains a radial component in the CF. An analytical analysis predicts that the CF suffers from a very high sensitivity to the OPN. This is a fundamental characteristic of this formation, which results from the amplification of this noise by diagonal components of the gravity gradient tensor (defined in the local frame) during the propagation into satellite gravity data. In contrast, the OPN in the data from PF and TF is only scaled by off-diagonal gravity gradient components, which are much smaller than the diagonal tensor components. A numerical analysis shows that the effect of the OPN is similar in the data collected by the TF and the PF. The amplification of the OPN errors for the CF leads to errors in the gravity model that are three orders of magnitude larger than those in case of the PF. This means that any implementation of the CF will most likely produce data with relatively low quality since this error dominates the error budget, especially at low frequencies. This is particularly critical for future gravimetric missions that will be equipped with highly accurate ranging sensors.

Enceladus Environmental Explorer (EVE): A Mission Concept

NASA Astrophysics Data System (ADS)

Lawson, M. J.; Amador, E. S.; Carrier, B. L.; Albuja, A.; Bapst, J.; Cahill, K. R. S.; Ebersohn, F.; Gainey, S.; Gartrelle, G.; Greenberger, R. N.; Hale, J. M.; Johnston, S.; Olivares, J.; Parcheta, C. E.; Sheehan, J. P.; Thorpe, A. K.; Zareh, S. K.

2014-12-01

Enceladus is an intriguing planetary body, which possibly has the ingredients needed for life. Further, it has numerous (over 100) continuously erupting geysers that eject material into the atmosphere which provide a unique opportunity to sample the body's internal chemistry from orbit. At JPL's Planetary Science Summer School, Team X and a group of students developed a mission concept to directly sample Enceladus' plumes. The mission, named Enceladus Environmental Explorer (EVE), follows NASA's Planetary Science Decadal survey and would assess the potential habitability of Saturn's icy satellite through analysis of the chemistry of the subsurface ocean and the nature of the organic chemistry in the plume. EVE would look at geological and geophysical surface processes of Enceladus by investigating the heat output of Enceladus, plumes' mechanics, the extent of the liquid subsurface reservoir(s), and gravitational variation. The EVE mission concept aimed for a January 2023 launch on an Atlas 551 class launch vehicle and would arrive at Saturn July 2031. A two-year-long Saturn moon tour would allow sufficient deceleration to permit a polar orbital insertion around Enceladus in March 2035, remaining stable for 54 weeks of observation. The proposed instrument payload includes: 1) SUb MilliMeter Enceladus Radiometer (SUMMER; equivalent to Rosetta MIRO), 2) Enceladus Dust and Gas Experiment (EDGE; an enhanced version of Rosetta COSIMA), 3) MAGnetometer for Ionic Concentration (MAGIC; equivalent to MMS/ InSIGHT magnetometer), 4) Visual Imaging Camera with Topographic Observational Resolution (VICTOR) and 5) Enceladus Radio Gravity Science (ERGS). Our suggested orbital timeline would allow the most comprehensive dataset yet collected of a moon in the outer solar system, mapping the entire surface twice with SUMMER and VICTOR, while sampling the plume directly 232 times with EDGE. MAGIC would also provide over a year of sampling of the magnetic field variations from orbit. Enceladus Environmental Explorer (EVE) offers a unique opportunity to determine the potential for life on Enceladus.

THE FINAL SPIN FROM BINARY BLACK HOLES IN QUASI-CIRCULAR ORBITS

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

Hofmann, Fabian; Rezzolla, Luciano; Barausse, Enrico

2016-07-10

We revisit the problem of predicting the spin magnitude and direction of the black hole (BH) resulting from the merger of two BHs with arbitrary masses and spins inspiraling in quasi-circular orbits. We do this by analyzing a catalog of 619 recent numerical-relativity simulations collected from the literature and spanning a large variety of initial conditions. By combining information from the post-Newtonian approximation, the extreme mass-ratio limit, and perturbative calculations, we improve our previously proposed phenomenological formulae for the final remnant spin. In contrast with alternative suggestions in the literature, and in analogy with our previous expressions, the new formulamore » is a simple algebraic function of the initial system parameters and is not restricted to binaries with spins aligned/anti-aligned with the orbital angular momentum but can be employed for fully generic binaries. The accuracy of the new expression is significantly improved, especially for almost extremal progenitor spins and for small mass ratios, yielding an rms error σ ≈ 0.002 for aligned/anti-aligned binaries and σ ≈ 0.006 for generic binaries. Our new formula is suitable for cosmological applications and can be employed robustly in the analysis of the gravitational waveforms from advanced interferometric detectors.« less

Spin-orbit-torque-induced magnetic domain wall motion in Ta/CoFe nanowires with sloped perpendicular magnetic anisotropy.

PubMed

Zhang, Yue; Luo, Shijiang; Yang, Xiaofei; Yang, Chang

2017-05-17

In materials with the gradient of magnetic anisotropy, spin-orbit-torque-induced magnetization behaviour has attracted attention because of its intriguing scientific principle and potential application. Most of the magnetization behaviours microscopically originate from magnetic domain wall motion, which can be precisely depicted using the standard cooperative coordinate method (CCM). However, the domain wall motion in materials with the gradient of magnetic anisotropy using the CCM remains lack of investigation. In this paper, by adopting CCM, we established a set of equations to quantitatively depict the spin-orbit-torque-induced motion of domain walls in a Ta/CoFe nanotrack with weak Dzyaloshinskii-Moriya interaction and magnetic anisotropy gradient. The equations were solved numerically, and the solutions are similar to those of a micromagnetic simulation. The results indicate that the enhanced anisotropy along the track acts as a barrier to inhibit the motion of the domain wall. In contrast, the domain wall can be pushed to move in a direction with reduced anisotropy, with the velocity being accelerated by more than twice compared with that for the constant anisotropy case. This substantial velocity manipulation by anisotropy engineering is important in designing novel magnetic information devices with high reading speeds.

The Evolution and Disruption of Planetary Systems

NASA Technical Reports Server (NTRS)

Laughlin, Gregory; DeVincenzi, Donald L. (Technical Monitor)

2000-01-01

Planetary systems that encounter passing stars can experience severe orbital disruption, and the efficiency of this process is greatly enhanced when the impinging systems are binary pairs rather than single stars. Using a Monte Carlo approach, we have performed nearly half a million numerical experiments to examine the long term ramifications of planetary scattering on planetary systems. We have concluded that systems which form in dense environments such as Orion's Trapezium cluster have roughly a ten percent chance of being seriously disrupted. We have also used our programs to explore the long-term prospects for our own Solar system. Given the current interstellar environment, we have computed the odds that Earth will find its orbit seriously disrupted prior to the emergence of a runaway greenhouse effect driven by the Sun's increasing luminosity. This estimate includes both direct disruption events and scattering processes that seriously alter the orbits of the Jovian planets, which then force severe changes upon the Earth's orbit. We then explore the consequences of the Earth being thrown into deep space. The surface biosphere would rapidly shut down under conditions of zero insolation, but the Earth's radioactive heat is capable of maintaining life deep underground, and perhaps in hydrothermal vent communities, for some time to come. Although unlikely for the Earth, this scenario may be common throughout the universe, since many environments where liquid water could exist (e.g., Europa and Callisto) must derive their energy from internal (rather than external) heating.

Resonant thickening of self-gravitating discs: imposed or self-induced orbital diffusion in the tightly wound limit

NASA Astrophysics Data System (ADS)

Fouvry, Jean-Baptiste; Pichon, Christophe; Chavanis, Pierre-Henri; Monk, Laura

2017-11-01

The secular thickening of a self-gravitating stellar galactic disc is investigated using the dressed collisionless Fokker-Planck equation and the inhomogeneous multicomponent Balescu-Lenard equation. The thick WKB limits for the diffusion fluxes are found using the epicyclic approximation, while assuming that only radially tightly wound transient spirals are sustained by the disc. This yields simple quadratures for the drift and diffusion coefficients, providing a clear understanding of the positions of maximum vertical orbital diffusion within the disc, induced by fluctuations either external or due to the finite number of particles. These thick limits also offer a consistent derivation of a thick disc Toomre parameter, which is shown to be exponentially boosted by the ratio of the vertical to radial scaleheights. Dressed potential fluctuations within the disc statistically induce a vertical bending of a subset of resonant orbits, triggering the corresponding increase in vertical velocity dispersion. When applied to a tepid stable tapered disc perturbed by shot noise, these two frameworks reproduce qualitatively the formation of ridges of resonant orbits towards larger vertical actions, as found in direct numerical simulations, but overestimates the time-scale involved in their appearance. Swing amplification is likely needed to resolve this discrepancy, as demonstrated in the case of razor-thin discs. Other sources of thickening are also investigated, such as fading sequences of slowing bars, or the joint evolution of a population of giant molecular clouds within the disc.

The interference aerodynamics caused by the wing elasticity during store separation

NASA Astrophysics Data System (ADS)

Lei, Yang; Zheng-yin, Ye

2016-04-01

Air-launch-to-orbit is the technology that has stores carried aloft and launched the store from the plane to the orbit. The separation between the aircraft and store is one of the most important and difficult phases in air-launch-to-orbit technology. There exists strong aerodynamic interference between the aircraft and the store in store separation. When the aspect ratio of the aircraft is large, the elastic deformations of the wing must be considered. The main purpose of this article is to study the influence of the interference aerodynamics caused by the elastic deformations of the wing to the unsteady aerodynamics of the store. By solving the coupled functions of unsteady Navier-Stokes equations, six degrees of freedom dynamic equations and structural dynamic equations simultaneously, the store separation with the elastic deformation of the aircraft considered is simulated numerically. And the interactive aerodynamic forces are analyzed. The study shows that the interference aerodynamics is obvious at earlier time during the separation, and the dominant frequency of the elastic wing determines the aerodynamic forces frequencies of the store. Because of the effect of the interference aerodynamics, the roll angle response and pitch angle response increase. When the store is mounted under the wingtip, the additional aerodynamics caused by the wingtip vortex is obvious, which accelerate the divergence of the lateral force and the lateral-directional attitude angle of the store. This study supports some beneficial conclusions to the engineering application of the air-launch-to-orbit.

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.

Polar orbits around binary stars

NASA Astrophysics Data System (ADS)

Egan, Greg

2018-01-01

Oks proposes the existence of a new class of stable planetary orbits around binary stars, in the shape of a helix on a conical surface whose axis of symmetry coincides with the interstellar axis, and rotates with the same orbital frequency as the binary pair. We show that this claim relies on the inappropriate use of an effective potential that is only applicable when the stars are held motionless. We also present numerical evidence that the only planetary orbits whose planes are initially orthogonal to the interstellar axis that remain stable on the time scale of the stellar orbit are ordinary polar orbits around one of the stars, and that the perturbations due to the binary companion do not rotate the plane of the orbit to maintain a fixed relationship with the axis.

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.

Common Orbital Infections ~ State of the Art ~ Part I

PubMed Central

Hamed-Azzam, Shirin; AlHashash, Islam; Briscoe, Daniel; Rose, Geoffrey E; Verity, David H.

2018-01-01

Infections of the orbit and periorbita are relatively frequent, and can cause significant local and systemic morbidity. Loss of vision occurs in more than 10% of patients, and systemic sequelae can include meningitis, intracranial abscess, and death. Numerous organisms infect the orbit, but the most common are bacteria. There are many methods through which orbital infections occur, with infection from the neighboring ethmoid sinuses the most likely cause for all age groups. Prompt management is essential in suspected orbital cellulitis, and involves urgent intravenous antibiotics, rehydration, and treatment of any co-existent underlying systemic disease, e.g., diabetes, renal failure. This review summarizes the common infectious processes of the orbit in both pediatric and adult groups. We review pathophysiology, symptoms, signs, and treatment for infectious orbital processes. PMID:29719647

EFFECTS OF DYNAMICAL EVOLUTION OF GIANT PLANETS ON SURVIVAL OF TERRESTRIAL PLANETS

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

Matsumura, Soko; Ida, Shigeru; Nagasawa, Makiko

2013-04-20

The orbital distributions of currently observed extrasolar giant planets allow marginally stable orbits for hypothetical, terrestrial planets. In this paper, we propose that many of these systems may not have additional planets on these ''stable'' orbits, since past dynamical instability among giant planets could have removed them. We numerically investigate the effects of early evolution of multiple giant planets on the orbital stability of the inner, sub-Neptune-like planets which are modeled as test particles, and determine their dynamically unstable region. Previous studies have shown that the majority of such test particles are ejected out of the system as a resultmore » of close encounters with giant planets. Here, we show that secular perturbations from giant planets can remove test particles at least down to 10 times smaller than their minimum pericenter distance. Our results indicate that, unless the dynamical instability among giant planets is either absent or quiet like planet-planet collisions, most test particles down to {approx}0.1 AU within the orbits of giant planets at a few AU may be gone. In fact, out of {approx}30% of survived test particles, about three quarters belong to the planet-planet collision cases. We find a good agreement between our numerical results and the secular theory, and present a semi-analytical formula which estimates the dynamically unstable region of the test particles just from the evolution of giant planets. Finally, our numerical results agree well with the observations, and also predict the existence of hot rocky planets in eccentric giant planet systems.« less

A Network of Direct Broadcast Antenna Systems to Provide Real-Time Infrared and Microwave Sounder Data for Numerical Weather Prediction

NASA Astrophysics Data System (ADS)

Gumley, L.

2013-12-01

The Space Science and Engineering Center at the University of Wisconsin-Madison is creating a network of direct broadcast satellite data reception stations to acquire and process infrared and microwave sounder data in real-time from polar orbiting meteorological satellites and deliver the resulting products to NOAA with low latency for assimilation in NCEP numerical weather prediction models. The network will include 4 antenna sites that will be operated directly by SSEC, including Madison WI, Honolulu HI, Miami FL, and Mayaguez PR. The network will also include partner antenna sites not directly controlled by SSEC, including Corvallis OR, Monterey CA, Suitland MD, Fairbanks AK, and Guam. All of the antenna sites will have a combined X/L-band reception system capable of receiving data via direct broadcast from polar orbiting satellites including Suomi NPP and JPSS-1, Metop-A/B, POES,Terra, and Aqua. Each site will collect raw data from these satellites locally, process it to Level 1 (SDR) and Level 2 (EDR) products, and transmit the products back to SSEC for delivery to NOAA/NCEP. The primary purpose of the antenna systems is to provide real-time infrared and microwave sounder data from Metop and Suomi-NPP to NOAA to support data assimilation for NOAA/NCEP operational numerical weather prediction models. At present, NOAA/NCEP use of advanced infrared (CrIS, IASI, AIRS) and microwave (ATMS, AMSU) sounder data over North America in NWP data assimilation is limited because of the latency of the products in relation to the cutoff times for assimilation runs. This network will deliver infrared and microwave sounder data to NCEP with the lowest latency possible, via the reception and processing of data received via direct broadcast. CIMSS/SSEC is managing the procurement and installation of the antenna systems at the two new sites, and will operate the stations remotely. NOAA will establish the reception priorities (Metop and SNPP will be at the highest priority) and SSEC will set the reception schedule to acquire data from these satellites, and any other satellites at lower priority as determined jointly by NOAA, CIMSS/SSEC, and the antenna site hosts. SSEC is providing a product generation server at each site (where applicable) as part of the installed hardware to create satellite products in real-time. The host locations will provide the necessary network resources to enable infrared sounder (CrIS, IASI, and AIRS) and microwave sounder (ATMS and AMSU) data to be sent back to SSEC (and hence to NOAA/NCEP) with low latency (< 15 minutes). This presentation will described how the network realizes the goal of providing data to end users within 15 minutes of observation, and will give examples of the positive impact already observed on NCEP forecast model skill from assimilating real-time infrared and microwave sounder data in the NAM regional domain.

Overcoming the sign problem at finite temperature: Quantum tensor network for the orbital eg model on an infinite square lattice

NASA Astrophysics Data System (ADS)

Czarnik, Piotr; Dziarmaga, Jacek; Oleś, Andrzej M.

2017-07-01

The variational tensor network renormalization approach to two-dimensional (2D) quantum systems at finite temperature is applied to a model suffering the notorious quantum Monte Carlo sign problem—the orbital eg model with spatially highly anisotropic orbital interactions. Coarse graining of the tensor network along the inverse temperature β yields a numerically tractable 2D tensor network representing the Gibbs state. Its bond dimension D —limiting the amount of entanglement—is a natural refinement parameter. Increasing D we obtain a converged order parameter and its linear susceptibility close to the critical point. They confirm the existence of finite order parameter below the critical temperature Tc, provide a numerically exact estimate of Tc, and give the critical exponents within 1 % of the 2D Ising universality class.

Hubble Space Telescope. Update: 18 months in orbit

NASA Technical Reports Server (NTRS)

1990-01-01

In April 1990, Space Shuttle Discovery launched the Hubble Space Telescope (HST). An 18 month in-orbit update of the operations and performance of the HST is presented. Numerous color photographs are shown of objects already observed, and mission plans are presented for future observations by the HST.

Summer Skies

ERIC Educational Resources Information Center

Science Scope, 2005

2005-01-01

During the evening hours of the summer of 2005, there will be numerous opportunities to observe several of the brighter planets as they move along their respective orbits, overtaking and passing one another, performing a planetary dance with the choreography set to orbital speeds. With the exception of Mars, the visible planets will all be in the…

Scalar self-force on eccentric geodesics in Schwarzschild spacetime: A time-domain computation

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

Haas, Roland

2007-06-15

We calculate the self-force acting on a particle with scalar charge moving on a generic geodesic around a Schwarzschild black hole. This calculation requires an accurate computation of the retarded scalar field produced by the moving charge; this is done numerically with the help of a fourth-order convergent finite-difference scheme formulated in the time domain. The calculation also requires a regularization procedure, because the retarded field is singular on the particle's world line; this is handled mode-by-mode via the mode-sum regularization scheme first introduced by Barack and Ori. This paper presents the numerical method, various numerical tests, and a samplemore » of results for mildly eccentric orbits as well as ''zoom-whirl'' orbits.« less

The Roles of Orbital Frontal Cortex in the Modulation of Antisocial Behavior

ERIC Educational Resources Information Center

Blair, R. J. R.

2004-01-01

This article considers potential roles of orbital frontal cortex in the modulation of antisocial behavior. Two forms of aggression are distinguished: reactive aggression elicited in response to frustration/threat and goal directed, instrumental aggression. It is suggested that orbital frontal cortex is directly involved in the modulation of…

A Gaussian quadrature method for total energy analysis in electronic state calculations

NASA Astrophysics Data System (ADS)

Fukushima, Kimichika

This article reports studies by Fukushima and coworkers since 1980 concerning their highly accurate numerical integral method using Gaussian quadratures to evaluate the total energy in electronic state calculations. Gauss-Legendre and Gauss-Laguerre quadratures were used for integrals in the finite and infinite regions, respectively. Our previous article showed that, for diatomic molecules such as CO and FeO, elliptic coordinates efficiently achieved high numerical integral accuracy even with a numerical basis set including transition metal atomic orbitals. This article will generalize straightforward details for multiatomic systems with direct integrals in each decomposed elliptic coordinate determined from the nuclear positions of picked-up atom pairs. Sample calculations were performed for the molecules O3 and H2O. This article will also try to present, in another coordinate, a numerical integral by partially using the Becke's decomposition published in 1988, but without the Becke's fuzzy cell generated by the polynomials of internuclear distance between the pair atoms. Instead, simple nuclear weights comprising exponential functions around nuclei are used. The one-center integral is performed with a Gaussian quadrature pack in a spherical coordinate, included in the author's original program in around 1980. As for this decomposition into one-center integrals, sample calculations are carried out for Li2.

Numerical Simulations of Naturally Tilted, Retrogradely Precessing, Nodal Superhumping Accretion Disks

NASA Astrophysics Data System (ADS)

Montgomery, M. M.

2012-02-01

Accretion disks around black hole, neutron star, and white dwarf systems are thought to sometimes tilt, retrogradely precess, and produce hump-shaped modulations in light curves that have a period shorter than the orbital period. Although artificially rotating numerically simulated accretion disks out of the orbital plane and around the line of nodes generate these short-period superhumps and retrograde precession of the disk, no numerical code to date has been shown to produce a disk tilt naturally. In this work, we report the first naturally tilted disk in non-magnetic cataclysmic variables using three-dimensional smoothed particle hydrodynamics. Our simulations show that after many hundreds of orbital periods, the disk has tilted on its own and this disk tilt is without the aid of radiation sources or magnetic fields. As the system orbits, the accretion stream strikes the bright spot (which is on the rim of the tilted disk) and flows over and under the disk on different flow paths. These different flow paths suggest the lift force as a source to disk tilt. Our results confirm the disk shape, disk structure, and negative superhump period and support the source to disk tilt, source to retrograde precession, and location associated with X-ray and He II emission from the disk as suggested in previous works. Our results identify the fundamental negative superhump frequency as the indicator of disk tilt around the line of nodes.

Candidates for direct laser cooling of diatomic molecules with the simplest 1Σ -1Σ electronic system

NASA Astrophysics Data System (ADS)

Li, Chuanliang; Li, Yachao; Ji, Zhonghua; Qiu, Xuanbing; Lai, Yunzhong; Wei, Jilin; Zhao, Yanting; Deng, Lunhua; Chen, Yangqin; Liu, Jinjun

2018-06-01

We propose to utilize the 1Σ-1Σ electronic transition system for direct laser cooling of heteronuclear diatomic molecules. AgH, as well as its deuterium isotopolog AgD, is used as an example to illustrate the cooling schemes. Potential-energy curves and relevant molecular parameters of both AgH and AgD, including the spin-orbit constants and the electronic transition dipole moments, are determined in internally contracted multiconfiguration-reference configuration interaction calculations. The highly diagonal Franck-Condon matrices of the A 1Σ+-X 1Σ+ transitions predicted by the calculations suggest the existence of quasi-closed-cycle transitions, which renders these molecules suitable for direct laser cooling. By solving rate equations numerically, we demonstrated that both AgH and AgD molecules can be cooled from 25 K to 2 mK temperature in approximately 20 ms. Our investigation elucidates and supports the hypothesis that molecules in the simplest 1Σ-1Σ system can serve as favorable candidates for direct laser cooling.

The disposition of impact ejecta resulting from the AIDA-DART mission to binary asteroid 65803 Didymos: an independent investigation

NASA Astrophysics Data System (ADS)

Richardson, James E.; O'Brien, David P.

2016-10-01

If all goes as planned, in the year 2020 a joint ESA and NASA mission will be launched that will rendezvous with the near-Earth binary asteroid system 65803 Didymos in the fall of 2022. The European component, the Asteroid Impact & Deflection Assessment (AIDA) spacecraft will arrive first and characterize the system, which consists of a ~800 m diameter primary and a ~160 m diameter secondary, orbiting a common center of mass at a semi-major axis distance of ~1200 m with a orbital period of 11.9 hr. Following system characterization, the AIDA spacecraft will remove to a safe distance while the NASA component, the 300 kg Double Asteroid Redirection Test (DART) spacecraft collides with the trailing edge of the secondary body (with respect to the binary's retrograde mutual orbit). Meanwhile, the AIDA spacecraft will conduct observations of this impact and its aftermath, specifically looking for changes made to the primary, the secondary, and their mutual orbit as a result of the DART collision. Of particular interest is the ballistic flight and final disposition of the ejecta produced by the impact cratering process, not just from the standpoint of scientific study, but also from the standpoint of AIDA spacecraft safety.In this study, we investigate a series of hypothetical DART impacts utilizing a semi-empirical, numerical impact ejecta plume model originally developed for the Deep Impact mission and designed specifically with impacts on small bodies in mind. The resulting excavated mass is discretized into 7200 individual tracer particles, each representing a unique combination of speed, mass, and ejected direction. The trajectory of each tracer is computed numerically under the gravitational influence of both primary and secondary, along with the effects of solar radiation pressure. Each tracer is followed until it either impacts a body or escapes the system, whereupon tracking is continued in the heliocentric frame using an N-body integrator. Various impact scenarios will be explored, along with a number of ejecta particle sizes, with the aim of characterizing the most likely final ejecta dispositions resulting from the DART impact, and the safest vantages from which the AIDA spacecraft can observe this event.

Orbital evolution of small binary asteroids

NASA Astrophysics Data System (ADS)

Ćuk, Matija; Nesvorný, David

2010-06-01

About 15% of both near-Earth and main-belt asteroids with diameters below 10 km are now known to be binary. These small asteroid binaries are relatively uniform and typically contain a fast-spinning, flattened primary and a synchronously rotating, elongated secondary that is 20-40% as large (in diameter) as the primary. The principal formation mechanism for these binaries is now thought to be YORP (Yarkovsky-O'Keefe-Radzievskii-Paddack) effect induced spin-up of the primary followed by mass loss and accretion of the secondary from the released material. It has previously been suggested (Ćuk, M. [2007]. Astrophys. J. 659, L57-L60) that the present population of small binary asteroids is in a steady state between production through YORP and destruction through binary YORP (BYORP), which should increase or decrease secondary's orbit, depending on the satellite's shape. However, BYORP-driven evolution has not been directly modeled until now. Here we construct a simple numerical model of the binary's orbital as well the secondary's rotational dynamics which includes BYORP and selected terms representing main solar perturbations. We find that many secondaries should be vulnerable to chaotic rotation even for relatively low-eccentricity mutual orbits. We also find that the precession of the mutual orbit for typical small binary asteroids might be dominated by the perturbations from the prolate and librating secondary, rather than the oblate primary. When we evolve the mutual orbit by BYORP we find that the indirect effects on the binary's eccentricity (through the coupling between the orbit and the secondary's spin) dominate over direct ones caused by the BYORP acceleration. In particular, outward evolution causes eccentricity to increase and eventually triggers chaotic rotation of the secondary. We conclude that the most likely outcome will be reestablishing of the synchronous lock with a "flipped" secondary which would then evolve back in. For inward evolution we find an initial decrease of eccentricity and secondary's librations, to be followed by later increase. We think that it is likely that various forms of dissipation we did not model may damp the secondary's librations close to the primary, allowing for further inward evolution and a possible merger. We conclude that a merger or a tidal disruption of the secondary are the most likely outcomes of the BYORP evolution. Dissociation into heliocentric pairs by BYORP alone should be very difficult, and satellite loss might be restricted to the minority of systems containing more than one satellite at the time.

Formation Flying of Tethered and Nontethered Spacecraft

NASA Technical Reports Server (NTRS)

Quadrelli, Marco B.

2005-01-01

A paper discusses the effect of the dynamic interaction taking place within a formation composed of a rigid and a deformable vehicle, and presents the concept of two or more tethered spacecraft flying in formation with one or more separated free-flying spacecraft. Although progress toward formation flight of nontethered spacecraft has already been achieved, the document cites potential advantages of tethering, including less consumption of fuel to maintain formation, very high dynamic stability of a rotating tethered formation, and intrinsically passive gravity-gradient stabilization. The document presents a theoretical analysis of the dynamics of a system comprising one free-flying spacecraft and two tethered spacecraft in orbit, as a prototype of more complex systems. The spacecraft are modeled as rigid bodies and the tether as a mass-less spring with structural viscous damping. Included in the analysis is a study of the feasibility of a centralized control system for maintaining a required formation in low Earth orbit. A numerical simulation of a retargeting maneuver is reported to show that even if the additional internal dynamics of the system caused by flexibility is considered, high pointing precision can be achieved if a fictitious rigid frame is used to track the tethered system, and it should be possible to position the spacecraft with centimeter accuracy and to orient the formation within arc seconds of the desired direction also in the presence of low Earth orbit environmental perturbations. The results of the study demonstrate that the concept is feasible in Earth orbit and point the way to further study of these hybrid tethered and free-flying systems for related applications in orbit around other Solar System bodies.

Dust distributions in debris disks: effects of gravity, radiation pressure and collisions

NASA Astrophysics Data System (ADS)

Krivov, A. V.; Löhne, T.; Sremčević, M.

2006-08-01

We model a typical debris disk, treated as an idealized ensemble of dust particles, exposed to stellar gravity and direct radiation pressure and experiencing fragmenting collisions. Applying the kinetic method of statistical physics, written in orbital elements, we calculate size and spatial distibutions expected in a steady-state disk, investigate timescales needed to reach the steady state, and calculate mass loss rates. Particular numerical examples are given for the debris disk around Vega. The disk should comprise a population of larger grains in bound orbits and a population of smaller particles in hyperbolic orbits. The cross section area is dominated by the smallest grains that still can stay in bound orbits, for Vega about 10 {μ m} in radius. The size distribution is wavy, implying secondary peaks in the size distribution at larger sizes. The radial profile of the pole-on surface density or the optical depth in the steady-state disk has a power-law index between about -1 and -2. It cannot be much steeper even if dust production is confined to a narrow planetesimal belt, because collisional grinding produces smaller and smaller grains, and radiation pressure pumps up their orbital eccentricities and spreads them outward, which flattens the radial profile. The timescales to reach a steady state depend on grain sizes and distance from the star. For Vega, they are about 1 Myr for grains up to some hundred {μ m} at 100 AU. The total mass of the Vega disk needed to produce the observed amount of micron and submillimeter-sized dust does not exceed several earth masses for an upper size limit of parent bodies of about 1 km. The collisional depletion of the disk occurs on Gyr timescales.

Sentry: An Automated Close Approach Monitoring System for Near-Earth Objects

NASA Astrophysics Data System (ADS)

Chamberlin, A. B.; Chesley, S. R.; Chodas, P. W.; Giorgini, J. D.; Keesey, M. S.; Wimberly, R. N.; Yeomans, D. K.

2001-11-01

In response to international concern about potential asteroid impacts on Earth, NASA's Near-Earth Object (NEO) Program Office has implemented a new system called ``Sentry'' to automatically update the orbits of all NEOs on a daily basis and compute Earth close approaches up to 100 years into the future. Results are published on our web site (http://neo.jpl.nasa.gov/) and updated orbits and ephemerides made available via the JPL Horizons ephemeris service (http://ssd.jpl.nasa.gov/horizons.html). Sentry collects new and revised astrometric observations from the Minor Planet Center (MPC) via their electronic circulars (MPECs) in near real time as well as radar and optical astrometry sent directly from observers. NEO discoveries and identifications are detected in MPECs and processed appropriately. In addition to these daily updates, Sentry synchronizes with each monthly batch of MPC astrometry and automatically updates all NEO observation files. Daily and monthly processing of NEO astrometry is managed using a queuing system which allows for manual intervention of selected NEOs without interfering with the automatic system. At the heart of Sentry is a fully automatic orbit determination program which handles outlier rejection and ensures convergence in the new solution. Updated orbital elements and their covariances are published via Horizons and our NEO web site, typically within 24 hours. A new version of Horizons, in development, will allow computation of ephemeris uncertainties using covariance data. The positions of NEOs with updated orbits are numerically integrated up to 100 years into the future and each close approach to any perturbing body in our dynamic model (all planets, Moon, Ceres, Pallas, Vesta) is recorded. Significant approaches are flagged for extended analysis including Monte Carlo studies. Results, such as minimum encounter distances and future Earth impact probabilities, are published on our NEO web site.

Tidal capture of stars by a massive black hole

NASA Technical Reports Server (NTRS)

Novikov, I. D.; Pethick, C. J.; Polnarev, A. G.

1992-01-01

The processes leading to tidal capture of stars by a massive black hole and the consequences of these processes in a dense stellar cluster are discussed in detail. When the amplitude of a tide and the subsequent oscillations are sufficiently large, the energy deposited in a star after periastron passage and formation of a bound orbit cannot be estimated directly using the linear theory of oscillations of a spherical star, but rather numerical estimates must be used. The evolution of a star after tidal capture is discussed. The maximum ratio R of the cross-section for tidal capture to that for tidal disruption is about 3 for real systems. For the case of a stellar system with an empty capture loss cone, even in the case when the impact parameter for tidal capture only slightly exceeds the impact parameter for direct tidal disruption, tidal capture would be much more important than tidal disruption.

APIC. Absolute Position Interfero-Coronagraph for direct exoplanet detection

NASA Astrophysics Data System (ADS)

Allouche, F.; Glindemann, A.; Aristidi, E.; Vakili, F.

2009-06-01

Context: For detecting and directly imaging exoplanets, coronagraphic methods are mandatory when the intensity ratio between a star and its orbiting planet can be as large as 10^6. In 1996, a concept of an achromatic interfero-coronagraph (AIC) was presented for detecting very faint stellar companions, such as exoplanets. Aims: We present a modified version of the AIC not only permitting these faint companions to be detected but also their relative position to be determined with respect to the parent star, a problem that was not solved in the original design of the AIC. Methods: In our modified design, two cylindrical lens doublets were used to remove the 180° ambiguity introduced by the AIC's original design. Results: Our theoretical study and the numerical computations show that the axis of symmetry is destroyed when one of the cylindrical doublets is rotated around the optical axis.

Mars Relay Spacecraft: A Low-Cost Approach

NASA Technical Reports Server (NTRS)

SvitekT, .; King, J.; Fulton, R.; McOmber, R.; Hastrup, R.; Miller, A.

1995-01-01

The next phase of Mars exploration will utilize numerous globally distributed small low-cost devices including landers penetrators microrovers and balloons. Direct-to-Earth communications links if required for these landers will drive the lander design for two reasons: a) mass and complexity needed for a steerable high-gain antenna and b) power requirements for a high-power amplifier (i.e. solar panel and battery mass). Total mass of the direct link hardware for several recent small-lander designs exceeded the mass of the scientific payload. Alternatively if communications are via a Mars-orbiting relay spacecraft resource requirements for the local UHF communication link are comparatively trivial: a simple whip antenna and less than 1 watt power. Clearly using a Mars relay spacecraft (MRS) is the preferred option if the MRS mission can be accomplished in an affordable and robust way. Our paper describes a point design for such a mission launched in the s001 or 2003 opportunity.

Orbit classification in an equal-mass non-spinning binary black hole pseudo-Newtonian system

NASA Astrophysics Data System (ADS)

Zotos, Euaggelos E.; Dubeibe, Fredy L.; González, Guillermo A.

2018-07-01

The dynamics of a test particle in a non-spinning binary black hole system of equal masses is numerically investigated. The binary system is modelled in the context of the pseudo-Newtonian circular restricted three-body problem, such that the primaries are separated by a fixed distance and move in a circular orbit around each other. In particular, the Paczyński-Wiita potential is used for describing the gravitational field of the two non-Newtonian primaries. The orbital properties of the test particle are determined through the classification of the initial conditions of the orbits, using several values of the Jacobi constant, in the Hill's regions of possible motion. The initial conditions are classified into three main categories: (i) bounded, (ii) escaping, and (iii) displaying close encounters. Using the smaller alignment index chaos indicator, we further classify bounded orbits into regular, sticky, or chaotic. To gain a complete view of the dynamics of the system, we define grids of initial conditions on different types of two-dimensional planes. The orbital structure of the configuration plane, along with the corresponding distributions of the escape and collision/close encounter times, allow us to observe the transition from the classical Newtonian to the pseudo-Newtonian regime. Our numerical results reveal a strong dependence of the properties of the considered basins with the Jacobi constant as well as with the Schwarzschild radius of the black holes.

The analysis of influence of field of co-rotation on motion of submicronic particles in the Earth's plasmasphere

NASA Astrophysics Data System (ADS)

Yakovlev, A. B.

2018-05-01

The analysis of the motion of micro-particles with radii of several dozens of nanometers in the Earth's plasmasphere has confirmed that the earlier proved statement about conservation of the form for an orbit of a particle with constant electric charge which moves in superposition of the central gravitational field and the field of a magnetic dipole is true also for the case of a quasi-equilibrium electric charge. For a wide range of altitudes and the sizes of micro-particles other forces that act on the charged grain make considerably smaller impact on its motion. On the basis of numerical simulation it has been shown that for motion in an equatorial plane the field of co-rotation leads to very small monotonous growth of the semimajor axis and an orbit eccentricity, and for not-equatorial orbits there are fluctuations of the semimajor axis, an eccentricity and an inclination of an orbit with the period that considerably exceeds the period of orbital motion. In this paper, on the basis of the analysis of the canonical equations of the motion of a micro-particle in superposition of the central gravitational field and the field of co-rotation the explanation of the time dependences obtained numerically for the basic characteristics of an orbit of a micro-particle is proposed.

A time-efficient implementation of Extended Kalman Filter for sequential orbit determination and a case study for onboard application

NASA Astrophysics Data System (ADS)

Tang, Jingshi; Wang, Haihong; Chen, Qiuli; Chen, Zhonggui; Zheng, Jinjun; Cheng, Haowen; Liu, Lin

2018-07-01

Onboard orbit determination (OD) is often used in space missions, with which mission support can be partially accomplished autonomously, with less dependency on ground stations. In major Global Navigation Satellite Systems (GNSS), inter-satellite link is also an essential upgrade in the future generations. To serve for autonomous operation, sequential OD method is crucial to provide real-time or near real-time solutions. The Extended Kalman Filter (EKF) is an effective and convenient sequential estimator that is widely used in onboard application. The filter requires the solutions of state transition matrix (STM) and the process noise transition matrix, which are always obtained by numerical integration. However, numerically integrating the differential equations is a CPU intensive process and consumes a large portion of the time in EKF procedures. In this paper, we present an implementation that uses the analytical solutions of these transition matrices to replace the numerical calculations. This analytical implementation is demonstrated and verified using a fictitious constellation based on selected medium Earth orbit (MEO) and inclined Geosynchronous orbit (IGSO) satellites. We show that this implementation performs effectively and converges quickly, steadily and accurately in the presence of considerable errors in the initial values, measurements and force models. The filter is able to converge within 2-4 h of flight time in our simulation. The observation residual is consistent with simulated measurement error, which is about a few centimeters in our scenarios. Compared to results implemented with numerically integrated STM, the analytical implementation shows results with consistent accuracy, while it takes only about half the CPU time to filter a 10-day measurement series. The future possible extensions are also discussed to fit in various missions.

Analytical and numerical algorthms for revelation and investigation of secular resonances in the motion of near earth space objects. (Russian Title: Численно-аналитическая методика выявления и исследования вековых резонансов в движении околоземных объектов)

NASA Astrophysics Data System (ADS)

Bordovitsyna, T. V.; Tomilova, I. V.; Chuvashov, I. N.

2011-07-01

In this paper complex of analytical and numerical algorithms for revelation and investigation of secular resonances in the motion of near Earth space objects are presented. Analytical numerical algorithm for revelation secular resonances and numerical ones for study of object's long-time orbital evolution are applied. Small denominators are used as indicators of the secular resonances presence. The program complex "The numerical model of the motion of the Earth artificial satellite systems" are used for investigation of the orbital evolution.

Orbits of the inner satellites of Neptune

NASA Astrophysics Data System (ADS)

Brozovic, Marina; Showalter, Mark R.; Jacobson, Robert Arthur; French, Robert S.; de Pater, Imke; Lissauer, Jack

2018-04-01

We report on the numerically integrated orbits of seven inner satellites of Neptune, including S/2004 N1, the last moon of Neptune to be discovered by the Hubble Space Telescope (HST). The dataset includes Voyager imaging data as well as the HST and Earth-based astrometric data. The observations span time period from 1989 to 2016. Our orbital model accounts for the equatorial bulge of Neptune, perturbations from the Sun and the planets, and perturbations from Triton. The initial orbital integration assumed that the satellites are massless, but the residuals improved significantly as the masses adjusted toward values that implied that the density of the satellites is in the realm of 1 g/cm3. We will discuss how the integrated orbits compare to the precessing ellipses fits, mean orbital elements, current orbital uncertainties, and the need for future observations.

Analytic model for the long-term evolution of circular Earth satellite orbits including lunar node regression

NASA Astrophysics Data System (ADS)

Zhu, Ting-Lei; Zhao, Chang-Yin; Zhang, Ming-Jiang

2017-04-01

This paper aims to obtain an analytic approximation to the evolution of circular orbits governed by the Earth's J2 and the luni-solar gravitational perturbations. Assuming that the lunar orbital plane coincides with the ecliptic plane, Allan and Cook (Proc. R. Soc. A, Math. Phys. Eng. Sci. 280(1380):97, 1964) derived an analytic solution to the orbital plane evolution of circular orbits. Using their result as an intermediate solution, we establish an approximate analytic model with lunar orbital inclination and its node regression be taken into account. Finally, an approximate analytic expression is derived, which is accurate compared to the numerical results except for the resonant cases when the period of the reference orbit approximately equals the integer multiples (especially 1 or 2 times) of lunar node regression period.

An Observational Study of Accretion Dynamics in Short-Period Pre-Main Sequence Binaries

NASA Astrophysics Data System (ADS)

Tofflemire, Benjamin; Mathieu, Robert; Herczeg, Greg; Johns-Krull, Christopher; Akeson, Rachel; Ciardi, David

2018-01-01

Over the past thirty years, a detailed picture of star formation has emerged that highlights the importance of the interaction between a pre-main sequence (pre-MS) star and its protoplanetary disk. The properties of an emergent star, the lifetime of a protoplanetary disk, and the formation of planets are all, in part, determined by this star-disk interaction. Many stars, however, form in binary or higher-order systems where orbital dynamics are capable of fundamentally altering this star-disk interaction. Orbital resonances, especially in short-period systems, are capable of clearing the central region of a protoplanetary disk, leaving the possibility for three stable accretion disks: a circumstellar disk around each star and a circumbinary disk. In this model, accretion onto the stars is predicted to proceed in periodic streams that form at the inner edge of the circumbinary disk, cross the dynamically cleared gap, and feed circumstellar disks or accrete directly onto the stars themselves. This pulsed-accretion paradigm predicts bursts of accretion that are periodic with the orbital period, where the duration, amplitude, location in orbital phase, and which star if preferentially fed, all depend on the orbital parameters. To test these predictions, we have carried out intensive observational campaigns combining time-series, optical and near-infrared photometry with time-series, optical spectroscopy. These data are capable of monitoring the stellar accretion rate, the properties of warm circumstellar dust, and the kinematics of accretion flows, all as a function of orbital phase. In our sample of 9 pre-MS binaries with diverse orbital parameters, we search for evidence of periodic accretion events and seek to determine the role orbital parameters have on the characteristics of accretion events. Two results from our campaign will be highlighted: 1) the detection of periodic pulsed accretion events in DQ Tau and TWA 3A, and 2) evidence that the TWA 3A primary is the dominant accretor in the system. We compare these findings to the results of numerical simulations and comment on the role of magnetospheric accretion in pre-MS binaries.

Star motion around rotating black hole in the Galactic Center in real time

NASA Astrophysics Data System (ADS)

Dokuchaev, Vyacheslav; Nazarova, Natalia

2017-12-01

The Event Horizon Telescope team intends by the 2020 to resolve the shadow of supermassive black hole SgrA* in the Galactic Center. It would be the first attempt for direct identification of the enigmatic black hole. In other words, it would be the first experimental verification of the General Relativity in the strong field limit. There is a chance to find a star moving on the relativistic orbit close to this black hole. We present the animated numerical model of the gravitational lensing of a star (or any other lighting probe), moving around rotating Kerr black hole in the Galactic Center and viewed by the distant observer.

Homoclinic orbits in three-dimensional Shilnikov-type chaotic systems

NASA Astrophysics Data System (ADS)

Feng, Jing-Jing; Zhang, Qi-Chang; Wang, Wei; Hao, Shu-Ying

2013-09-01

In this paper, the Padé approximant and analytic solution in the neighborhood of the initial value are introduced into the process of constructing the Shilnikov type homoclinic trajectories in three-dimensional nonlinear dynamical systems. The PID controller system with quadratic and cubic nonlinearities, the simplified solar-wind-driven-magnetosphere-ionosphere system, and the human DNA sequence system are considered. With the aid of presenting a new condition, the solutions of solving the boundary-value problems which are formulated for the trajectory and evaluating the initial amplitude values become available. At the same time, the value of the bifurcation parameter is obtained directly, which is almost consistent with the numerical result.

Revealing Exo-Zody and Exo-Planets from Solar System Dust Measurements: ALADDIN-2 for the Solar Power Sail Mission

NASA Astrophysics Data System (ADS)

Yano, Hajime; Hirai, Takayuki

2016-07-01

The dust structure of our Solar System provides a benchmark information of dust disks of other exo-planetary systems in general, just like the Sun as the closest main sequence G-star that we can study with the most details. Heliocentric dust distributions and gravitational and orbital interactions with planets such as mean motion resonances (MMRs) of dust flux of our Solar System are what we can transfer the knowledge of our Solar System dust apply to infer anisotropic exo-zodiacal brightness, or spatial structures within a exo-planetary dust disks with information about potentially embedded planets inside. In the coming era of disk resolved observations by ALMA, TMT and other new telescopes, we will be able to apply what we find in the Solar System to the rest of planetary systems. In 2010-11, the IKAROS solar sail spacecraft carried the ALADDIN large area dust detector array to study large meteoroids between the Earth and Venus orbits. Yano et al. directly detected both the Earth's and Venus' MMRs dust structures, being consistent with numerical simulations that predict the existence of such local enhancements of dust distribution around these terrestrial planets, as well as Neptune. JAXA's Solar Power Sail mission plans to carry even larger dust detector inherited the technology onboard IKAROS, namely ALADDIN-2 in order to search for such MMRs in the Mars and Jupiter orbits, as predicted by Kuchner et al.(2000), in addition to make a continuous measurement of large dust flux from 1.0 to 5.2 AU crossing the main asteroid belt up to Jupiter Trojan region. It is also noted that recent reanalysis of the Pioneer 10 and 11 photo polarimeter data suggests a small enhancement of the brightness towards the anti-solar direction near Jupiter the largest planet of our Solar System, implying a possible existence of a dust belt related to the planet. The spatial density of dust particles directly measured by the ALADDIN-2 will provide a more conclusive and direct proof due to the insusceptibility to the background brightness from the stars and the galaxy.

Chaos and nonlinear dynamics of single-particle orbits in a magnetotaillike magnetic field

NASA Technical Reports Server (NTRS)

Chen, J.; Palmadesso, P. J.

1986-01-01

The properties of charged-particle motion in Hamiltonian dynamics are studied in a magnetotaillike magnetic field configuration. It is shown by numerical integration of the equation of motion that the system is generally nonintegrable and that the particle motion can be classified into three distinct types of orbits: bounded integrable orbits, unbounded stochastic orbits, and unbounded transient orbits. It is also shown that different regions of the phase space exhibit qualitatively different responses to external influences. The concept of 'differential memory' in single-particle distributions is proposed. Physical implications for the dynamical properties of the magnetotail plasmas and the possible generation of non-Maxwellian features in the distribution functions are discussed.

Orbit computation of the TELECOM-2D satellite with a Genetic Algorithm

NASA Astrophysics Data System (ADS)

Deleflie, Florent; Coulot, David; Vienne, Alain; Decosta, Romain; Richard, Pascal; Lasri, Mohammed Amjad

2014-07-01

In order to test a preliminary orbit determination method, we fit an orbit of the geostationary satellite TELECOM-2D, as if we did not know any a priori information on its trajectory. The method is based on a genetic algorithm coupled to an analytical propagator of the trajectory, that is used over a couple of days, and that uses a whole set of altazimutal data that are acquired by the tracking network made up of the two TAROT telescopes. The adjusted orbit is then compared to a numerical reference. The method is described, and the results are analyzed, as a step towards an operational method of preliminary orbit determination for uncatalogued objects.

Orbit-attitude coupled motion around small bodies: Sun-synchronous orbits with Sun-tracking attitude motion

NASA Astrophysics Data System (ADS)

Kikuchi, Shota; Howell, Kathleen C.; Tsuda, Yuichi; Kawaguchi, Jun'ichiro

2017-11-01

The motion of a spacecraft in proximity to a small body is significantly perturbed due to its irregular gravity field and solar radiation pressure. In such a strongly perturbed environment, the coupling effect of the orbital and attitude motions exerts a large influence that cannot be neglected. However, natural orbit-attitude coupled dynamics around small bodies that are stationary in both orbital and attitude motions have yet to be observed. The present study therefore investigates natural coupled motion that involves both a Sun-synchronous orbit and Sun-tracking attitude motion. This orbit-attitude coupled motion enables a spacecraft to maintain its orbital geometry and attitude state with respect to the Sun without requiring active control. Therefore, the proposed method can reduce the use of an orbit and attitude control system. This paper first presents analytical conditions to achieve Sun-synchronous orbits and Sun-tracking attitude motion. These analytical solutions are then numerically propagated based on non-linear coupled orbit-attitude equations of motion. Consequently, the possibility of implementing Sun-synchronous orbits with Sun-tracking attitude motion is demonstrated.

Techniques of orbital decay and long-term ephemeris prediction for satellites in earth orbit

NASA Technical Reports Server (NTRS)

Barry, B. F.; Pimm, R. S.; Rowe, C. K.

1971-01-01

In the special perturbation method, Cowell and variation-of-parameters formulations of the motion equations are implemented and numerically integrated. Variations in the orbital elements due to drag are computed using the 1970 Jacchia atmospheric density model, which includes the effects of semiannual variations, diurnal bulge, solar activity, and geomagnetic activity. In the general perturbation method, two-variable asymptotic series and automated manipulation capabilities are used to obtain analytical solutions to the variation-of-parameters equations. Solutions are obtained considering the effect of oblateness only and the combined effects of oblateness and drag. These solutions are then numerically evaluated by means of a FORTRAN program in which an updating scheme is used to maintain accurate epoch values of the elements. The atmospheric density function is approximated by a Fourier series in true anomaly, and the 1970 Jacchia model is used to periodically update the Fourier coefficients. The accuracy of both methods is demonstrated by comparing computed orbital elements to actual elements over time spans of up to 8 days for the special perturbation method and up to 356 days for the general perturbation method.

Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics

NASA Astrophysics Data System (ADS)

Koon, Wang Sang; Lo, Martin W.; Marsden, Jerrold E.; Ross, Shane D.

2000-06-01

In this paper we apply dynamical systems techniques to the problem of heteroclinic connections and resonance transitions in the planar circular restricted three-body problem. These related phenomena have been of concern for some time in topics such as the capture of comets and asteroids and with the design of trajectories for space missions such as the Genesis Discovery Mission. The main new technical result in this paper is the numerical demonstration of the existence of a heteroclinic connection between pairs of periodic orbits: one around the libration point L1 and the other around L2, with the two periodic orbits having the same energy. This result is applied to the resonance transition problem and to the explicit numerical construction of interesting orbits with prescribed itineraries. The point of view developed in this paper is that the invariant manifold structures associated to L1 and L2 as well as the aforementioned heteroclinic connection are fundamental tools that can aid in understanding dynamical channels throughout the solar system as well as transport between the ``interior'' and ``exterior'' Hill's regions and other resonant phenomena.

Effects of perturbations on space debris in supersynchronous storage orbits

NASA Astrophysics Data System (ADS)

Luu, Khanh Kim

1998-12-01

Accumulation of space debris in the geosynchronous region (GEO) has raised attention among spacefaring nations. The current mitigation measure supported is to boost satellites into supersynchronous orbits in the time before station-keeping fuel is expected to be exhausted. Because this solution does not remove mass from space, debris generation by fragmentation events remains a possibility. The collision hazard between inactive satellites in the supersynchronous region raises questions about the consequences of collisions in this regime and possible interaction with GEO. In considering the use of supersynchronous orbits for satellite disposal, the first concern is to determine the minimum safe distance above GEO such that objects in the disposal orbits will not interfere with the GEO population in the future. This involves defining the useful GEO area and studying the perturbation effects on objects in supersynchronous orbits. Thus far, research has focused on propagating the orbits of intact objects. However, in the aftermath of a collision, pieces of varying sizes and shapes can be found in orbits quite different from the parent objects' orbits. This document summarizes background information on debris in the GEO region, sources and management strategies, and then addresses the problem: Will orbits of fragments from a collision in a storage orbit occupy GEO altitudes at some time after the collision? If so, at what altitude should the storage orbit occupy such that collision fragments will not interfere with the GEO population? The methods and tools by which the effects of collisions in the supersynchronous region can be analyzed are discussed. A low-velocity collision model is employed to provide delta-velocities imparted to the fragments. An analytical study of perturbation effects, including solar and lunar third body gravitation, Earth oblateness through degree and order four, and solar radiation pressure, follows in order to evaluate the magnitude of these disturbing forces on the fragmentation debris. Validation of these results by numerical analysis using proven numerical and semianalytical orbit propagators is discussed. The results show that currently practiced reorbiting distances above GEO do not isolate debris from GEO after the occurrence of collisions in the storage orbit.

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.

Consistency of Post-Newtonian Waveforms with Numerical Relativity

NASA Technical Reports Server (NTRS)

Baker, John G.; vanMeter, James R.; McWilliams, Sean T.; Centrella, Joan; Kelly, Bernard J.

2007-01-01

General relativity predicts the gravitational radiation signatures of mergers of compact binaries,such as coalescing binary black hole systems. Derivations of waveform predictions for such systems are required for optimal scientific analysis of observational gravitational wave data, and have so far been achieved primarily with the aid of the post-Newtonian (PN) approximation. The quaIity of this treatment is unclear, however, for the important late inspiral portion. We derive late-inspiral wave forms via a complementary approach, direct numerical simulation of Einstein's equations, which has recently matured sufficiently for such applications. We compare waveform phasing from simulations covering the last approximately 14 cycles of gravitational radiation from an equal-mass binary system of nonspinning black holes with corresponding 3PN and 3.5PN waveforms. We find phasing agreement consistent with internal error estimates based in either approach, at the level of one radian over approximately 10 cycles. The result suggests that PN waveforms for this system are effective roughly until the system reaches its last stable orbit just prior to the final merger.

Non-numeric computation for high eccentricity orbits. [Earth satellite orbit perturbation

NASA Technical Reports Server (NTRS)

Sridharan, R.; Renard, M. L.

1975-01-01

Geocentric orbits of large eccentricity (e = 0.9 to 0.95) are significantly perturbed in cislunar space by the sun and moon. The time-history of the height of perigee, subsequent to launch, is particularly critical. The determination of 'launch windows' is mostly concerned with preventing the height of perigee from falling below its low initial value before the mission lifetime has elapsed. Between the extremes of high accuracy digital integration of the equations of motion and of using an approximate, but very fast, stability criteria method, this paper is concerned with the developement of a method of intermediate complexity using non-numeric computation. The computer is used as the theory generator to generalize Lidov's theory using six osculating elements. Symbolic integration is completely automatized and the output is a set of condensed formulae well suited for repeated applications in launch window analysis. Examples of applications are given.

Bouncing ball problem: stability of the periodic modes.

PubMed

Barroso, Joaquim J; Carneiro, Marcus V; Macau, Elbert E N

2009-02-01

Exploring all its ramifications, we give an overview of the simple yet fundamental bouncing ball problem, which consists of a ball bouncing vertically on a sinusoidally vibrating table under the action of gravity. The dynamics is modeled on the basis of a discrete map of difference equations, which numerically solved fully reveals a rich variety of nonlinear behaviors, encompassing irregular nonperiodic orbits, subharmonic and chaotic motions, chattering mechanisms, and also unbounded nonperiodic orbits. For periodic motions, the corresponding conditions for stability and bifurcation are determined from analytical considerations of a reduced map. Through numerical examples, it is shown that a slight change in the initial conditions makes the ball motion switch from periodic to chaotic orbits bounded by a velocity strip v=+/-Gamma(1-epsilon) , where Gamma is the nondimensionalized shaking acceleration and epsilon the coefficient of restitution which quantifies the amount of energy lost in the ball-table collision.

An energy- and charge-conserving, nonlinearly implicit, electromagnetic 1D-3V Vlasov-Darwin particle-in-cell algorithm

NASA Astrophysics Data System (ADS)

Chen, G.; Chacón, L.

2014-10-01

A recent proof-of-principle study proposes a nonlinear electrostatic implicit particle-in-cell (PIC) algorithm in one dimension (Chen et al., 2011). The algorithm employs a kinetically enslaved Jacobian-free Newton-Krylov (JFNK) method, and conserves energy and charge to numerical round-off. In this study, we generalize the method to electromagnetic simulations in 1D using the Darwin approximation to Maxwell's equations, which avoids radiative noise issues by ordering out the light wave. An implicit, orbit-averaged, time-space-centered finite difference scheme is employed in both the 1D Darwin field equations (in potential form) and the 1D-3V particle orbit equations to produce a discrete system that remains exactly charge- and energy-conserving. Furthermore, enabled by the implicit Darwin equations, exact conservation of the canonical momentum per particle in any ignorable direction is enforced via a suitable scattering rule for the magnetic field. We have developed a simple preconditioner that targets electrostatic waves and skin currents, and allows us to employ time steps O(√{mi /me } c /veT) larger than the explicit CFL. Several 1D numerical experiments demonstrate the accuracy, performance, and conservation properties of the algorithm. In particular, the scheme is shown to be second-order accurate, and CPU speedups of more than three orders of magnitude vs. an explicit Vlasov-Maxwell solver are demonstrated in the "cold" plasma regime (where kλD ≪ 1).

Orbit determination and gravity field recovery from Doppler tracking data to the Lunar Reconnaissance Orbiter

NASA Astrophysics Data System (ADS)

Maier, Andrea; Baur, Oliver

2016-03-01

We present results for Precise Orbit Determination (POD) of the Lunar Reconnaissance Orbiter (LRO) based on two-way Doppler range-rates over a time span of ~13 months (January 3, 2011 to February 9, 2012). Different orbital arc lengths and various sets of empirical parameters were tested to seek optimal parametrization. An overlap analysis covering three months of Doppler data shows that the most precise orbits are obtained using an arc length of 2.5 days and estimating arc-wise constant empirical accelerations in along track direction. The overlap analysis over the entire investigated time span of 13 months indicates an orbital precision of 13.79 m, 14.17 m, and 1.28 m in along track, cross track, and radial direction, respectively, with 21.32 m in total position. We compare our orbits to the official science orbits released by the US National Aeronautics and Space Administration (NASA). The differences amount to 9.50 m, 6.98 m, and 1.50 m in along track, cross track, and radial direction, respectively, as well as 12.71 m in total position. Based on the reconstructed LRO orbits, we estimated lunar gravity field coefficients up to spherical harmonic degree and order 60. The results are compared to gravity field solutions derived from data collected by other lunar missions.

Fast numerics for the spin orbit equation with realistic tidal dissipation and constant eccentricity

NASA Astrophysics Data System (ADS)

Bartuccelli, Michele; Deane, Jonathan; Gentile, Guido

2017-08-01

We present an algorithm for the rapid numerical integration of a time-periodic ODE with a small dissipation term that is C^1 in the velocity. Such an ODE arises as a model of spin-orbit coupling in a star/planet system, and the motivation for devising a fast algorithm for its solution comes from the desire to estimate probability of capture in various solutions, via Monte Carlo simulation: the integration times are very long, since we are interested in phenomena occurring on timescales of the order of 10^6-10^7 years. The proposed algorithm is based on the high-order Euler method which was described in Bartuccelli et al. (Celest Mech Dyn Astron 121(3):233-260, 2015), and it requires computer algebra to set up the code for its implementation. The payoff is an overall increase in speed by a factor of about 7.5 compared to standard numerical methods. Means for accelerating the purely numerical computation are also discussed.

On the accuracy and precision of numerical waveforms: effect of waveform extraction methodology

NASA Astrophysics Data System (ADS)

Chu, Tony; Fong, Heather; Kumar, Prayush; Pfeiffer, Harald P.; Boyle, Michael; Hemberger, Daniel A.; Kidder, Lawrence E.; Scheel, Mark A.; Szilagyi, Bela

2016-08-01

We present a new set of 95 numerical relativity simulations of non-precessing binary black holes (BBHs). The simulations sample comprehensively both black-hole spins up to spin magnitude of 0.9, and cover mass ratios 1-3. The simulations cover on average 24 inspiral orbits, plus merger and ringdown, with low initial orbital eccentricities e\\lt {10}-4. A subset of the simulations extends the coverage of non-spinning BBHs up to mass ratio q = 10. Gravitational waveforms at asymptotic infinity are computed with two independent techniques: extrapolation and Cauchy characteristic extraction. An error analysis based on noise-weighted inner products is performed. We find that numerical truncation error, error due to gravitational wave extraction, and errors due to the Fourier transformation of signals with finite length of the numerical waveforms are of similar magnitude, with gravitational wave extraction errors dominating at noise-weighted mismatches of ˜ 3× {10}-4. This set of waveforms will serve to validate and improve aligned-spin waveform models for gravitational wave science.

Tides and tsunamis

NASA Technical Reports Server (NTRS)

Zetler, B. D.

1972-01-01

Although tides and tsunamis are both shallow water waves, it does not follow that they are equally amenable to an observational program using an orbiting altimeter on a satellite. A numerical feasibility investigation using a hypothetical satellite orbit, real tide observations, and sequentially increased levels of white noise has been conducted to study the degradation of the tidal harmonic constants caused by adding noise to the tide data. Tsunami waves, possibly a foot high and one hundred miles long, must be measured in individual orbits, thus requiring high relative resolution.

Topological quantum phase transitions and edge states in spin-orbital coupled Fermi gases.

PubMed

Zhou, Tao; Gao, Yi; Wang, Z D

2014-06-11

We study superconducting states in the presence of spin-orbital coupling and Zeeman field. It is found that a phase transition from a Fulde-Ferrell-Larkin-Ovchinnikov state to the topological superconducting state occurs upon increasing the spin-orbital coupling. The nature of this topological phase transition and its critical property are investigated numerically. Physical properties of the topological superconducting phase are also explored. Moreover, the local density of states is calculated, through which the topological feature may be tested experimentally.

Electric control of superconducting transition through a spin-orbit coupled interface

PubMed Central

Ouassou, Jabir Ali; Di Bernardo, Angelo; Robinson, Jason W. A.; Linder, Jacob

2016-01-01

We demonstrate theoretically all-electric control of the superconducting transition temperature using a device comprised of a conventional superconductor, a ferromagnetic insulator, and semiconducting layers with intrinsic spin-orbit coupling. By using analytical calculations and numerical simulations, we show that the transition temperature of such a device can be controlled by electric gating which alters the ratio of Rashba to Dresselhaus spin-orbit coupling. The results offer a new pathway to control superconductivity in spintronic devices. PMID:27426887

On the small-x behavior of the orbital angular momentum distributions in QCD

NASA Astrophysics Data System (ADS)

Hatta, Yoshitaka; Yang, Dong-Jing

2018-06-01

We present the numerical solution of the leading order QCD evolution equation for the orbital angular momentum distributions of quarks and gluons and discuss its implications for the nucleon spin sum rule. We observe that at small-x, the gluon helicity and orbital angular momentum distributions are roughly of the same magnitude but with opposite signs, indicating a significant cancellation between them. A similar cancellation occurs also in the quark sector. We explain analytically the reason for this cancellation.

Exact Delaunay normalization of the perturbed Keplerian Hamiltonian with tesseral harmonics

NASA Astrophysics Data System (ADS)

Mahajan, Bharat; Vadali, Srinivas R.; Alfriend, Kyle T.

2018-03-01

A novel approach for the exact Delaunay normalization of the perturbed Keplerian Hamiltonian with tesseral and sectorial spherical harmonics is presented in this work. It is shown that the exact solution for the Delaunay normalization can be reduced to quadratures by the application of Deprit's Lie-transform-based perturbation method. Two different series representations of the quadratures, one in powers of the eccentricity and the other in powers of the ratio of the Earth's angular velocity to the satellite's mean motion, are derived. The latter series representation produces expressions for the short-period variations that are similar to those obtained from the conventional method of relegation. Alternatively, the quadratures can be evaluated numerically, resulting in more compact expressions for the short-period variations that are valid for an elliptic orbit with an arbitrary value of the eccentricity. Using the proposed methodology for the Delaunay normalization, generalized expressions for the short-period variations of the equinoctial orbital elements, valid for an arbitrary tesseral or sectorial harmonic, are derived. The result is a compact unified artificial satellite theory for the sub-synchronous and super-synchronous orbit regimes, which is nonsingular for the resonant orbits, and is closed-form in the eccentricity as well. The accuracy of the proposed theory is validated by comparison with numerical orbit propagations.

Trajectory optimization for an asymmetric launch vehicle. M.S. Thesis - MIT

NASA Technical Reports Server (NTRS)

Sullivan, Jeanne Marie

1990-01-01

A numerical optimization technique is used to fully automate the trajectory design process for an symmetric configuration of the proposed Advanced Launch System (ALS). The objective of the ALS trajectory design process is the maximization of the vehicle mass when it reaches the desired orbit. The trajectories used were based on a simple shape that could be described by a small set of parameters. The use of a simple trajectory model can significantly reduce the computation time required for trajectory optimization. A predictive simulation was developed to determine the on-orbit mass given an initial vehicle state, wind information, and a set of trajectory parameters. This simulation utilizes an idealized control system to speed computation by increasing the integration time step. The conjugate gradient method is used for the numerical optimization of on-orbit mass. The method requires only the evaluation of the on-orbit mass function using the predictive simulation, and the gradient of the on-orbit mass function with respect to the trajectory parameters. The gradient is approximated with finite differencing. Prelaunch trajectory designs were carried out using the optimization procedure. The predictive simulation is used in flight to redesign the trajectory to account for trajectory deviations produced by off-nominal conditions, e.g., stronger than expected head winds.

Creating optical near-field orbital angular momentum in a gold metasurface.

PubMed

Chen, Ching-Fu; Ku, Chen-Ta; Tai, Yi-Hsin; Wei, Pei-Kuen; Lin, Heh-Nan; Huang, Chen-Bin

2015-04-08

Nanocavities inscribed in a gold thin film are optimized and designed to form a metasurface. We demonstrate both numerically and experimentally the creation of surface plasmon (SP) vortex carrying orbital angular momentum in the metasurface under linearly polarized optical excitation that carries no optical angular momentum. Moreover, depending on the orientation of the exciting linearly polarized light, we show that the metasurface is capable of providing dynamic switching between SP vortex formation or SP subwavelength focusing. The resulting SP intensities are experimentally measured using a near-field scanning optical microscope and are found in excellent quantitative agreements as compared to the numerical results.

Shuttle optical environment; Proceedings of the Meeting, Washington, DC, April 23, 24, 1981

NASA Technical Reports Server (NTRS)

Miller, E. R. (Editor); Fazio, G. G.

1982-01-01

The numerical modeling, instrumentation, identification, and procedures to characterize and/or control contamination hazards to equipment used on the Shuttle are discussed. On-orbit pollutants include molecular offgassing and outgassing, particulate material, and substances from thrusters, vents, and leaks. Clean-rooms are being implemented in ground assembly and integration facilities. Attention is given to an upgraded SPACE program for numerically modeling contamination pathways and appropriate procedures to protect instrumentation from film and particulate deposition. Finally, attention is given to military cryogenic IR detectors being employed to quantify the Shuttle thermal and solid pollutant environment on-orbit as a prelude to future operational IR sensors.

A new empirical solar radiation pressure model for BeiDou GEO satellites

NASA Astrophysics Data System (ADS)

Liu, Junhong; Gu, Defeng; Ju, Bing; Shen, Zhen; Lai, Yuwang; Yi, Dongyun

2016-01-01

Two classic empirical solar radiation pressure (SRP) models, the Extended Center for Orbit Determination in Europe (CODE) Orbit Model ECOM 5 and ECOM 9 have been widely used for Global Positioning System (GPS) Medium Earth Orbit (MEO) satellites precise orbit determination (POD). However, these two models are not suitable for BeiDou Geostationary Earth Orbit (GEO) satellites due to their special attitude control mode. With the experimental design method this paper proposes a new empirical SRP model for BeiDou GEO satellites, which is featured by three constant terms in DYX directions, two sine terms in DX directions and one cosine term in the Y direction. It is the first time to reveal that the periodic terms in the D direction are more important than those in YX directions for BeiDou GEO satellites. Compared with ECOM 5 and ECOM 9, the BeiDou GEO satellite orbits are significantly stabilized with the new SRP force model. The average orbit overlapping root mean square (RMS) achieved by the proposed model is 7.5 cm in the radial component, which is evidently improved over those of 37.4 and 13.2 cm for ECOM 5 and ECOM 9, respectively. In addition, the correlation coefficients between GEO orbit overlaps precision and the elevation angle of the Sun have been decreased to -0.12, 0.21, and -0.03 in radial, along-track and cross-track components by using the proposed model, while they are -0.94, -0.79 and -0.29 for ECOM 5 and -0.70, 0.21 and 0.10 for ECOM 9. Moreover, the standard deviation (STD) of Satellite Laser Ranging (SLR) data residuals for the GEO satellite C01 is reduced by 37.4% and 16.1% compared with those of ECOM 5 and ECOM 9 SRP models.

A comparison of Lorentz, planetary gravitational, and satellite gravitational resonances

NASA Technical Reports Server (NTRS)

Hamilton, Douglas P.

1994-01-01

We consider a charged dust grain whose orbital motion is dominated by a planet's point-source gravity, but perturbed by higher-order terms in the planet's gravity field as well as by the Lorentz force arising from an asymmetric planetary magnetic field. Perturbations to Keplerian orbits due to a nonspherical gravity field are expressed in the traditional way: in terms of a disturbing function which can be expanded in a series of spherical harmonics (W. M. Kaula, 1966). In order to calculate the electromagnetic perturbation, we first write the Lorentz force in terms of the orbital elements and then substitute it into Gauss' perturbation equations. We use our result to derive strengths of Lorentz resonances and elucidate their properties. In particular, we compare Lorentz resonances to two types of gravitational resonances: those arising from periodic tugs of a satellite and those due to the attraction of an arbitrarily shaped planet. We find that Lorentz resonances share numerous properties with their gravitational counterparts and show, using simple physical arguments, that several of these patterns are fundamental, applying not only to our expansions, but to all quantities expressed in terms of orbital elements. Some of these patterns have been previously called 'd'Alembert rules' for satellite resonances. Other similarities arise because, to first-order in the perturbing force, the three problems share an integral of the motion. Yet there are also differences; for example, first-order inclination resonances exist for perturbations arising from planetary gravity and from the Lorentz force, but not for those due to an orbiting satellite. Finally, we provide a heuristic treatment of a particle's orbital evolution under the influence of drag and resonant forces. Particles brought into mean-motion resonances experience either trapping or resonant 'jumps,' depending on the direction from which the resonance is approached. We show that this behavior does not depend on the details of the perturbing force but rather is fundamental to all mean-motion resonances.

Trojan resonant dynamics, stability, and chaotic diffusion, for parameters relevant to exoplanetary systems

NASA Astrophysics Data System (ADS)

Páez, Rocío Isabel; Efthymiopoulos, Christos

2015-02-01

The possibility that giant extrasolar planets could have small Trojan co-orbital companions has been examined in the literature from both viewpoints of the origin and dynamical stability of such a configuration. Here we aim to investigate the dynamics of hypothetical small Trojan exoplanets in domains of secondary resonances embedded within the tadpole domain of motion. To this end, we consider the limit of a massless Trojan companion of a giant planet. Without other planets, this is a case of the elliptic restricted three body problem (ERTBP). The presence of additional planets (hereafter referred to as the restricted multi-planet problem, RMPP) induces new direct and indirect secular effects on the dynamics of the Trojan body. The paper contains a theoretical and a numerical part. In the theoretical part, we develop a Hamiltonian formalism in action-angle variables, which allows us to treat in a unified way resonant dynamics and secular effects on the Trojan body in both the ERTBP or the RMPP. In both cases, our formalism leads to a decomposition of the Hamiltonian in two parts, . , called the basic model, describes resonant dynamics in the short-period (epicyclic) and synodic (libration) degrees of freedom, while contains only terms depending trigonometrically on slow (secular) angles. is formally identical in the ERTBP and the RMPP, apart from a re-definition of some angular variables. An important physical consequence of this analysis is that the slow chaotic diffusion along resonances proceeds in both the ERTBP and the RMPP by a qualitatively similar dynamical mechanism. We found that this is best approximated by the paradigm of `modulational diffusion'. In the paper's numerical part, we then focus on the ERTBP in order to make a detailed numerical demonstration of the chaotic diffusion process along resonances. Using color stability maps, we first provide a survey of the resonant web for characteristic mass parameter values of the primary, in which the secondary resonances from 1:5 to 1:12 (ratio of the short over the synodic period), as well as their transverse resonant multiplets, appear. We give numerical examples of diffusion of weakly chaotic orbits in the resonant web. We finally make a statistics of the escaping times in the resonant domain, and find power-law tails of the distribution of the escaping times for the slowly diffusing chaotic orbits. Implications of resonant dynamics in the search for Trojan exoplanets are discussed.

Electric-field control of a hydrogenic donor's spin in a semiconductor

NASA Astrophysics Data System (ADS)

de, Amrit; Pryor, Craig E.; Flatté, Michael E.

2009-03-01

The orbital wave function of an electron bound to a single donor in a semiconductor can be modulated by an applied AC electric field, which affects the electron spin dynamics via the spin-orbit interaction. Numerical calculations of the spin dynamics of a single hydrogenic donor (Si) using a real-space multi-band k.p formalism show that in addition to breaking the high symmetry of the hydrogenic donor state, the g-tensor has a strong nonlinear dependence on the applied fields. By explicitly integrating the time dependent Schr"odinger equation it is seen that Rabi oscillations can be obtained for electric fields modulated at sub-harmonics of the Larmor frequency. The Rabi frequencies obtained from sub-harmonic modulation depend on the magnitudes of the AC and DC components of the electric field. For a purely AC field, the highest Rabi frequency is obtained when E is driven at the 2nd sub-harmonic of the Larmor frequency. Apart from suggesting ways to measure g-tensor anisotropies and nonlinearities, these results also suggest the possibility of direct frequency domain measurements of Rabi frequencies.

Turbulence mitigation scheme based on spatial diversity in orbital-angular-momentum multiplexed system

NASA Astrophysics Data System (ADS)

Zou, Li; Wang, Le; Zhao, Shengmei

2017-10-01

Atmospheric turbulence (AT) induced crosstalk can significantly impair the performance of free-space optical (FSO) communication link using orbital angular momentum (OAM) multiplexing. In this paper, we propose a spatial diversity (SD) turbulence mitigation scheme in an OAM-multiplexed FSO communication link. First, we present a SD mitigation model for the OAM-multiplexed FSO communication link under AT. Then we present a SD combining technique based on equal gain to enhance AT tolerance of the OAM-multiplexed FSO communication link. The numerical results show that performance of the OAM-multiplexed communication link has greatly improved by the proposed scheme. When the turbulence strength Cn2 is 5 × 10-15m - 2 / 3, the transmission distance is 1000 m and the channel signal-to-noise ratio (SNR) is 20 dB, the bit-error-rate (BER) performance of four spatial multiplexed OAM modes lm = + 1 , + 2 , + 3 , + 4 are 3 fold increase in comparison with those results without the proposed scheme. The proposed scheme is a promising direction for compensating the interference caused by AT in the OAM-multiplexed FSO communication link.

Incorporating Planetary-Scale Waves Into the VTGCM: Understanding the Waves Impact on the Upper Atmosphere of Venus.

NASA Technical Reports Server (NTRS)

Brecht, A. S.; Bougher, S. W.; Shields, D.; Liu, H.

2017-01-01

Venus has proven to have a very dynamic upper atmosphere. The upper atmosphere of Venus has been observed for many decades by multiple means of observation (e.g. ground-based, orbiters, probes, fly-by missions going to other planets). As of late, the European Space Agency Venus Express (VEX) orbiter has been a main observer of the Venusian atmosphere. Specifically, observations of Venus' O2 IR nightglow emission have been presented to show its variability. Nightglow emission is directly connected to Venus' circulation and is utilized as a tracer for the atmospheric global wind system. More recent observations are adding and augmenting temperature and density (e.g. CO, CO2, SO2) datasets. These additional datasets provide a means to begin analyzing the variability and study the potential drivers of the variability. A commonly discussed driver of variability is wave deposition. Evidence of waves has been observed, but these waves have not been completely analyzed to understand how and where they are important. A way to interpret the observations and test potential drivers is by utilizing numerical models.

Probability of coincidental similarity among the orbits of small bodies - I. Pairing

NASA Astrophysics Data System (ADS)

Jopek, Tadeusz Jan; Bronikowska, Małgorzata

2017-09-01

Probability of coincidental clustering among orbits of comets, asteroids and meteoroids depends on many factors like: the size of the orbital sample searched for clusters or the size of the identified group, it is different for groups of 2,3,4,… members. Probability of coincidental clustering is assessed by the numerical simulation, therefore, it depends also on the method used for the synthetic orbits generation. We have tested the impact of some of these factors. For a given size of the orbital sample we have assessed probability of random pairing among several orbital populations of different sizes. We have found how these probabilities vary with the size of the orbital samples. Finally, keeping fixed size of the orbital sample we have shown that the probability of random pairing can be significantly different for the orbital samples obtained by different observation techniques. Also for the user convenience we have obtained several formulae which, for given size of the orbital sample can be used to calculate the similarity threshold corresponding to the small value of the probability of coincidental similarity among two orbits.

14 CFR 417.3 - Definitions and acronyms.

Code of Federal Regulations, 2010 CFR

2010-01-01

... vehicle during— (i) The ascent to initial orbital insertion and through at least one complete orbit; and (ii) Each subsequent orbital maneuver or burn from initial park orbit, or direct ascent to a higher or... launch vehicle achieves orbit or can no longer reach a populated or other protected area. Command...

14 CFR 417.3 - Definitions and acronyms.

Code of Federal Regulations, 2011 CFR

2011-01-01

... vehicle during— (i) The ascent to initial orbital insertion and through at least one complete orbit; and (ii) Each subsequent orbital maneuver or burn from initial park orbit, or direct ascent to a higher or... launch vehicle achieves orbit or can no longer reach a populated or other protected area. Command...

14 CFR 417.3 - Definitions and acronyms.

Code of Federal Regulations, 2014 CFR

2014-01-01

... vehicle during— (i) The ascent to initial orbital insertion and through at least one complete orbit; and (ii) Each subsequent orbital maneuver or burn from initial park orbit, or direct ascent to a higher or... launch vehicle achieves orbit or can no longer reach a populated or other protected area. Command...

14 CFR 417.3 - Definitions and acronyms.

Code of Federal Regulations, 2012 CFR

2012-01-01

... vehicle during— (i) The ascent to initial orbital insertion and through at least one complete orbit; and (ii) Each subsequent orbital maneuver or burn from initial park orbit, or direct ascent to a higher or... launch vehicle achieves orbit or can no longer reach a populated or other protected area. Command...

14 CFR 417.3 - Definitions and acronyms.

Code of Federal Regulations, 2013 CFR

2013-01-01

... vehicle during— (i) The ascent to initial orbital insertion and through at least one complete orbit; and (ii) Each subsequent orbital maneuver or burn from initial park orbit, or direct ascent to a higher or... launch vehicle achieves orbit or can no longer reach a populated or other protected area. Command...

Finite Larmor radius effects on weak turbulence transport

NASA Astrophysics Data System (ADS)

Kryukov, N.; Martinell, J. J.

2018-06-01

Transport of test particles in two-dimensional weak turbulence with waves propagating along the poloidal direction is studied using a reduced model. Finite Larmor radius (FLR) effects are included by gyroaveraging over one particle orbit. For low wave amplitudes the motion is mostly regular with particles trapped in the potential wells. As the amplitude increases the trajectories become chaotic and the Larmor radius modifies the orbits. For a thermal distribution of Finite Larmor radii the particle distribution function (PDF) is Gaussian for small th$ (thermal gyroradius) but becomes non-Gaussian for large th$ . However, the time scaling of transport is diffusive, as characterized by a linear dependence of the variance of the PDF with time. An explanation for this behaviour is presented that provides an expression for an effective diffusion coefficient and reproduces the numerical results for large wave amplitudes which implies generalized chaos. When a shear flow is added in the direction of wave propagation, a modified model is obtained that produces free-streaming particle trajectories in addition to trapped ones; these contribute to ballistic transport for low wave amplitude but produce super-ballistic transport in the chaotic regime. As in the previous case, the PDF is Gaussian for low th$ becoming non-Gaussian as it increases. The perpendicular transport presents the same behaviour as in the case with no flow but the diffusion is faster in the presence of the flow.

Orbit-based analysis of nonlinear energetic ion dynamics in tokamaks. II. Mechanisms for rapid chirping and convective amplification

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

Bierwage, Andreas; Shinohara, Kouji

2016-04-15

The nonlinear interactions between shear Alfvén modes and tangentially injected beam ions in the 150–400 keV range are studied numerically in realistic geometry for a JT-60U tokamak scenario. In Paper I, which was reported in the companion paper, the recently developed orbit-based resonance analysis method was used to track the resonant frequency of fast ions during their nonlinear evolution subject to large magnetic and electric drifts. Here, that method is applied to map the wave-particle power transfer from the canonical guiding center phase space into the frequency-radius plane, where it can be directly compared with the evolution of the fluctuation spectramore » of fast-ion-driven modes. Using this technique, we study the nonlinear dynamics of strongly driven shear Alfvén modes with low toroidal mode numbers n = 1 and n = 3. In the n = 3 case, both chirping and convective amplification can be attributed to the mode following the resonant frequency of the radially displaced particles, i.e., the usual one-dimensional phase locking process. In the n = 1 case, a new chirping mechanism is found, which involves multiple dimensions, namely, wave-particle trapping in the radial direction and phase mixing across velocity coordinates.« less

Nonreciprocal Transverse Photonic Spin and Magnetization-Induced Electromagnetic Spin-Orbit Coupling

PubMed Central

Levy, Miguel; Karki, Dolendra

2017-01-01

We present a formulation of electromagnetic spin-orbit coupling in magneto-optic media, and propose an alternative source of spin-orbit coupling to non-paraxial optics vortices. Our treatment puts forth a formulation of nonreciprocal transverse-spin angular-momentum-density shifts for evanescent waves in magneto-optic waveguide media. It shows that magnetization-induced electromagnetic spin-orbit coupling is possible, and that it leads to unequal spin to orbital angular momentum conversion in magneto-optic media evanescent waves in opposite propagation-directions. Generation of free-space helicoidal beams based on this conversion is shown to be spin-helicity- and magnetization-dependent. We show that transverse-spin to orbital angular momentum coupling into magneto-optic waveguide media engenders spin-helicity-dependent unidirectional propagation. This unidirectional effect produces different orbital angular momenta in opposite directions upon excitation-spin-helicity reversals. PMID:28059120

Does Newton’s gravitational constant vary sinusoidally with time? Orbital motions say no

NASA Astrophysics Data System (ADS)

Iorio, Lorenzo

2016-02-01

A sinusoidally time-varying pattern of the values of Newton’s constant of gravitation G measured in Earth-based laboratories over the last few decades has been recently reported in the literature. We put to the test the hypothesis that the aforementioned harmonic variation may pertain to G itself in a direct and independent way. We numerically integrated the ad hoc modified equations of motion of the major bodies of the Solar System, finding that the orbits of the planets would be altered by an unacceptably larger amount in view of the present-day high accuracy astrometric measurements. In the case of Saturn, its geocentric right ascension α, declination δ and range ρ would be affected by up to {10}4-{10}5 milliarcseconds and 105 km, respectively; the present-day residuals of such observables are as little as about 4 milliarcseconds and 10-1 km, respectively. We analytically calculated the long-term orbital effects induced by the putative harmonic variation of G at hand, finding non-zero rates of change for the semimajor axis a, the eccentricity e and the argument of pericenter ω of a test particle. For the LAGEOS satellite, an orbital increase as large as 3.9 m yr-1 is predicted, in contrast with the observed decay of -0.203 ± 0.035 m yr-1. An anomalous perihelion precession as large as 14 arcseconds per century is implied for Saturn, while latest observations constrain it to the 10-4 arcseconds per century level. The rejection level provided by the Mercury’s perihelion rate is of the same order of magnitude.

Products of the SNPP VIIRS SD Screen Transmittance and the SD BRDFs From Both Yaw Maneuver and Regular On-Orbit Data

NASA Technical Reports Server (NTRS)

Lei, Ning; Xiong, Xiaoxiong

2017-01-01

To ensure data quality, the Earth-observing Visible Infrared Imaging Radiometer Suite (VIIRS) on the Suomi National Polar-orbiting Partnership satellite regularly performs on-orbit radiometric calibration of its 22 spectral bands. The primary radiance source for the calibration of the VIIRS reflective solar bands (RSBs) is a sunlit onboard solar diffuser (SD).During the calibration process, sunlight goes through a perforated plate (the SD screen) and then strikes the SD. The sunlight, scattered off the SD of near-Lambertian property, is used for the calibration. Consequently, the spectral radiance of the scattered sunlight is proportional to the product of the SD screen transmittance and the SD bidirectional reflectance distribution function (BRDF) value at the observation direction. The BRDF value is decomposed to the product of its initial value at launch and a numerical degradation factor that quantifies the decrease from the initial value. The degradation factor is determined by an onboard SD stability monitor (SDSM). During the BRDF degradation factor determination process, the SDSM receives the SD scattered sunlight and the sunlight that goes through another perforated plate at almost the same time. The ratio of the signal strengths from the two observations is used to determine the BRDF degradation factor. Consequently, the RSB radiometric calibration requires the accurate knowledge of the product of the SD screen transmittance and the initial BRDF value as sensed by the RSB and the SDSM detectors. We use both yaw maneuver and a small portion of regular on-orbit data to determine the products.

The onset of chaos in orbital pilot-wave dynamics.

PubMed

Tambasco, Lucas D; Harris, Daniel M; Oza, Anand U; Rosales, Rodolfo R; Bush, John W M

2016-10-01

We present the results of a numerical investigation of the emergence of chaos in the orbital dynamics of droplets walking on a vertically vibrating fluid bath and acted upon by one of the three different external forces, specifically, Coriolis, Coulomb, or linear spring forces. As the vibrational forcing of the bath is increased progressively, circular orbits destabilize into wobbling orbits and eventually chaotic trajectories. We demonstrate that the route to chaos depends on the form of the external force. When acted upon by Coriolis or Coulomb forces, the droplet's orbital motion becomes chaotic through a period-doubling cascade. In the presence of a central harmonic potential, the transition to chaos follows a path reminiscent of the Ruelle-Takens-Newhouse scenario.

Optimized effective potential in real time: Problems and prospects in time-dependent density-functional theory

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

Mundt, Michael; Kuemmel, Stephan

2006-08-15

The integral equation for the time-dependent optimized effective potential (TDOEP) in time-dependent density-functional theory is transformed into a set of partial-differential equations. These equations only involve occupied Kohn-Sham orbitals and orbital shifts resulting from the difference between the exchange-correlation potential and the orbital-dependent potential. Due to the success of an analog scheme in the static case, a scheme that propagates orbitals and orbital shifts in real time is a natural candidate for an exact solution of the TDOEP equation. We investigate the numerical stability of such a scheme. An approximation beyond the Krieger-Li-Iafrate approximation for the time-dependent exchange-correlation potential ismore » analyzed.« less

The Disposal of Spacecraft and Launch Vehicle Stages in Low Earth Orbit

NASA Technical Reports Server (NTRS)

Johnson, Nicholas L.

2007-01-01

Spacecraft and launch vehicle stages abandoned in Earth orbit have historically been a primary source of debris from accidental explosions. In the future, such satellites will become the principal cause of orbital debris via inadvertent collisions. To curtail both the near-term and far-term risks posed by derelict spacecraft and launch vehicle stages to operational space systems, numerous national and international orbital debris mitigation guidelines specifically recommend actions which could prevent or limit such future debris generation. Although considerable progress has been made in implementing these recommendations, some changes to existing vehicle designs can be difficult. Moreover, the nature of some missions also can present technological and budgetary challenges to be compliant with widely accepted orbital debris mitigation measures.

Star-disc interaction in galactic nuclei: orbits and rates of accreted stars

NASA Astrophysics Data System (ADS)

Kennedy, Gareth F.; Meiron, Yohai; Shukirgaliyev, Bekdaulet; Panamarev, Taras; Berczik, Peter; Just, Andreas; Spurzem, Rainer

2016-07-01

We examine the effect of an accretion disc on the orbits of stars in the central star cluster surrounding a central massive black hole by performing a suite of 39 high-accuracy direct N-body simulations using state-of-the art software and accelerator hardware, with particle numbers up to 128k. The primary focus is on the accretion rate of stars by the black hole (equivalent to their tidal disruption rate for black holes in the small to medium mass range) and the eccentricity distribution of these stars. Our simulations vary not only the particle number, but disc model (two models examined), spatial resolution at the centre (characterized by the numerical accretion radius) and softening length. The large parameter range and physically realistic modelling allow us for the first time to confidently extrapolate these results to real galactic centres. While in a real galactic centre both particle number and accretion radius differ by a few orders of magnitude from our models, which are constrained by numerical capability, we find that the stellar accretion rate converges for models with N ≥ 32k. The eccentricity distribution of accreted stars, however, does not converge. We find that there are two competing effects at work when improving the resolution: larger particle number leads to a smaller fraction of stars accreted on nearly circular orbits, while higher spatial resolution increases this fraction. We scale our simulations to some nearby galaxies and find that the expected boost in stellar accretion (or tidal disruption, which could be observed as X-ray flares) in the presence of a gas disc is about a factor of 10. Even with this boost, the accretion of mass from stars is still a factor of ˜100 slower than the accretion of gas from the disc. Thus, it seems accretion of stars is not a major contributor to black hole mass growth.

Kuiper Belt Dust Grains as a Source of Interplanetary Dust Particles

NASA Technical Reports Server (NTRS)

Liou, Jer-Chyi; Zook, Herbert A.; Dermott, Stanley F.

1996-01-01

The recent discovery of the so-called Kuiper belt objects has prompted the idea that these objects produce dust grains that may contribute significantly to the interplanetary dust population. In this paper, the orbital evolution of dust grains, of diameters 1 to 9 microns, that originate in the region of the Kuiper belt is studied by means of direct numerical integration. Gravitational forces of the Sun and planets, solar radiation pressure, as well as Poynting-Robertson drag and solar wind drag are included. The interactions between charged dust grains and solar magnetic field are not considered in the model. Because of the effects of drag forces, small dust grains will spiral toward the Sun once they are released from their large parent bodies. This motion leads dust grains to pass by planets as well as encounter numerous mean motion resonances associated with planets. Our results show that about 80% of the Kuiper belt grains are ejected from the Solar System by the giant planets, while the remaining 20% of the grains evolve all the way to the Sun. Surprisingly, the latter dust grains have small orbital eccentricities and inclinations when they cross the orbit of the Earth. This makes them behave more like asteroidal than cometary-type dust particles. This also enhances their chances of being captured by the Earth and makes them a possible source of the collected interplanetary dust particles; in particular, they represent a possible source that brings primitive/organic materials from the outer Solar System to the Earth. When collisions with interstellar dust grains are considered, however, Kuiper belt dust grains around 9 microns appear likely to be collisionally shattered before they can evolve toward the inner part of the Solar System. The collision destruction can be applied to Kuiper belt grains up to about 50 microns. Therefore, Kuiper belt dust grains within this range may not be a significant part of the interplanetary dust complex in the inner Solar System.

Summary of the AIAA/NASA/DOD Orbital Debris Conference - Technical issues and future directions

NASA Technical Reports Server (NTRS)

Potter, A.; Kessler, D.; Nieder, R.; Reynolds, R.

1990-01-01

An international conference on orbital debris was held on April 16-19, 1990, in Baltimore, Maryland. Topics of the conference included the implications of orbital debris for space flight, orbital debris measurements, modeling of the orbital debris environment, and methods to reduce the growth of the orbital debris population. Significant results from this meeting are summarized.

Examples of the nonlinear dynamics of ballistic capture and escape in the earth-moon system

NASA Technical Reports Server (NTRS)

Belbruno, Edward A.

1990-01-01

An example of a trajectory is given which is initially captured in an elliptic resonant orbit about the earth and then ballistically escapes the earth-moon system. This is demonstrated by a numerical example in three-dimensions using a planetary ephemeris. Another example shows a mechanism of how an elliptic orbit about the earth can increase its energy by performing a complex nonlinear transition to an elliptic orbit of a larger semi-major axis. Capture is also considered. An application of ballistic capture at the moon via an unstable periodic orbit using the four-body sun-earth-moon-S/C interaction is described.

Review of investigations performed in the USSR on close approaches of comets to Jupiter and the evolution of cometary orbits

NASA Technical Reports Server (NTRS)

Kazimirchak-Polonskaya, E. I.

1976-01-01

Methods are reviewed for calculating the evolution of cometary orbits with emphasis on the orbital changes that take place when comets pass within the spheres of action of giant planets. Topics discussed include: differences and difficulties in methods used for the calculation of large perturbations by Jupiter; the construction of numerical theories of motion covering the whole period of observations of each comet, allowing for planetary perturbations and the effects of nongravitational forces; and investigations of the evolution of cometary orbits over the 400 year interval 1660-2060. The classical theory of cometary capture is briefly discussed.

Of Modeling the Radiation Hazards Along Trajectory Space Vehicles Various Purpose

NASA Astrophysics Data System (ADS)

Grichshenko, Valentina

2016-07-01

The paper discusses the results of the simulation of radiation hazard along trajectory low-orbit spacecraft for various purposes, geostationary and navigation satellites. Developed criteria of reliability of memory cells in Space, including influence of cosmic rays (CR), differences of geophysical and geomagnetic situation on SV orbit are discussed. Numerical value of vertical geomagnetic stiffness, of CR flux and assessment of correlation failures of memory cells along low-orbit spacecrafts trajectory are presented. Obtained results are used to forecasting the radiation situation along SV orbit, reliability of memory cells in the Space and to optimize nominal equipment kit and payload of Kazakhstan SV.

The long-term motion of comet Halley

NASA Technical Reports Server (NTRS)

Yeomans, D. K.; Kiang, T.

1981-01-01

The orbital motion of comet Halley is numerically integrated back to 1404 BC. Starting with an orbit based on the 1759, 1682, and 1607 observations of the comet, the integration was run back in time with full planetary perturbations and nongravitational forces taken into account at each 0.5 day time-step. Small empirical corrections were made to the computed perihelion passage time in 837 and to the osculating orbital eccentricity in 800. In nine cases, the perihelion passage times calculated by Kiang (1971) from Chinese observations have been redetermined, and osculating orbital elements are given at each apparition from 1910 back to 1404 BC.

Removing the solar exclusion with high altitude satellites [Orbital strategies to mitigate the Solar Exclusion Effect on Space-Based Observation of the Geosynchronous Belt

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

Vallado, David A.; Cefola, Paul J.; Kiziah, Rex R.

Here, observing geosynchronous satellites has numerous applications. Lighting conditions near the equinoxes routinely cause problems for traditional observations of sensors near the equator – the solar exclusion. We investigate using sensors on satellites (in polar and high- altitude orbits) to observe satellites that are in geosynchronous orbit. It is hoped that these satellite configurations will alleviate many of these problems. Assessing the orbit insertion and station-keeping requirements are important to understand. We summarize the literature to understand the relevant perturbing forces and assess the delta-v requirements.

The orbiter mate/demate device

NASA Technical Reports Server (NTRS)

Miller, A. J.; Binkley, W. H.

1985-01-01

The numerous components and systems of the space shuttle orbiter mate/demate device (MDD) are discussed. Special emphasis is given, mechanisms and mechanical systems to discuss in general their requirements, functions, and design; and, where applicable, to relate any unusual problems encountered during the initial concept studies, final design, and construction are discussed. The MDD and its electrical, machinery, and mechanical systems, including the main hoisting system, power operated access service platform, wind restrain and adjustment mechanism, etc., were successfully designed and constructed. The MDD was used routinely during the initial orbiter-747 approach and landing test and the more recent orbiter flight tests recovery and mate operations.

Removing the solar exclusion with high altitude satellites [Orbital strategies to mitigate the Solar Exclusion Effect on Space-Based Observation of the Geosynchronous Belt

DOE PAGES

Vallado, David A.; Cefola, Paul J.; Kiziah, Rex R.; ...

2016-09-09

Here, observing geosynchronous satellites has numerous applications. Lighting conditions near the equinoxes routinely cause problems for traditional observations of sensors near the equator – the solar exclusion. We investigate using sensors on satellites (in polar and high- altitude orbits) to observe satellites that are in geosynchronous orbit. It is hoped that these satellite configurations will alleviate many of these problems. Assessing the orbit insertion and station-keeping requirements are important to understand. We summarize the literature to understand the relevant perturbing forces and assess the delta-v requirements.

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

Suh, In-Saeng; Mathews, Grant J.; Haywood, J. Reese

The spatially conformally flat approximation (CFA) is a viable method to deduce initial conditions for the subsequent evolution of binary neutron stars employing the full Einstein equations. Here in this paper, we analyze the viability of the CFA for the general relativistic hydrodynamic initial conditions of binary neutron stars. We illustrate the stability of the conformally flat condition on the hydrodynamics by numerically evolving ~100 quasicircular orbits. We illustrate the use of this approximation for orbiting neutron stars in the quasicircular orbit approximation to demonstrate the equation of state dependence of these initial conditions and how they might affect themore » emergent gravitational wave frequency as the stars approach the innermost stable circular orbit.« less

On the Post-Keplerian Corrections to the Orbital Periods of a Two-body System and Their Application to the Galactic Center

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

Iorio, Lorenzo; Zhang, Fupeng, E-mail: lorenzo.iorio@libero.it, E-mail: zhangfp7@mail.sysu.edu.cn

We perform detailed numerical analyses of the orbital motion of a test particle around a spinning primary, with the aim of investigating the possibility of using the post-Keplerian (pK) corrections to the orbiter’s periods (draconitic, anomalistic, and sidereal) as a further opportunity to perform new tests of post-Newtonian gravity. As a specific scenario, the S-stars orbiting the massive black hole (MBH) supposedly lurking in Sgr A* at the center of the Galaxy are adopted. We first study the effects of the pK Schwarzchild, Lense–Thirring, and quadrupole moment accelerations experienced by a target star for various possible initial orbital configurations. Itmore » turns out that the results of the numerical simulations are consistent with the analytical ones in the small eccentricity approximation for which almost all the latter ones were derived. For highly elliptical orbits, the sizes of the three pK corrections considered turn out to increase remarkably. The periods of the observed S2 and S0-102 stars as functions of the MBH’s spin axis orientation are considered as well. The pK accelerations lead to corrections of the orbital periods of the order of 1–100 days (Schwarzschild), 0.1–10 hr (Lense–Thirring), and 1–10{sup 3} s (quadrupole) for a target star with a = 300–800 au and e ≈ 0.8, which could be measurable with future facilities.« less

Synchronization of finite-size particles by a traveling wave in a cylindrical flow

NASA Astrophysics Data System (ADS)

Melnikov, D. E.; Pushkin, D. O.; Shevtsova, V. M.

2013-09-01

Motion of small finite-size particles suspended in a cylindrical thermocapillary flow with an azimuthally traveling wave is studied experimentally and numerically. At certain flow regimes the particles spontaneously align in dynamic accumulation structures (PAS) of spiral shape. We find that long-time trajectories of individual particles in this flow fall into three basic categories that can be described, borrowing the dynamical systems terminology, as the stable periodic, the quasiperiodic, and the quasistable periodic orbits. Besides these basic types of orbits, we observe the "doubled" periodic orbits and shuttle-like particle trajectories. We find that ensembles of particles having periodic orbits give rise to one-dimensional spiral PAS, while ensembles of particles having quasiperiodic orbits form two-dimensional PAS of toroidal shape. We expound the reasons why these types of orbits and the emergence of the corresponding accumulation structures should naturally be anticipated based on the phase locking theory of PAS formation. We give a further discussion of PAS features, such as the finite thickness of PAS spirals and the probable scenarios of the spiral PAS destruction. Finally, in numerical simulations of inertial particles we observe formation of the spiral structures corresponding to the 3:1 "resonance" between the particle turnover frequency and the wave oscillations frequency, thus confirming another prediction of the phase locking theory. In view of the generality of the arguments involved, we expect the importance of this structure-forming mechanism to go far beyond the realm of the laboratory-friendly thermocapillary flows.

Orbit classification in an equal-mass non-spinning binary black hole pseudo-Newtonian system

NASA Astrophysics Data System (ADS)

Zotos, Euaggelos E.; Dubeibe, F. L.; González, Guillermo A.

2018-04-01

The dynamics of a test particle in a non-spinning binary black hole system of equal masses is numerically investigated. The binary system is modeled in the context of the pseudo-Newtonian circular restricted three-body problem, such that the primaries are separated by a fixed distance and move in a circular orbit around each other. In particular, the Paczyński-Wiita potential is used for describing the gravitational field of the two non-Newtonian primaries. The orbital properties of the test particle are determined through the classification of the initial conditions of the orbits, using several values of the Jacobi constant, in the Hill's regions of possible motion. The initial conditions are classified into three main categories: (i) bounded, (ii) escaping and (iii) displaying close encounters. Using the smaller alignment index (SALI) chaos indicator, we further classify bounded orbits into regular, sticky or chaotic. To gain a complete view of the dynamics of the system, we define grids of initial conditions on different types of two-dimensional planes. The orbital structure of the configuration plane, along with the corresponding distributions of the escape and collision/close encounter times, allow us to observe the transition from the classical Newtonian to the pseudo-Newtonian regime. Our numerical results reveal a strong dependence of the properties of the considered basins with the Jacobi constant as well as with the Schwarzschild radius of the black holes.

Method for the numerical integration of equations of perturbed satellite motion in problems of space geodesy

NASA Astrophysics Data System (ADS)

Plakhov, Iu. V.; Mytsenko, A. V.; Shel'Pov, V. A.

A numerical integration method is developed that is more accurate than Everhart's (1974) implicit single-sequence approach for integrating orbits. This method can be used to solve problems of space geodesy based on the use of highly precise laser observations.

Orbital Reconstruction: Patient-Specific Orbital Floor Reconstruction Using a Mirroring Technique and a Customized Titanium Mesh.

PubMed

Tarsitano, Achille; Badiali, Giovanni; Pizzigallo, Angelo; Marchetti, Claudio

2016-10-01

Enophthalmos is a severe complication of primary reconstruction of orbital floor fractures. The goal of secondary reconstruction procedures is to restore symmetrical globe positions to recover function and aesthetics. The authors propose a new method of orbital floor reconstruction using a mirroring technique and a customized titanium mesh, printed using a direct metal laser-sintering method. This reconstructive protocol involves 4 steps: mirroring of the healthy orbit at the affected site, virtual design of a patient-specific orbital floor mesh, CAM procedures for direct laser-sintering of the customized titanium mesh, and surgical insertion of the device. Using a computed tomography data set, the normal, uninjured side of the craniofacial skeleton was reflected onto the contralateral injured side, and a reconstructive orbital floor mesh was designed virtually on the mirrored orbital bone surface. The solid-to-layer files of the mesh were then manufactured using direct metal laser sintering, which resolves the shaping and bending biases inherent in the indirect method. An intraoperative navigation system ensured accuracy of the entire procedure. Clinical outcomes were assessed using 3dMD photogrammetry and computed tomography data in 7 treated patients. The technique described here appears to be a viable method to correct complex orbital floor defects needing delayed reconstruction. This study represents the first step in the development of a wider experimental protocol for orbital floor reconstruction using computer-assisted design-computer-assisted manufacturing technology.

Pervasive orbital eccentricities dictate the habitability of extrasolar earths.

PubMed

Kita, Ryosuke; Rasio, Frederic; Takeda, Genya

2010-09-01

The long-term habitability of Earth-like planets requires low orbital eccentricities. A secular perturbation from a distant stellar companion is a very important mechanism in exciting planetary eccentricities, as many of the extrasolar planetary systems are associated with stellar companions. Although the orbital evolution of an Earth-like planet in a stellar binary system is well understood, the effect of a binary perturbation on a more realistic system containing additional gas-giant planets has been very little studied. Here, we provide analytic criteria confirmed by a large ensemble of numerical integrations that identify the initial orbital parameters leading to eccentric orbits. We show that an extrasolar earth is likely to experience a broad range of orbital evolution dictated by the location of a gas-giant planet, which necessitates more focused studies on the effect of eccentricity on the potential for life.

M2K Planet Search: Spectroscopic Screening and Transit Photometry

NASA Astrophysics Data System (ADS)

Mann, Andrew; Gaidos, E.; Fischer, D.; Lepine, S.

2010-10-01

The M2K project is a search for planets orbiting nearby early M and late K dwarf drawn from the SUPERBLINK catalog. M and K dwarfs are highly attractive targets for finding low-mass and habitable planets because (1) close-in planets are more likely to orbit within their habitable zone, (2) planets orbiting them induce a larger Doppler signal and have deeper transits than similar planets around F, G, and early K type stars, (3) planet formation models predict they hold an abundance of super-Earth sized planets, and (4) they represent the vast majority of the stars close enough for direct imaging techniques. In spite of this, only 10% of late K and early M dwarfs are being monitored by current Doppler surveys. As part of the M2K project we have obtained low-resolution spectra for more than 2000 of our sample of 10,000 M and K dwarfs. We vet our sample by screening these stars for high metallicity and low chromospheric activity. We search for transits on targets showing high RMS Doppler signal and photometry candidates provided by SuperWASP project. By using "snapshot” photometry have been able to achieve sub-millimag photometry on numerous transit targets in the same night. With further follow-up observations we will be able to detect planets smaller than 10 Earth masses.

Galactic star formation enhanced and quenched by ram pressure in groups and clusters

NASA Astrophysics Data System (ADS)

Bekki, Kenji

2014-02-01

We investigate how ram pressure of intragroup and intracluster medium can influence the spatial and temporal variations of star formation (SF) of disc galaxies with halo masses (Mh) ranging from 1010 to 1012 M⊙ (i.e. from dwarf irregular to Milky Way-type) in groups and clusters with 1013 ≤ Mh/M⊙ ≤ 1015 by using numerical simulations with a new model for time-varying ram pressure. The long-term evolution of SF rates and Hα morphologies corresponding to the distributions of star-forming regions are particularly investigated for different model parameters. The principal results are as follows. Whether ram pressure can enhance or reduce SF depends on Mh of disc galaxies and inclination angles of gas discs with respect to their orbital directions for a given orbit and a given environment. For example, SF can be moderately enhanced in disc galaxies with Mh = 1012 M⊙ at the pericentre passages in a cluster with Mh = 1014 M⊙ whereas it can be completely shut down (`quenching') for low-mass discs with Mh = 1010 M⊙. Ram pressure can reduce the Hα-to-optical-disc-size ratios of discs and the level of the reduction depends on Mh and orbits of disc galaxies for a given environment. Disc galaxies under strong ram pressure show characteristic Hα morphologies such as ring-like, one-sided and crescent-like distributions.

Planetary Migration and Kuiper Belt Dynamics

NASA Astrophysics Data System (ADS)

Malhotra, Renu

The Kuiper belt holds memory of the dynamical processes that shaped the architecture of the solar system, including the orbital migration history of the giant planets. We propose studies of the orbital dynamics of the Kuiper Belt in order to understand the origin of its complex dynamical structure and its link to the orbital migration history of the giant planets. By means of numerical simulations, statistical tests, as well as analytical calculations we will (1) investigate the origin of resonant Kuiper belt objects to test alternative scenarios of Neptune's migration history, (2) investigate the long term dynamical evolution of the Haumea family of Kuiper Belt objects in order to improve the age estimate of this family, and (3) investigate resonance-sticking behavior and the Kozai-Lidov mechanism and its role in the origin of the extended scattered disk. These studies directly support the goals of the NASA-OSS program by improving our understanding of the origin of the solar system's architecture. Our results will provide constraints on the nature and timing of the dynamical excitation event that is thought to have occurred in early solar system history and to have determined the architecture of the present-day solar system; our results will also provide deeper theoretical understanding of sticky mean motion resonances which contribute greatly to the longevity of many small bodies, improve our understanding of dynamical transport of planetesimals in planetary systems, and help interpret observations of other planetary systems.

VIIRS reflective solar bands on-orbit calibration and performance: a three-year update

NASA Astrophysics Data System (ADS)

Sun, Junqiang; Wang, Menghua

2014-11-01

The on-orbit calibration of the reflective solar bands (RSBs) of VIIRS and the result from the analysis of the up-to-date 3 years of mission data are presented. The VIIRS solar diffuser (SD) and lunar calibration methodology are discussed, and the calibration coefficients, called F-factors, for the RSBs are given for the latest reincarnation. The coefficients derived from the two calibrations are compared and the uncertainties of the calibrations are discussed. Numerous improvements are made, with the major improvement to the calibration result come mainly from the improved bidirectional reflectance factor (BRF) of the SD and the vignetting functions of both the SD screen and the sun-view screen. The very clean results, devoid of many previously known noises and artifacts, assures that VIIRS has performed well for the three years on orbit since launch, and in particular that the solar diffuser stability monitor (SDSM) is functioning essentially without flaws. The SD degradation, or H-factors, for most part shows the expected decline except for the surprising rise on day 830 lasting for 75 days signaling a new degradation phenomenon. Nevertheless the SDSM and the calibration methodology have successfully captured the SD degradation for RSB calibration. The overall improvement has the most significant and direct impact on the ocean color products which demands high accuracy from RSB observations.

New catalogue of single-apparition comets discovered in the years 1901-1950. Part I

NASA Astrophysics Data System (ADS)

Królikowska, M.; Sitarski, G.; Pittich, E.; Szutowicz, S.; Ziołkowski, K.; Rickman, H.; Gabryszewski, R.; Rickman, B.

2014-07-01

A new catalogue of cometary orbits derived using a completely homogeneous method of data treatment, accurate methods of numerical integration, and modern model of the Solar System is presented. We constructed a sample of near-parabolic comets from the first half of the twentieth century with original reciprocals of semimajor axes less than 0.000130 au^{-1} in the Marsden and Williams Catalogue of Cometary Orbits (2008, hereafter MW08), i.e., comets of original semimajor axes larger than 7700 au. We found 38 such comets in MW08, where 32 have first-quality orbits (class 1A or 1B) and the remaining 6 have second-quality orbits (2A or 2B). We presented satisfactory non-gravitational (hereafter NG) models for thirteen of the investigated comets. The four main features, distinguishing this catalogue of orbits of single- apparition comets discovered in the early twentieth century from other catalogues of orbits of similarly old objects, are the following. 1. Old cometary positional observations require a very careful analysis. For the purpose of this new catalogue, great emphasis has been placed in collecting sets of observations as complete as possible for the investigated comets. Moreover, for many observations, comet-minus-star-type measurements were also available. This type of data was particularly valuable as the most original measurements of comet positions and has allowed us to recalculate new positions of comets using the PPM star catalogue. 2. Old cometary observations were prepared by observers usually as apparent positions in Right Ascension and Declination or as reduced positions for the epoch of the beginning of the year of a given observation. This was a huge advantage of these data, because this allows us to uniformly take into account all necessary corrections associated with the data reduction to the standard epoch. 3. The osculating orbits of single-apparition comets discovered more than sixty years ago have been formerly determined with very different numerical methods and assumptions on the model of the Solar System, including the number of planets taken into account. This new catalogue changes this situation. We offer a new catalogue of cometary orbits derived using completely homogeneous methods of data treatment, accurate methods of numerical integration, and a modern model of the Solar System. 4. The osculating, original, and future sets of orbits are presented for each catalogue comet. In the case of a comet with detectable NG effects, we give both types of orbit: purely gravitational and non- gravitational. We concluded, however, that all thirteen NG orbital solutions given in the catalogue better represent the actual motions of the investigated comets. Surprisingly, the NG effects were detectable in data for five comets of second-quality-class orbits. Among these five are three comets with hyperbolic original, barycentric GR orbits. This publication will be accompanied by an online catalogue available at ssdp.cbk.waw.pl/LPCs, providing entries to orbital elements of considered comets as well as to full swarms of original and future virtual comets that formed the basis for the further analysis of dynamical evolution.

Yarkovsky-Schach effect on space debris motion

NASA Astrophysics Data System (ADS)

Murawiecka, M.; Lemaitre, A.

2018-02-01

The Yarkovsky-Schach effect is a small perturbation affecting Earth satellites and space debris illuminated by the Sun. It was first applied to the orbit of LAGEOS satellites as an explanation of the residuals in orbital elements. In this work, we carry out several numerical integration tests taking into consideration various orbit and rotation parameters, in order to analyse this effect in a broader context. The semi-major axis variations remain small and depend on the spin axis attitude with respect to the Sun. We show that the force amplitude is maximised for orbits inclined with i ≈ 20-30°. We also observe the influence on other orbital elements, notably on the orbit inclination. However, these effects are clearly observed only on long timescales; in our simulations, we propagated the orbits for 200 y. The Yarkovsky-Schach effect is thus confirmed to have a minuscule magnitude. It should be taken into account in studies requiring high-precision orbit determination, or on expanded timescales.

Analytical method for the effects of the asteroid belt on planetary orbits

NASA Technical Reports Server (NTRS)

Mayo, A. P.

1979-01-01

Analytic expressions are derived for the perturbation of planetary orbits due to a thick constant-density asteroid belt. The derivations include extensions and adaptations of Plakhov's (1968) analytic expressions for the perturbations in five of the orbital elements for closed orbits around Saturn's rings. The equations of Plakhov are modified to include the effect of ring thickness, and additional equations are derived for the perturbations in the sixth orbital element, the mean anomaly. The gravitational potential and orbital perturbations are derived for the asteroid belt with and without thickness, and for a hoop approximation to the belt. The procedures are also applicable to Saturn's rings and the newly discovered rings of Uranus. The effects of the asteroid belt thickness on the gravitational potential coefficients and the orbital motions are demonstrated. Comparisons between the Mars orbital perturbations obtained by using the analytic expressions and those obtained by numerical integration are discussed. The effects of the asteroid belt on earth-based ranging to Mars are also demonstrated.

Atomic-scale visualization of surface-assisted orbital order

PubMed Central

Kim, Howon; Yoshida, Yasuo; Lee, Chi-Cheng; Chang, Tay-Rong; Jeng, Horng-Tay; Lin, Hsin; Haga, Yoshinori; Fisk, Zachary; Hasegawa, Yukio

2017-01-01

Orbital-related physics attracts growing interest in condensed matter research, but direct real-space access of the orbital degree of freedom is challenging. We report a first, real-space, imaging of a surface-assisted orbital ordered structure on a cobalt-terminated surface of the well-studied heavy fermion compound CeCoIn5. Within small tip-sample distances, the cobalt atoms on a cleaved (001) surface take on dumbbell shapes alternatingly aligned in the [100] and [010] directions in scanning tunneling microscopy topographies. First-principles calculations reveal that this structure is a consequence of the staggered dxz-dyz orbital order triggered by enhanced on-site Coulomb interaction at the surface. This so far overlooked surface-assisted orbital ordering may prevail in transition metal oxides, heavy fermion superconductors, and other materials. PMID:28948229

Coulomb-free and Coulomb-distorted recolliding quantum orbits in photoelectron holography

NASA Astrophysics Data System (ADS)

Maxwell, A. S.; Figueira de Morisson Faria, C.

2018-06-01

We perform a detailed analysis of the different types of orbits in the Coulomb quantum orbit strong-field approximation (CQSFA), ranging from direct to those undergoing hard collisions. We show that some of them exhibit clear counterparts in the standard formulations of the strong-field approximation for direct and rescattered above-threshold ionization, and show that the standard orbit classification commonly used in Coulomb-corrected models is over-simplified. We identify several types of rescattered orbits, such as those responsible for the low-energy structures reported in the literature, and determine the momentum regions in which they occur. We also find formerly overlooked interference patterns caused by backscattered Coulomb-corrected orbits and assess their effect on photoelectron angular distributions. These orbits improve the agreement of photoelectron angular distributions computed with the CQSFA with the outcome of ab initio methods for high energy phtotoelectrons perpendicular to the field polarization axis.

In situ Orbit Extraction from Live, High Precision Collisionless Simulations of Systems Formed by Cold Collapse

NASA Astrophysics Data System (ADS)

Noriega-Mendoza, H.; Aguilar, L. A.

2018-04-01

We performed high precision, N-body simulations of the cold collapse of initially spherical, collisionless systems using the GYRFALCON code of Dehnen (2000). The collapses produce very prolate spheroidal configurations. After the collapse, the systems are simulated for 85 and 170 half-mass radius dynamical timescales, during which energy conservation is better than 0.005%. We use this period to extract individual particle orbits directly from the simulations. We then use the TAXON code of Carpintero and Aguilar (1998) to classify 1 to 1.5% of the extracted orbits from our final, relaxed configurations: less than 15% are chaotic orbits, 30% are box orbits and 60% are tube orbits (long and short axis). Our goal has been to prove that direct orbit extraction is feasible, and that there is no need to "freeze" the final N-body system configuration to extract a time-independent potential.

Simple control laws for low-thrust orbit transfers

NASA Technical Reports Server (NTRS)

Petropoulos, Anastassios E.

2003-01-01

Two methods are presented by which to determine both a thrust direction and when to apply thrust to effect specified changes in any of the orbit elements except for true anomaly, which is assumed free. The central body is assumed to be a point mass, and the initial and final orbits are assumed closed. Thrust, when on, is of a constant value, and specific impulse is constant. The thrust profiles derived from the two methods are not propellant-optimal, but are based firstly on the optimal thrust directions and location on the osculating orbit for changing each of the orbit elements and secondly on the desired changes in the orbit elements. Two examples of transfers are presented, one in semimajor axis and inclination, and one in semimajor axis and eccentricity. The latter compares favourably with a propellant-optimized transfer between the same orbits. The control laws have few input parameters, but can still capture the complexity of a wide variety of orbit transfers.

Control of nonlinear systems using periodic parametric perturbations with application to a reversed field pinch

NASA Astrophysics Data System (ADS)

Mirus, Kevin Andrew

In this thesis, the possibility of controlling low- and high-dimensional chaotic systems by periodically driving an accessible system parameter is examined. This method has been carried out on several numerical systems and the MST Reversed Field Pinch. The numerical systems investigated include the logistic equation, the Lorenz equations, the Rossler equations, a coupled lattice of logistic equations, a coupled lattice of Lorenz equations, the Yoshida equations, which model tearing mode fluctuations in a plasma, and a neural net model for magnetic fluctuations on MST. This method was tested on the MST by sinusoidally driving a magnetic flux through the toroidal gap of the device. Numerically, periodic drives were found to be most effective at producing limit cycle behavior or significantly reducing the dimension of the system when the perturbation frequency was near natural frequencies of unstable periodic orbits embedded in the attractor of the unperturbed system. Several different unstable periodic orbits have been stabilized in this way for the low-dimensional numerical systems, sometimes with perturbation amplitudes that were less than 5% of the nominal value of the parameter being perturbed. In high- dimensional systems, limit cycle behavior and significant decreases in the system dimension were also achieved using perturbations with frequencies near the natural unstable periodic orbit frequencies. Results for the MST were not this encouraging, most likely because of an insufficient drive amplitude, the extremely high dimension of the plasma behavior, large amounts of noise, and a lack of stationarity in the transient plasma pulses.

Conjugate gradient determination of optimal plane changes for a class of three-impulse transfers between noncoplanar circular orbits

NASA Technical Reports Server (NTRS)

Burrows, R. R.

1972-01-01

A particular type of three-impulse transfer between two circular orbits is analyzed. The possibility of three plane changes is recognized, and the problem is to optimally distribute these plane changes to minimize the sum of the individual impulses. Numerical difficulties and their solution are discussed. Numerical results obtained from a conjugate gradient technique are presented for both the case where the individual plane changes are unconstrained and for the case where they are constrained. Possibly not unexpectedly, multiple minima are found. The techniques presented could be extended to the finite burn case, but primarily the contents are addressed to preliminary mission design and vehicle sizing.

MEGNO-analysis of the orbital evolution of GEO objects. (Russian Title: MEGNO-анализ орбитальной эволюции объектов зоны ГЕО )

NASA Astrophysics Data System (ADS)

Aleksandrova, A. G.; Chuvashov, I. N.; Bordovitsyna, T. V.

2011-07-01

The results of investigations of the instability of orbits in the GEO are presentеd. Average parameter MEGNO as main indicator of chaotic state has been used. The parameter is computed by combined numerical integration of equations of the motion, equations in variation and equations of MEGNO parameters. The results have been obtained using software package "Numerical model of the systems artificial satellite motion", implemented on the cluster "Skiff Cyberia".

On estimating gravity anomalies from gradiometer data. [by numerical analysis

NASA Technical Reports Server (NTRS)

Argentiero, P.; Garza-Robles, R.

1976-01-01

The Gravsat-gradiometer mission involves flying a gradiometer on a gravity satellite (Gravsat) which is in a low, polar, and circular orbit. Results are presented of a numerical simulation of the mission which demonstrates that, if the satellite is in a 250-km orbit, 3- and 5-degree gravity anomalies may be estimated with accuracies of 0.03 and 0.01 mm/square second (3 and 1 mgal), respectively. At an altitude of 350 km, the results are 0.07 and 0.025 mm.square second (7 and 2.5 mgal), respectively. These results assume a rotating type gradiometer with a 0.1 -etvos unit accuracy. The results can readily be scaled to reflect another accuracy level.

Early Program Development

NASA Image and Video Library

1970-01-01

Managed by Marshall Space Flight Center, the Space Tug was a reusable multipurpose space vehicle designed to transport payloads to different orbital inclinations. Utilizing mission-specific combinations of its three primary modules (crew, propulsion, and cargo) and a variety of supplementary kits, the Space Tug was capable of numerous space applications. This 1970 artist's concept depicts the Tug's propulsion module launching a space probe into lunar orbit.

Introduction to Computational Chemistry: Teaching Hu¨ckel Molecular Orbital Theory Using an Excel Workbook for Matrix Diagonalization

ERIC Educational Resources Information Center

Litofsky, Joshua; Viswanathan, Rama

2015-01-01

Matrix diagonalization, the key technique at the heart of modern computational chemistry for the numerical solution of the Schrödinger equation, can be easily introduced in the physical chemistry curriculum in a pedagogical context using simple Hückel molecular orbital theory for p bonding in molecules. We present details and results of…

Accuracy of Estimating Solar Radiation Pressure for GEO Debris with Tumbling Effect

NASA Astrophysics Data System (ADS)

Chao, Chia-Chun George

2009-03-01

The accuracy of estimating solar radiation pressure for GEO debris is examined and demonstrated, via numerical simulations, by fitting a batch (months) of simulated position vectors. These simulated position vectors are generated from a "truth orbit" with added white noise using high-precision numerical integration tools. After the long-arc fit of the simulated observations (position vectors), one can accurately and reliably determine how close the estimated value of solar radiation pressure is to the truth. Results of this study show that the inherent accuracy in estimating the solar radiation pressure coefficient can be as good as 1% if a long-arc fit span up to 180 days is used and the satellite is not tumbling. The corresponding position prediction accuracy can be as good as, in maximum error, 1 km along in-track, 0.3 km along radial and 0.1 km along cross-track up to 30 days. Similar accuracies can be expected when the object is tumbling as long as the rate of attitude change is different from the orbit rate. Results of this study reveal an important phenomenon that the solar radiation pressure significantly affects the orbit motion when the spin rate is equal to the orbit rate.

Analytical modeling of soliton interactions in a nonlocal nonlinear medium analogous to gravitational force

NASA Astrophysics Data System (ADS)

Zeng, Shihao; Chen, Manna; Zhang, Ting; Hu, Wei; Guo, Qi; Lu, Daquan

2018-01-01

We illuminate an analytical model of soliton interactions in lead glass by analogizing to a gravitational force system. The orbits of spiraling solitons under a long-range interaction are given explicitly and demonstrated to follow Newton's second law of motion and the Binet equation by numerical simulations. The condition for circular orbits is obtained and the oscillating orbits are proved not to be closed. We prove the analogy between the nonlocal nonlinear optical system and gravitational system and specify the quantitative relation of the quantity between the two models.

Joint Polar Satellite System

NASA Technical Reports Server (NTRS)

Trenkle, Timothy; Driggers, Phillip

2011-01-01

The Joint Polar Satellite System (JPSS) is a joint NOAA/NASA mission comprised of a series of polar orbiting weather and climate monitoring satellites which will fly in a sun-synchronous orbit, with a 1330 equatorial crossing time. JPSS resulted from the decision to reconstitute the National Polar-orbiting Operational Environmental Satellite System (NPOESS) into two separate programs, one to be run by the Department of Defense (DOD) and the other by NOAA. This decision was reached in early 2010, after numerous development issues caused a series of unacceptable delays in launching the NPOESS system.

Satellite Orbit Under Influence of a Drag - Analytical Approach

NASA Astrophysics Data System (ADS)

Martinović, M. M.; Šegan, S. D.

2017-12-01

The report studies some changes in orbital elements of the artificial satellites of Earth under influence of atmospheric drag. In order to develop possibilities of applying the results in many future cases, an analytical interpretation of the orbital element perturbations is given via useful, but very long expressions. The development is based on the TD88 air density model, recently upgraded with some additional terms. Some expressions and formulae were developed by the computer algebra system Mathematica and tested in some hypothetical cases. The results have good agreement with iterative (numerical) approach.

Accretional evolution of a planetesimal swarm. I - A new simulation

NASA Technical Reports Server (NTRS)

Spaute, Dominique; Weidenschilling, Stuart J.; Davis, Donald R.; Marzari, Francesco

1991-01-01

This novel simulation of planetary accretion simultaneously treats many interacting heliocentric distance zones and characterizes planetesimals via Keplerian elements. The numerical code employed, in addition to following the size distribution and the orbit-element distribution of a planetesimal swarm from arbitrary size and orbit distributions, treats a small number of the largest bodies as discrete objects with individual orbits. The accretion algorithm used yields good agreement with the analytic solutions; agreement is also obtained with the results of Weatherill and Stewart (1989) for gravitational accretion of planetesimals having equivalent initial conditions.

The ideas of K. E. Tsiolkovsky on orbital space stations

NASA Technical Reports Server (NTRS)

Kolchenko, I. A.; Strazheva, I. V.

1977-01-01

The concepts presented by K. E. Tsiolkovsky concerning the construction of orbital space stations are cited. Tsiolkovsky, a Russian scientist and founder of astronautics, substantiated these ideas at the end of the 19th and beginning of the 20th century. Considered settlements outside the earth were proposed feasible using solar energy. The substance of numerous asteroids would be used as construction materials for space settlements and rockets. Extraordinary farsightedness was shown by Tsiolkovsky when comparisons of his projects with those of modern orbital stations are made.

Use and Protection of GPS Sidelobe Signals for Enhanced Navigation Performance in High Earth Orbit

NASA Technical Reports Server (NTRS)

Parker, Joel J. K.; Valdez, Jennifer E.; Bauer, Frank H.; Moreau, Michael C.

2016-01-01

GPS (Global Positioning System) Space Service Volume (SSV) signal environment is from 3,000-36,000 kilometers altitude. Current SSV specifications only capture performance provided by signals transmitted within 23.5(L1) or 26(L2-L5) off-nadir angle. Recent on-orbit data lessons learned show significant PNT (Positioning, Navigation and Timing) performance improvements when the full aggregate signal is used. Numerous military civil operational missions in High Geosynchronous Earth Orbit (HEOGEO) utilize the full signal to enhance vehicle PNT performance

A Survey of Symplectic and Collocation Integration Methods for Orbit Propagation

NASA Technical Reports Server (NTRS)

Jones, Brandon A.; Anderson, Rodney L.

2012-01-01

Demands on numerical integration algorithms for astrodynamics applications continue to increase. Common methods, like explicit Runge-Kutta, meet the orbit propagation needs of most scenarios, but more specialized scenarios require new techniques to meet both computational efficiency and accuracy needs. This paper provides an extensive survey on the application of symplectic and collocation methods to astrodynamics. Both of these methods benefit from relatively recent theoretical developments, which improve their applicability to artificial satellite orbit propagation. This paper also details their implementation, with several tests demonstrating their advantages and disadvantages.

Optimal multiple-pass aeroassisted plane change

NASA Technical Reports Server (NTRS)

Vinh, Nguyen X.; Ma, Der-Ming

1990-01-01

This paper presents the exact dimensionless equation of motion and the necessary conditions for the computation of the optimal trajectories of a hypervelocity vehicle flying through a non-rotating spherical planetary atmosphere. Numerical solution is then presented for the case when the vehicle makes several passages through the atmosphere near the perigee of its orbit. While the orbit is slowly contracting, aerodynamic maneuver is performed to obtain the maximum plane change. Several plots were presented to show the optimal variations of the lift coefficient and the bank angle and the various elements of the orbit.

Tidally-induced thermal runaway on extrasolar Earth: Impact on habitability

NASA Astrophysics Data System (ADS)

Behounkova, M.; Tobie, G.; Choblet, G.; Cadek, O.

2010-12-01

Low mass extrasolar bodies start to be discovered owing to the increased precision of detection surveys. As the detection probability decreases with the star-body distance, these planets (and the numerous candidates already announced for the coming years) are likely to orbit their parent stars in a close distance. These short-period planets undergo a strong tidal forcing and their orbits are tidally locked. The associated heat production may influence the internal thermal evolution of these bodies: it has even been suggested that the habitable zone could be influenced by tidal heating (Barnes et al. 2008; Henning et al. 2009). In this study, we further investigate the effect of tidal heating on thermal evolution of tidally locked Earth-like planets. Owing to the strong temperature dependence of the mechanical properties of both the long-term evolution and the tidal deformations, the two processes are coupled. Nevertheless, the tidal deformation has no direct effect on the convective flow and only the dissipative part is included as a heat source for mantle dynamics since the time scales of the two processes strongly differs. For significant tidal dissipation rates, the strong positive feedback leads, in some cases, to thermal runaways. We focus here on the susceptibility of Earth-like planets to tidal dissipation for fixed orbital parameters (eccentricity, orbital period and the spin-orbit resonance type) and on the associated timescales for runaway (if any). In order to describe this behavior and the three dimensional nature of both the tidal forcing and the temperature anomalies, a fully three-dimensional approach solving the two processes simultaneously is employed (Běhounková et al., JGR, in press). We consider an extrasolar planet having the internal properties similar to the Earth. Two modes for heat transfer are modeled through the choice of convective parameters (Rayleigh number and temperature dependence of viscosity, amount of radiogenic heating): a relatively effective plate-tectonics-like regime and a one-plate (stagnant lid) regime. For all numerical experiments sharing the same initial temperature conditions, the reciprocal value of the runaway timescale depends linearly on the initial tidal dissipation. Moreover, the occurrence of tidally driven runaways is associated to large scale melting of the interior having an impact on the habitability of the planet. In the case of runaway timescales between 0.1 and 1Gy and for the plate-tectonics-like heat transfer, the habitable zone is affected by the thermal runaway only for high eccentricities (e≳0.2) for 0.1M sun stars and 1:1 resonance. In the case of the 3:2 orbital resonance, whatever the eccentricity is, the runaway affects the habitable zone for orbital periods lower than 7-12 days. The impact on the habitable zone is even higher for one-plate planets due to the ineffective heat transfer. For more massive stars (>0.5M sun), tidal heating in the habitable zone is not significant and has no impact on the internal evolution.

The self-consistent multiparticle-multihole configuration mixing. Motivations, state of the art and perspectives

NASA Astrophysics Data System (ADS)

Pillet, N.; Robin, C.; Dupuis, M.; Hupin, G.; Berger, J.-F.

2017-03-01

The main objective of this paper is to review the state of the art of the multiparticle-multihole configuration mixing approach which was proposed and implemented using the Gogny interaction ˜ 10 years ago. Various theoretical aspects are re-analyzed when a Hamiltonian description is chosen: the link with exact many-body theories, the impact of truncations in the multiconfigurational space, the importance of defining single-particle orbitals which are consistent with the correlations introduced in the many-body wave function, the role of the self-consistency, and more practically the numerical convergence algorithm. Several applications done with the phenomenological effective Gogny interaction are discussed. Finally, future directions to extend and generalize the method are discussed.

Development of an integrated BEM approach for hot fluid structure interaction

NASA Technical Reports Server (NTRS)

Dargush, Gary F.; Banerjee, Prasanta K.; Honkala, Keith A.

1988-01-01

In the present work, the boundary element method (BEM) is chosen as the basic analysis tool, principally because the definition of temperature, flux, displacement and traction are very precise on a boundary-based discretization scheme. One fundamental difficulty is, of course, that a BEM formulation requires a considerable amount of analytical work, which is not needed in the other numerical methods. Progress made toward the development of a boundary element formulation for the study of hot fluid-structure interaction in Earth-to-Orbit engine hot section components is reported. The primary thrust of the program to date has been directed quite naturally toward the examination of fluid flow, since boundary element methods for fluids are at a much less developed state.

Gravitational lensing of a star by a rotating black hole

NASA Astrophysics Data System (ADS)

Dokuchaev, V. I.; Nazarova, N. O.

2017-11-01

The gravitational lensing of a finite star moving around a rotating Kerr black hole has been numerically simulated. Calculations for the direct image of the star and for the first and second light echoes have been performed for the star moving with an orbital period of 3.22 h around the supermassive black hole SgrA* at the center of the Galaxy. The time dependences for the observed position of the star on the celestial sphere, radiation flux from the star, frequency of detected radiation, and major and minor semiaxes of the lensed image of the star have been calculated and plotted. The detailed observation of such lensing requires a space interferometer such as the Russian Millimetron project.

Dynamical evolution of dense star clusters in galactic nuclei

NASA Astrophysics Data System (ADS)

Haas, Jaroslav; Šubr, Ladislav

2014-05-01

By means of direct numerical N-body modeling, we investigate the orbital evolution of an initially thin, central mass dominated stellar disk. We include the perturbative gravitational influence of an extended spherically symmetric star cluster and the mutual gravitational interaction of the stars within the disk. Our results show that the two-body relaxation of the disk leads to significant changes of its radial density profile. In particular, the disk naturally evolves, for a variety of initial configurations, a similar broken power-law surface density profile. Hence, it appears that the single power-law surface density profile ∝R -2 suggested by various authors to describe the young stellar disk observed in the Sgr A* region does not match theoretical expectations.

Lunar Reconnaissance Orbiter Orbit Determination Accuracy Analysis

NASA Technical Reports Server (NTRS)

Slojkowski, Steven E.

2014-01-01

Results from operational OD produced by the NASA Goddard Flight Dynamics Facility for the LRO nominal and extended mission are presented. During the LRO nominal mission, when LRO flew in a low circular orbit, orbit determination requirements were met nearly 100% of the time. When the extended mission began, LRO returned to a more elliptical frozen orbit where gravity and other modeling errors caused numerous violations of mission accuracy requirements. Prediction accuracy is particularly challenged during periods when LRO is in full-Sun. A series of improvements to LRO orbit determination are presented, including implementation of new lunar gravity models, improved spacecraft solar radiation pressure modeling using a dynamic multi-plate area model, a shorter orbit determination arc length, and a constrained plane method for estimation. The analysis presented in this paper shows that updated lunar gravity models improved accuracy in the frozen orbit, and a multiplate dynamic area model improves prediction accuracy during full-Sun orbit periods. Implementation of a 36-hour tracking data arc and plane constraints during edge-on orbit geometry also provide benefits. A comparison of the operational solutions to precision orbit determination solutions shows agreement on a 100- to 250-meter level in definitive accuracy.

BinCat: a Catalog of Nearby Binary Stars with Tools for Calculating Light-Leakage for Direct Imaging Missions

NASA Astrophysics Data System (ADS)

Holte, Elias Peter; Sirbu, Dan; Belikov, Ruslan

2018-01-01

Binary stars have been largely left out of direct imaging surveys for exoplanets, specifically for earth-sized planets in their star's habitable zone. Utilizing new direct imaging techniques brings us closer to being able to detect earth-like exoplanets around binary stars. In preparation for the upcoming WFIRST mission and other direct imaging-capable missions (HabEx, LUVIOR) it is important to understand the expected science yield resulting from the implementation of these imaging techniques. BinCat is a catalog of binary systems within 30 parsecs to be used as a target list for future direct imaging missions. There is a non-static component along with BinCat that allows researchers to predict the expected light-leakage between a binary component and its off-axis companion (a value critical to the aforementioned techniques) at any epoch. This is accomplished by using orbital elements from the Sixth Orbital Catalog to model the orbits of the binaries. The software was validated against the historical data used to generate the orbital parameters. When orbital information is unknown or the binaries are purely optical the proper motion of the pair taken from the Washington Double Star catalog is integrated in time to estimate expected light-leakage.

Study of orbiter/payload interface communications configuration control board directive from an operational perspective

NASA Technical Reports Server (NTRS)

Addis, A. W.; Tatosian, C. G.; Lidsey, J. F.

1974-01-01

Orbiter/payload data and communications interface was examined. It was found that the Configuration Control Board Directive (CCBD) greatly increases the capability of the orbiter to communicate with a wide variety of projected shuttle payloads. Rather than being derived from individual payload communication requirements, the CCBD appears to be based on an operational philosophy that requires the orbiter to duplicate or augment the ground network/payload communication links. It is suggested that the implementation of the CCBD be reviewed and compared with the Level 1 Program Requirements Document, differences reconciled, and interface characteristics defined.

A new analytical solar radiation pressure model for current BeiDou satellites: IGGBSPM

PubMed Central

Tan, Bingfeng; Yuan, Yunbin; Zhang, Baocheng; Hsu, Hou Ze; Ou, Jikun

2016-01-01

An analytical solar radiation pressure (SRP) model, IGGBSPM (an abbreviation for Institute of Geodesy and Geophysics BeiDou Solar Pressure Model), has been developed for three BeiDou satellite types, namely, geostationary orbit (GEO), inclined geosynchronous orbit (IGSO) and medium earth orbit (MEO), based on a ray-tracing method. The performance of IGGBSPM was assessed based on numerical integration, SLR residuals and analyses of empirical SRP parameters (except overlap computations). The numerical results show that the integrated orbit resulting from IGGBSPM differs from the precise ephemerides by approximately 5 m and 2 m for GEO and non-GEO satellites, respectively. Moreover, when IGGBSPM is used as an a priori model to enhance the ECOM (5-parameter) model with stochastic pulses, named ECOM + APR, for precise orbit determination, the SLR RMS residual improves by approximately 20–25 percent over the ECOM-only solution during the yaw-steering period and by approximately 40 percent during the yaw-fixed period. For the BeiDou GEO01 satellite, improvements of 18 and 32 percent can be achieved during the out-of-eclipse season and during the eclipse season, respectively. An investigation of the estimated ECOM D0 parameters indicated that the β-angle dependence that is evident in the ECOM-only solution is no longer present in the ECOM + APR solution. PMID:27595795

A new analytical solar radiation pressure model for current BeiDou satellites: IGGBSPM.

PubMed

Tan, Bingfeng; Yuan, Yunbin; Zhang, Baocheng; Hsu, Hou Ze; Ou, Jikun

2016-09-06

An analytical solar radiation pressure (SRP) model, IGGBSPM (an abbreviation for Institute of Geodesy and Geophysics BeiDou Solar Pressure Model), has been developed for three BeiDou satellite types, namely, geostationary orbit (GEO), inclined geosynchronous orbit (IGSO) and medium earth orbit (MEO), based on a ray-tracing method. The performance of IGGBSPM was assessed based on numerical integration, SLR residuals and analyses of empirical SRP parameters (except overlap computations). The numerical results show that the integrated orbit resulting from IGGBSPM differs from the precise ephemerides by approximately 5 m and 2 m for GEO and non-GEO satellites, respectively. Moreover, when IGGBSPM is used as an a priori model to enhance the ECOM (5-parameter) model with stochastic pulses, named ECOM + APR, for precise orbit determination, the SLR RMS residual improves by approximately 20-25 percent over the ECOM-only solution during the yaw-steering period and by approximately 40 percent during the yaw-fixed period. For the BeiDou GEO01 satellite, improvements of 18 and 32 percent can be achieved during the out-of-eclipse season and during the eclipse season, respectively. An investigation of the estimated ECOM D0 parameters indicated that the β-angle dependence that is evident in the ECOM-only solution is no longer present in the ECOM + APR solution.

THE INFLUENCE OF ORBITAL ECCENTRICITY ON TIDAL RADII OF STAR CLUSTERS

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

Webb, Jeremy J.; Harris, William E.; Sills, Alison

2013-02-20

We have performed N-body simulations of star clusters orbiting in a spherically symmetric smooth galactic potential. The model clusters cover a range of initial half-mass radii and orbital eccentricities in order to test the historical assumption that the tidal radius of a cluster is imposed at perigalacticon. The traditional assumption for globular clusters is that since the internal relaxation time is larger than its orbital period, the cluster is tidally stripped at perigalacticon. Instead, our simulations show that a cluster with an eccentric orbit does not need to fully relax in order to expand. After a perigalactic pass, a clustermore » recaptures previously unbound stars, and the tidal shock at perigalacticon has the effect of energizing inner region stars to larger orbits. Therefore, instead of the limiting radius being imposed at perigalacticon, it more nearly traces the instantaneous tidal radius of the cluster at any point in the orbit. We present a numerical correction factor to theoretical tidal radii calculated at perigalacticon which takes into consideration both the orbital eccentricity and current orbital phase of the cluster.« less

Orbiter entry aerothermodynamics

NASA Technical Reports Server (NTRS)

Ried, R. C.

1985-01-01

The challenge in the definition of the entry aerothermodynamic environment arising from the challenge of a reliable and reusable Orbiter is reviewed in light of the existing technology. Select problems pertinent to the orbiter development are discussed with reference to comprehensive treatments. These problems include boundary layer transition, leeward-side heating, shock/shock interaction scaling, tile gap heating, and nonequilibrium effects such as surface catalysis. Sample measurements obtained from test flights of the Orbiter are presented with comparison to preflight expectations. Numerical and wind tunnel simulations gave efficient information for defining the entry environment and an adequate level of preflight confidence. The high quality flight data provide an opportunity to refine the operational capability of the orbiter and serve as a benchmark both for the development of aerothermodynamic technology and for use in meeting future entry heating challenges.

A preliminary analysis of the orbit of the Mars Trojan asteroid (5261) Eureka

NASA Technical Reports Server (NTRS)

Mikkola, Seppo; Innanen, Kimmo; Muinonen, Karri; Bowell, Edward

1994-01-01

Observations and results of orbit determination of the first known Mars Trojan asteroid (5261) Eureka are presented. We have numerically calculated the evolution of the orbital elements, and have analyzed the behavior of the motion during the next 2 Myr. Strong perturbations by planets other than Mars seem to stabilize the eccentricity of the asteroid by stirring the high order resonances present in the elliptic restricted problem. As a result, the orbit appears stable at least on megayear timescales. The difference of the mean longitudes of Mars and Eureka and the semimajor axis of the asteroid form a pair of variables that essentially behave in an adiabatic manner, while the evolution of the other orbital elements is largely determined by the pertubations due to other planets.

Low-thrust trajectory optimization of asteroid sample return mission with multiple revolutions and moon gravity assists

NASA Astrophysics Data System (ADS)

Tang, Gao; Jiang, FanHuag; Li, JunFeng

2015-11-01

Near-Earth asteroids have gained a lot of interest and the development in low-thrust propulsion technology makes complex deep space exploration missions possible. A mission from low-Earth orbit using low-thrust electric propulsion system to rendezvous with near-Earth asteroid and bring sample back is investigated. By dividing the mission into five segments, the complex mission is solved separately. Then different methods are used to find optimal trajectories for every segment. Multiple revolutions around the Earth and multiple Moon gravity assists are used to decrease the fuel consumption to escape from the Earth. To avoid possible numerical difficulty of indirect methods, a direct method to parameterize the switching moment and direction of thrust vector is proposed. To maximize the mass of sample, optimal control theory and homotopic approach are applied to find the optimal trajectory. Direct methods of finding proper time to brake the spacecraft using Moon gravity assist are also proposed. Practical techniques including both direct and indirect methods are investigated to optimize trajectories for different segments and they can be easily extended to other missions and more precise dynamic model.

Calculation of plasma dielectric response in inhomogeneous magnetic field near electron cyclotron resonance

NASA Astrophysics Data System (ADS)

Evstatiev, Evstati; Svidzinski, Vladimir; Spencer, Andy; Galkin, Sergei

2014-10-01

Full wave 3-D modeling of RF fields in hot magnetized nonuniform plasma requires calculation of nonlocal conductivity kernel describing the dielectric response of such plasma to the RF field. In many cases, the conductivity kernel is a localized function near the test point which significantly simplifies numerical solution of the full wave 3-D problem. Preliminary results of feasibility analysis of numerical calculation of the conductivity kernel in a 3-D hot nonuniform magnetized plasma in the electron cyclotron frequency range will be reported. This case is relevant to modeling of ECRH in ITER. The kernel is calculated by integrating the linearized Vlasov equation along the unperturbed particle's orbits. Particle's orbits in the nonuniform equilibrium magnetic field are calculated numerically by one of the Runge-Kutta methods. RF electric field is interpolated on a specified grid on which the conductivity kernel is discretized. The resulting integrals in the particle's initial velocity and time are then calculated numerically. Different optimization approaches of the integration are tested in this feasibility analysis. Work is supported by the U.S. DOE SBIR program.

Polynomial equations for science orbits around Europa

NASA Astrophysics Data System (ADS)

Cinelli, Marco; Circi, Christian; Ortore, Emiliano

2015-07-01

In this paper, the design of science orbits for the observation of a celestial body has been carried out using polynomial equations. The effects related to the main zonal harmonics of the celestial body and the perturbation deriving from the presence of a third celestial body have been taken into account. The third body describes a circular and equatorial orbit with respect to the primary body and, for its disturbing potential, an expansion in Legendre polynomials up to the second order has been considered. These polynomial equations allow the determination of science orbits around Jupiter's satellite Europa, where the third body gravitational attraction represents one of the main forces influencing the motion of an orbiting probe. Thus, the retrieved relationships have been applied to this moon and periodic sun-synchronous and multi-sun-synchronous orbits have been determined. Finally, numerical simulations have been carried out to validate the analytical results.

Suppression of the overlap between Majorana fermions by orbital magnetic effects in semiconducting-superconducting nanowires

NASA Astrophysics Data System (ADS)

Dmytruk, Olesia; Klinovaja, Jelena

2018-04-01

We study both analytically and numerically the role of orbital effects caused by a magnetic field applied along the axis of a semiconducting Rashba nanowire in the topological regime hosting Majorana fermions. We demonstrate that the orbital effects can be effectively taken into account in a one-dimensional model by shifting the chemical potential and thus modifying the topological criterion. We focus on the energy splitting between two Majorana fermions in a finite nanowire and find a striking interplay between orbital and Zeeman effects on this splitting. In the limit of strong spin-orbit interaction, we find regimes where the amplitude of the oscillating splitting stays constant or even decays with increasing the magnetic field, in stark contrast to the commonly studied case where orbital effects of the magnetic field are neglected. The period of these oscillations is found to be almost constant in many parameter regimes.

Meteor showers associated with 2003EH1

NASA Astrophysics Data System (ADS)

Babadzhanov, P. B.; Williams, I. P.; Kokhirova, G. I.

2008-06-01

Using the Everhart RADAU19 numerical integration method, the orbital evolution of the near-Earth asteroid 2003EH1 is investigated. This asteroid belongs to the Amor group and is moving on a comet-like orbit. The integrations are performed over one cycle of variation of the perihelion argument ω. Over such a cycle, the orbit intersect that of the Earth at eight different values of ω. The orbital parameters are different at each of these intersections and so a meteoroid stream surrounding such an orbit can produce eight different meteor showers, one at each crossing. The geocentric radiants and velocities of the eight theoretical meteor showers associated with these crossing points are determined. Using published data, observed meteor showers are identified with each of the theoretically predicted showers. The character of the orbit and the existence of observed meteor showers associated with 2003EH1 confirm the supposition that this object is an extinct comet.

Development of a hardware-in-loop attitude control simulator for a CubeSat satellite

NASA Astrophysics Data System (ADS)

Tapsawat, Wittawat; Sangpet, Teerawat; Kuntanapreeda, Suwat

2018-01-01

Attitude control is an important part in satellite on-orbit operation. It greatly affects the performance of satellites. Testing of an attitude determination and control subsystem (ADCS) is very challenging since it might require attitude dynamics and space environment in the orbit. This paper develops a low-cost hardware-in-loop (HIL) simulator for testing an ADCS of a CubeSat satellite. The simulator consists of a numerical simulation part, a hardware part, and a HIL interface hardware unit. The numerical simulation part includes orbital dynamics, attitude dynamics and Earth’s magnetic field. The hardware part is the real ADCS board of the satellite. The simulation part outputs satellite’s angular velocity and geomagnetic field information to the HIL interface hardware. Then, based on this information, the HIL interface hardware generates I2C signals mimicking the signals of the on-board rate-gyros and magnetometers and consequently outputs the signals to the ADCS board. The ADCS board reads the rate-gyro and magnetometer signals, calculates control signals, and drives the attitude actuators which are three magnetic torquers (MTQs). The responses of the MTQs sensed by a separated magnetometer are feedback to the numerical simulation part completing the HIL simulation loop. Experimental studies are conducted to demonstrate the feasibility and effectiveness of the simulator.

Analysis of the long and short-period terms due the nonsphericity of the central body: applications for Mercury

NASA Astrophysics Data System (ADS)

Carvalho, J. P. S.

2017-10-01

In this work, we present an approach taking into account the single-averaged equations and unaveraged equations to investigate the dynamics of artificial satellites on the effect due to the non-spherical shape of the planet Mercury. An analysis considering the long-period terms and another taking into account the short-period terms is presented. The numerical integrations of the equations developed are performed using the Maple software. We consider the numerical values of the most updated spherical harmonic coefficients in the literature. Emphasis is given to analyze the effect of the C22 term in the dynamics of the spacecraft. We show that the two techniques are in agreement (average or not average). We found orbits that librates around an equilibrium point with small variation of the orbital elements, in particular the eccentricity and argument of the pericenter. We also note that the C22 term contributes to reduce the growth of the orbital eccentricity.

State dependent model predictive control for orbital rendezvous using pulse-width pulse-frequency modulated thrusters

NASA Astrophysics Data System (ADS)

Li, Peng; Zhu, Zheng H.; Meguid, S. A.

2016-07-01

This paper studies the pulse-width pulse-frequency modulation based trajectory planning for orbital rendezvous and proximity maneuvering near a non-cooperative spacecraft in an elliptical orbit. The problem is formulated by converting the continuous control input, output from the state dependent model predictive control, into a sequence of pulses of constant magnitude by controlling firing frequency and duration of constant-magnitude thrusters. The state dependent model predictive control is derived by minimizing the control error of states and control roughness of control input for a safe, smooth and fuel efficient approaching trajectory. The resulting nonlinear programming problem is converted into a series of quadratic programming problem and solved by numerical iteration using the receding horizon strategy. The numerical results show that the proposed state dependent model predictive control with the pulse-width pulse-frequency modulation is able to effectively generate optimized trajectories using equivalent control pulses for the proximity maneuvering with less energy consumption.

Eighth-order explicit two-step hybrid methods with symmetric nodes and weights for solving orbital and oscillatory IVPs

NASA Astrophysics Data System (ADS)

Franco, J. M.; Rández, L.

The construction of new two-step hybrid (TSH) methods of explicit type with symmetric nodes and weights for the numerical integration of orbital and oscillatory second-order initial value problems (IVPs) is analyzed. These methods attain algebraic order eight with a computational cost of six or eight function evaluations per step (it is one of the lowest costs that we know in the literature) and they are optimal among the TSH methods in the sense that they reach a certain order of accuracy with minimal cost per step. The new TSH schemes also have high dispersion and dissipation orders (greater than 8) in order to be adapted to the solution of IVPs with oscillatory solutions. The numerical experiments carried out with several orbital and oscillatory problems show that the new eighth-order explicit TSH methods are more efficient than other standard TSH or Numerov-type methods proposed in the scientific literature.

Flavors of Chaos in the Asteroid Belt

NASA Astrophysics Data System (ADS)

Tsiganis, Kleomenis

2016-10-01

The asteroid belt is a natural laboratory for studying chaos, as a large fraction of asteroids actually reside on chaotic orbits. Numerous studies over the past 25 years have unveiled a multitude of dynamical chaos-generating mechanisms, operating on different time-scales and dominating over different regions of the belt. In fact, the distribution of chaotic asteroids in orbital space can be largely understood as the outcome of the combined action of resonant gravitational perturbations and the Yarkovsky effect - two topics on which Paolo Farinella has made an outstanding contribution! - notwithstanding the fact that the different "flavors" of chaos can give rise to a wide range of outcomes, from fast escape (e.g. to NEA space) to slow (~100s My) macroscopic diffusion (e.g. spreading of families) and strange, stable-looking, chaotic orbits (ultra-slow diffusion). In this talk I am going to present an overview of these mechanisms, presenting both analytical and numerical results, and their role in understanding the long-term evolution and stability of individual bodies, asteroid groups and families.

Analytical investigation of the dynamics of tethered constellations in Earth orbit, phase 2

NASA Technical Reports Server (NTRS)

Lorenzini, Enrico C.; Gullahorn, Gordon E.; Cosmo, Mario L.; Estes, Robert D.; Grossi, Mario D.

1994-01-01

This final report covers nine years of research on future tether applications and on the actual flights of the Small Expendable Deployment System (SEDS). Topics covered include: (1) a description of numerical codes used to simulate the orbital and attitude dynamics of tethered systems during station keeping and deployment maneuvers; (2) a comparison of various tethered system simulators; (3) dynamics analysis, conceptual design, potential applications and propagation of disturbances and isolation from noise of a variable gravity/microgravity laboratory tethered to the Space Station; (4) stability of a tethered space centrifuge; (5) various proposed two-dimensional tethered structures for low Earth orbit for use as planar array antennas; (6) tethered high gain antennas; (7) numerical calculation of the electromagnetic wave field on the Earth's surface on an electrodynamically tethered satellite; (8) reentry of tethered capsules; (9) deployment dynamics of SEDS-1; (10) analysis of SEDS-1 flight data; and (11) dynamics and control of SEDS-2.

Contraction of high eccentricity satellite orbits using uniformly regular KS canonical elements with oblate diurnally varying atmosphere.

NASA Astrophysics Data System (ADS)

Raj, Xavier James

2016-07-01

Accurate orbit prediction of an artificial satellite under the influence of air drag is one of the most difficult and untraceable problem in orbital dynamics. The orbital decay of these satellites is mainly controlled by the atmospheric drag effects. The effects of the atmosphere are difficult to determine, since the atmospheric density undergoes large fluctuations. The classical Newtonian equations of motion, which is non linear is not suitable for long-term integration. Many transformations have emerged in the literature to stabilize the equations of motion either to reduce the accumulation of local numerical errors or allowing the use of large integration step sizes, or both in the transformed space. One such transformation is known as KS transformation by Kustaanheimo and Stiefel, who regularized the nonlinear Kepler equations of motion and reduced it into linear differential equations of a harmonic oscillator of constant frequency. The method of KS total energy element equations has been found to be a very powerful method for obtaining numerical as well as analytical solution with respect to any type of perturbing forces, as the equations are less sensitive to round off and truncation errors. The uniformly regular KS canonical equations are a particular canonical form of the KS differential equations, where all the ten KS Canonical elements αi and βi are constant for unperturbed motion. These equations permit the uniform formulation of the basic laws of elliptic, parabolic and hyperbolic motion. Using these equations, developed analytical solution for short term orbit predictions with respect to Earth's zonal harmonic terms J2, J3, J4. Further, these equations were utilized to include the canonical forces and analytical theories with air drag were developed for low eccentricity orbits (e < 0.2) with different atmospheric models. Using uniformly regular KS canonical elements developed analytical theory for high eccentricity (e > 0.2) orbits by assuming the atmosphere to be oblate only. In this paper a new non-singular analytical theory is developed for the motion of high eccentricity satellite orbits with oblate diurnally varying atmosphere in terms of the uniformly regular KS canonical elements. The analytical solutions are generated up to fourth-order terms using a new independent variable and c (a small parameter dependent on the flattening of the atmosphere). Due to symmetry, only two of the nine equations need to be solved analytically to compute the state vector and change in energy at the end of each revolution. The theory is developed on the assumption that density is constant on the surfaces of spheroids of fixed ellipticity ɛ (equal to the Earth's ellipticity, 0.00335) whose axes coincide with the Earth's axis. Numerical experimentation with the analytical solution for a wide range of perigee height, eccentricity, and orbital inclination has been carried out up to 100 revolutions. Comparisons are made with numerically integrated values and found that they match quite well. Effectiveness of the present analytical solutions will be demonstrated by comparing the results with other analytical solutions in the literature.

Wave Journal Bearings Under Dynamic Loads

NASA Technical Reports Server (NTRS)

Hendricks, Robert C.; Dimofte, Florin

2002-01-01

The dynamic behavior of the wave journal bearing was determined by running a three-wave bearing with an eccentrically mounted shaft. A transient analysis was developed and used to predict numerical data for the experimental cases. The three-wave journal bearing ran stably under dynamic loads with orbits well inside the bearing clearance. The orbits were almost circular and nearly free of the influence of, but dynamically dependent on, bearing wave shape. Experimental observations for both the absolute bearing-housing-center orbits and the relative bearing-housing-center-to-shaft-center orbits agreed well with the predictions. Moreover, the subsynchronous whirl motion generated by the fluid film was found experimentally and predicted theoretically for certain speeds.

The Orbital precession around oblate spheroids

NASA Astrophysics Data System (ADS)

Montanus, J. M. C.

2006-07-01

An exact series will be given for the gravitational potential generated by an oblate gravitating source. To this end the corresponding Epstein-Hubbell type elliptic integral is evaluated. The procedure is based on the Legendre polynomial expansion method and on combinatorial techniques. The result is of interest for gravitational models based on the linearity of the gravitational potential. The series approximation for such potentials is of use for the analysis of orbital motions around a nonspherical source. It can be considered advantageous that the analysis is purely algebraic. Numerical approximations are not required. As an important example, the expression for the orbital precession will be derived for an object orbiting around an oblate homogeneous spheroid.

The study of the physics of cometary nuclei

NASA Technical Reports Server (NTRS)

Whipple, Fred L.

1987-01-01

The numerical calculations of stability for many possible orbits of the double nucleus for P/Holmes showed that the likelihood of such a precollision history was quite high. A number of investigations were made of hypothetical orbits for particles about the asteroid Amphitrite to test for stability. The purpose was to establish more favorable fly-by orbits close to the asteroid for the Galileo missions en-route to Jupiter, reducing the collisional hazards. A statistical study was made of the orbits of long-period comets with small original semi-major axes recently perturbed from the great Opik-Oort Cloud. The results from the space missions to Halley's comet are partially reported in the two papers in the appendices.

Spin-orbit splitted excited states using explicitly-correlated equation-of-motion coupled-cluster singles and doubles eigenvectors

NASA Astrophysics Data System (ADS)

Bokhan, Denis; Trubnikov, Dmitrii N.; Perera, Ajith; Bartlett, Rodney J.

2018-04-01

An explicitly-correlated method of calculation of excited states with spin-orbit couplings, has been formulated and implemented. Developed approach utilizes left and right eigenvectors of equation-of-motion coupled-cluster model, which is based on the linearly approximated explicitly correlated coupled-cluster singles and doubles [CCSD(F12)] method. The spin-orbit interactions are introduced by using the spin-orbit mean field (SOMF) approximation of the Breit-Pauli Hamiltonian. Numerical tests for several atoms and molecules show good agreement between explicitly-correlated results and the corresponding values, calculated in complete basis set limit (CBS); the highly-accurate excitation energies can be obtained already at triple- ζ level.

Rigorous Numerics for ill-posed PDEs: Periodic Orbits in the Boussinesq Equation

NASA Astrophysics Data System (ADS)

Castelli, Roberto; Gameiro, Marcio; Lessard, Jean-Philippe

2018-04-01

In this paper, we develop computer-assisted techniques for the analysis of periodic orbits of ill-posed partial differential equations. As a case study, our proposed method is applied to the Boussinesq equation, which has been investigated extensively because of its role in the theory of shallow water waves. The idea is to use the symmetry of the solutions and a Newton-Kantorovich type argument (the radii polynomial approach) to obtain rigorous proofs of existence of the periodic orbits in a weighted ℓ1 Banach space of space-time Fourier coefficients with exponential decay. We present several computer-assisted proofs of the existence of periodic orbits at different parameter values.

Transition between order and chaos in a composite disk galaxy model with a massive nucleus and a dark matter halo

NASA Astrophysics Data System (ADS)

Caranicolas, Nicolaos D.; Zotos, Euaggelos E.

2013-02-01

We investigate the transition from regular to chaotic motion in a composite galaxy model with a disk-halo, a massive dense nucleus and a dark halo component. We obtain relationships connecting the critical value of the mass of the nucleus or the critical value of the angular momentum Lzc, with the mass Mh of the dark halo, where the transition from regular motion to chaos occurs. We also present 3D diagrams connecting the mass of nucleus the energy and the percentage of stars that can show chaotic motion. The fraction of the chaotic orbits observed in the (r,pr) phase plane, as a function of the mass of the dark halo is also computed. We use a semi-numerical method, that is a combination of theoretical and numerical procedure. The theoretical results obtained using the version 8.0 of the Mathematica package, while all the numerical calculations were made using a Bulirsch-Stöer FORTRAN routine in double precision. The results can be obtained in semi-numerical or numerical form and give good description for the connection of the physical quantities entering the model and the transition between regular and chaotic motion. We observe that the mass of the dark halo, the mass of the dense nucleus and the Lz component of the angular momentum, are important physical quantities, as they are linked to the regular or chaotic character of orbits in disk galaxies described by the model. Our numerical experiments suggest, that the amount of the dark matter plays an important role in disk galaxies represented by the model, as the mass of the halo affects, not only the regular or chaotic nature of motion but it is also connected with the existence of the different families of regular orbits. Comparison of the present results with earlier work is also presented.

Models of Angular Momentum Input to a Circumterrestrial Swarm from Encounters with Heliocentric Planetesimals

NASA Technical Reports Server (NTRS)

Davis, D. R.; Greenberg, R.; Hebert, F.

1985-01-01

Models of lunar origin in which the Moon accretes in orbit about the Earth from material approaching the Earth from heliocentric orbits must overcome a fundamental problem: the approach orbits of such material would be, in the simplest approximation, equally likely to be prograde or retrograde about the Earth, with the result that accretion of such material adds mass but not angular momentum to circumterrestrial satellites. Satellite orbits would then decay due to the resulting drag, ultimately impacting onto the Earth. One possibility for adding both material and angular momentum to Earth orbit is investigated: imbalance in the delivered angular momentum between pro and retrograde Earth passing orbits which arises from the three body dynamics of planetesimals approaching the Earth from heliocentric space. In order to study angular momentum delivery to circumterrestrial satellites, the near Earth velocities were numerically computed as a function of distance from the Earth for a large array of orbits systematically spanning heliocentric phase space.

How long will asteroids on retrograde orbits survive?

NASA Astrophysics Data System (ADS)

Kankiewicz, Paweł; Włodarczyk, Ireneusz

2018-05-01

Generally, a common scenario for the origin of minor planets with high orbital inclinations does not exist. This applies especially to objects whose orbital inclinations are much greater than 90° (retrograde asteroids). Since the discovery of Dioretsa in 1999, approximately 100 small bodies now are classified as retrograde asteroids. A small number of them were reclassified as comets, due to cometary activity. There are only 25 multi-opposition retrograde asteroids, with a relatively large number of observations and well-determined orbits. We studied the orbital evolution of numbered and multi-opposition retrograde asteroids by numerical integration up to 1 Gy forward and backward in time. Additionally, we analyzed the propagation of orbital elements with the observational errors, determined dynamical lifetimes and studied their chaotic properties. Conclusively, we obtained quantitative parameters describing the long-term stability of orbits relating to the past and the future. In turn, we were able to estimate their lifetimes and how long these objects will survive in the Solar System.

Tidal formation of Hot Jupiters in binary star systems

NASA Astrophysics Data System (ADS)

Bataille, M.; Libert, A.-S.; Correia, A. C. M.

2015-10-01

More than 150 Hot Jupiters with orbital periods less than 10 days have been detected. Their in-situ formation is physically unlikely. We need therefore to understand the migration of these planets from high distance (several AUs). Three main models are currently extensively studied: disk-planet interactions (e.g. [3]), planet-planet scattering (e.g. [4]) and Kozai migration (e.g. [2]). Here we focus on this last mechanism, and aim to understand which dynamical effects are the most active in the accumulation of planetary companions with low orbital periods in binary star systems. To do so, we investigate the secular evolution of Hot Jupiters in binary star systems. Our goal is to study analytically the 3-day pile-up observed in their orbital period. Our framework is the hierarchical three-body problem, with the effects of tides, stellar oblateness, and general relativity. Both the orbital evolution and the spin evolution are considered. Using the averaged equations of motion in a vectorial formalism of [1], we have performed # 100000 numerical simulations of well diversified three-body systems, reproducing and generalizing the numerical results of [2]. Based on a thorough analysis of the initial and final configurations of the systems, we have identified different categories of secular evolutions present in the simulations, and proposed for each one a simplified set of equations reproducing the evolution. Statistics about spin-orbit misalignements and mutual inclinations between the orbital planes of the Hot Jupiter and the star companion are also provided. Finally, we show that the extent of the 3 day pile-up is very dependent on the initial parameters of the simulations.

Irregular wave functions of a hydrogen atom in a uniform magnetic field

NASA Technical Reports Server (NTRS)

Wintgen, D.; Hoenig, A.

1989-01-01

The highly excited irregular wave functions of a hydrogen atom in a uniform magnetic field are investigated analytically, with wave function scarring by periodic orbits considered quantitatively. The results obtained confirm that the contributions of closed classical orbits to the spatial wave functions vanish in the semiclassical limit. Their disappearance, however, is slow. This discussion is illustrated by numerical examples.

Constraining the primordial orbits of the terrestrial planets

NASA Astrophysics Data System (ADS)

Brasser, R.; Walsh, K. J.; Nesvorný, D.

2013-08-01

Evidence in the Solar system suggests that the giant planets underwent an epoch of radial migration that was very rapid, with an e-folding time-scale shorter than 1 Myr. It is probable that the cause of this migration was that the giant planets experienced an orbital instability that caused them to encounter each other, resulting in radial migration. A promising and heavily studied way to accomplish such a fast migration is for Jupiter to have scattered one of the ice giants outwards; this event has been called the `jumping Jupiter' scenario. Several works suggest that this dynamical instability occurred `late', long after all the planets had formed and the solar nebula had dissipated. Assuming that the terrestrial planets had already formed, then their orbits would have been affected by the migration of the giant planets as many powerful resonances would sweep through the terrestrial planet region. This raises two questions. First, what is the expected increase in dynamical excitement of the terrestrial planet orbits caused by late and very fast giant planet migration? And secondly, assuming that the migration occurred late, can we use this migration of the giant planets to obtain information on the primordial orbits of the terrestrial planets? In this work, we attempt to answer both of these questions using numerical simulations. We directly model a large number of terrestrial planet systems and their response to the smooth migration of Jupiter and Saturn, and also two jumping Jupiter simulations. We study the total dynamical excitement of the terrestrial planet system with the angular momentum deficit (AMD) value, including the way it is shared among the planets. We conclude that to reproduce the current AMD with a reasonable probability (˜20 per cent) after late rapid giant planet migration and a favourable jumping Jupiter evolution, the primordial AMD should have been lower than ˜70 per cent of the current value, but higher than 10 per cent. We find that a late giant planet migration scenario that initially had five giant planets rather than four had a higher probability of satisfying the orbital constraints of the terrestrial planets. Assuming late migration, we predict that Mars was initially on an eccentric and inclined orbit while the orbits of Mercury, Venus and Earth were more circular and coplanar. The lower primordial dynamical excitement and the peculiar partitioning between planets impose new constraints for terrestrial planet formation simulations.

On non-coplanar Hohmann transfer using angles as parameters

NASA Astrophysics Data System (ADS)

Rincón, Ángel; Rojo, Patricio; Lacruz, Elvis; Abellán, Gabriel; Díaz, Sttiwuer

2015-09-01

We study a more complex case of Hohmann orbital transfer of a satellite by considering non-coplanar and elliptical orbits, instead of planar and circular orbits. We use as parameter the angle between the initial and transference planes that minimizes the energy, and therefore the fuel of a satellite, through the application of two non-tangential impulses for all possible cases. We found an analytical expression that minimizes the energy for each configuration. Some reasonable physical constraints are used: we apply impulses at perigee or apogee of the orbit, we consider the duration of the impulse to be short compared to the duration of the trip, we take the nodal line of three orbits to be coincident and the three semimajor axes to lie in the same plane. We study the only four possible cases but assuming non-coplanar elliptic orbits. In addition, we validate our method through a numerical solution obtained by using some of the actual orbital elements of Sputnik I and Vanguard I satellites. For these orbits, we found that the most fuel-efficient transfer is obtained by applying the initial impulse at apocenter and keeping the transfer orbit aligned with the initial orbit.

Flight Performance Handbook for Orbital Operations: Orbital Mechanics and Astrodynamics Formulae, Theorems, Techniques, and Applications

NASA Technical Reports Server (NTRS)

Ambrosio, Alphonso; Blitzer, Leon; Conte, S.D.; Cooper, Donald H.; Dergarabedian, P.; Dethlefsen, D.G.; Lunn, Richard L.; Ireland, Richard O.; Jensen, Arnold A.; Kang, Garfield;

Direct Imaging Of Long Period Radial Velocity Targets With NICI

NASA Astrophysics Data System (ADS)

Salter, Graeme S.; Tinney, Chris G.; Wittenmyer, Robert A.; Jenkins, James S.; Jones, Hugh R. A.; O'Toole, Simon J.

2014-01-01

We are finally entering an era where radial velocity and direct imaging parameter spaces are starting to overlap. Radial velocity measurements provide us with a minimum mass for an orbiting companion (the mass as a function of the inclination of the system). By following up these long period radial velocity detections with direct imaging we can determine whether a trend seen is due to an orbiting planet at low inclination or an orbiting brown dwarf at high inclination. In the event of a non-detection we are still able to put a limit on the maximum mass of the orbiting body. The Anglo-Australian Planet Search is one of the longest baseline radial velocity planet searches in existence, amongst its targets are many that show long period trends in the data. Here we present our direct imaging survey of these objects with our results to date. ADI Observations have been made using NICI (Near Infrared Coronagraphic Imager) on Gemini South and analysed using an in house, LOCI-like, post processing.

Can Eccentric Debris Disks Be Long-lived? A First Numerical Investigation and Application to Zeta(exp 2) Reticuli

NASA Technical Reports Server (NTRS)

Faramaz, V.; Beust, H.; Thebault, P.; Augereau, J.-C.; Bonsor, A.; delBurgo, C.; Ertel, S.; Marshall, J. P.; Milli, J.; Montesinos, B.;

Measurement-based perturbation theory and differential equation parameter estimation with applications to satellite gravimetry

NASA Astrophysics Data System (ADS)

Xu, Peiliang

2018-06-01

The numerical integration method has been routinely used by major institutions worldwide, for example, NASA Goddard Space Flight Center and German Research Center for Geosciences (GFZ), to produce global gravitational models from satellite tracking measurements of CHAMP and/or GRACE types. Such Earth's gravitational products have found widest possible multidisciplinary applications in Earth Sciences. The method is essentially implemented by solving the differential equations of the partial derivatives of the orbit of a satellite with respect to the unknown harmonic coefficients under the conditions of zero initial values. From the mathematical and statistical point of view, satellite gravimetry from satellite tracking is essentially the problem of estimating unknown parameters in the Newton's nonlinear differential equations from satellite tracking measurements. We prove that zero initial values for the partial derivatives are incorrect mathematically and not permitted physically. The numerical integration method, as currently implemented and used in mathematics and statistics, chemistry and physics, and satellite gravimetry, is groundless, mathematically and physically. Given the Newton's nonlinear governing differential equations of satellite motion with unknown equation parameters and unknown initial conditions, we develop three methods to derive new local solutions around a nominal reference orbit, which are linked to measurements to estimate the unknown corrections to approximate values of the unknown parameters and the unknown initial conditions. Bearing in mind that satellite orbits can now be tracked almost continuously at unprecedented accuracy, we propose the measurement-based perturbation theory and derive global uniformly convergent solutions to the Newton's nonlinear governing differential equations of satellite motion for the next generation of global gravitational models. Since the solutions are global uniformly convergent, theoretically speaking, they are able to extract smallest possible gravitational signals from modern and future satellite tracking measurements, leading to the production of global high-precision, high-resolution gravitational models. By directly turning the nonlinear differential equations of satellite motion into the nonlinear integral equations, and recognizing the fact that satellite orbits are measured with random errors, we further reformulate the links between satellite tracking measurements and the global uniformly convergent solutions to the Newton's governing differential equations as a condition adjustment model with unknown parameters, or equivalently, the weighted least squares estimation of unknown differential equation parameters with equality constraints, for the reconstruction of global high-precision, high-resolution gravitational models from modern (and future) satellite tracking measurements.

Gravity field models from kinematic orbits of CHAMP, GRACE and GOCE satellites

NASA Astrophysics Data System (ADS)

Bezděk, Aleš; Sebera, Josef; Klokočník, Jaroslav; Kostelecký, Jan

2014-02-01

The aim of our work is to generate Earth's gravity field models from GPS positions of low Earth orbiters. Our inversion method is based on Newton's second law, which relates the observed acceleration of the satellite with forces acting on it. The observed acceleration is obtained as numerical second derivative of kinematic positions. Observation equations are formulated using the gradient of the spherical harmonic expansion of the geopotential. Other forces are either modelled (lunisolar perturbations, tides) or provided by onboard measurements (nongravitational perturbations). From this linear regression model the geopotential harmonic coefficients are obtained. To this basic scheme of the acceleration approach we added some original elements, which may be useful in other inversion techniques as well. We tried to develop simple, straightforward and still statistically correct model of observations. (i) The model is linear in the harmonic coefficients, no a priori gravity field model is needed, no regularization is applied. (ii) We use the generalized least squares to successfully mitigate the strong amplification of noise due to numerical second derivative. (iii) The number of other fitted parameters is very small, in fact we use only daily biases, thus we can monitor their behaviour. (iv) GPS positions have correlated errors. The sample autocorrelation function and especially the partial autocorrelation function indicate suitability of an autoregressive model to represent the correlation structure. The decorrelation of residuals improved the accuracy of harmonic coefficients by a factor of 2-3. (v) We found it better to compute separate solutions in the three local reference frame directions than to compute them together at the same time; having obtained separate solutions for along-track, cross-track and radial components, we combine them using the normal matrices. Relative contribution of the along-track component to the combined solution is 50 percent on average. (vi) The computations were performed on an ordinary PC up to maximum degree and order 120. We applied the presented method to orbits of CHAMP and GRACE spanning seven years (2003-2009) and to two months of GOCE (Nov/Dec 2009). The obtained long-term static gravity field models are of similar or better quality compared to other published solutions. We also tried to extract the time-variable gravity signal from CHAMP and GRACE orbits. The acquired average annual signal shows clearly the continental areas with important and known hydrological variations.

Input profile for satellite orbit transfer by tether mechanism; Part I: Tether length profile using feed-forward procedure

NASA Astrophysics Data System (ADS)

Hokamoto, Shinji

This study deals with orbital transfer of a satellite using a tether extension / retrieval mechanism. Instead of using propellant for the orbital transfer, the present concept uses electrical energy. By controlling the pitch motion of the tether system, we can achieve a prescribed velocity of the satellite at a prescribed position. By cutting the tether at that instant, we can inject the satellite into a designed new orbit. This paper considers co-planar motion and proposes a technique to achieve the desired tether length, pitch angle, and pitch angular rate at a designated position in orbit by using only tether length control. These three state variables are adjusted to their target values in three consecutive sections in the orbit; 1) control for the angular momentum of the pitching motion, which implies to adjust the tether length, 2) control for the pitch angle, and 3) control for the pitch angular rate. In each section, a pitch acceleration profile can be formed by using Fourier series as an alternative input for tether length profile. Their coefficients can be obtained without numerical iterations by using the simple initial / final relationships for the pitch angle and pitch angular rate. Therefore, this proposed procedure requires less computational cost than a numerical search, is easily applicable for different models and orbits, and can cope with physical restrictions of the system, such as tether tension or maximum tether length. Furthermore, the resulting final states precisely coincide with the target values. To demonstrate that the proposed procedure can successfully generate proper input profiles, this paper presents an orbital transfer problem as an example, and verifies its effectiveness. The simulation results show that the maximum tether length is less than 5km, and that the tether tension is kept positive during the mission.

The dynamics and control of solar-sail spacecraft in displaced lunar orbits

NASA Astrophysics Data System (ADS)

Wawrzyniak, Geoffrey George

Trajectory generation for any spacecraft mission application typically involves either well-developed analytical approximations or a linearization with respect to a known solution. Such approximations are based on the well-understood dynamics of behavior in the system. However, when two or more large bodies (e.g., the Earth and the Moon or the Sun, the Earth and the Moon) are present, trajectories in the multi-body gravitational field can evolve chaotically. The problem is further complicated when an additional force from a solar sail is included. Solar sail trajectories are often developed in a Sun-centered reference frame in which the sunlight direction is fixed. New challenges arise when modeling a solar-sail trajectory in a reference frame attached to the Earth and the Moon (a frame that rotates in inertial space). Advantages accrue from geometry and symmetry properties that are available in this Earth--Moon reference frame, but the Sun location and the sunlight direction change with time. Current trajectory design tools can reveal many solutions within these regimes. Recent work using numerical boundary value problem (BVP) solvers has demonstrated great promise for uncovering additional and, sometimes, "better" solutions to problems in spacecraft trajectory design involving solar sails. One such approach to solving BVPs is the finite-difference method. Derivatives that appear in the differential equations are replaced with their respective finite differences and evaluated at node points along the trajectory. The solution process is iterative. A candidate solution, such as an offset circle or a point, is discretized into nodes, and the equations that represent the relationships at the nodes are solved simultaneously. Finite-difference methods (FDMs) exploit coarse initial approximations and, with the system constraints (such as the continuous visibility of the spacecraft from a point on the lunar surface), to develop orbital solutions in regions where the structure of the solution space is not well known. Because of their simplicity and speed, the FDM is used to populate a survey to assist in the understanding of the available design space. Trajectories generated by FDMs can also be used to initialize other nonlinear BVP solvers. Any solution is only as accurate as the model used to generate it, especially when the trajectory is dynamically unstable, certainly the case when an orbit is purposefully offset from the Moon. Perturbations, such as unmodeled gravitational forces, variations in the solar flux, as well as mis-modeling of the sail and bus properties, all shift the spacecraft off the reference trajectory and, potentially, into a regime from which the vehicle is unrecoverable. Therefore, some type of flight-path control is required to maintain the vehicle near the reference path. Reference trajectories, supplied by FDMs, are used to develop guidance algorithms based on other, more accurate, numerical procedures, such as multiple shooting. The primary motivation of this investigation is to determine what level of technology is required to displace a solar sail spacecraft sufficiently such that a vehicle equipped with a sail supplies a continuous relay between the Earth and an outpost at the lunar south pole. To accomplish this objective, numerical methods to generate reference orbits that meet mission constraints are examined, as well as flight-path control strategies to ensure that a sailcraft follows those reference trajectories. A survey of the design space is also performed to highlight vehicle-performance and ground-based metrics critical to a mission that monitors the lunar south pole at all times. Finally, observations about the underlying dynamical structure of solar sail motion in a multi-body system are summarized.

The Impact of Current and Future Polar Orbiting Satellite Data on Numerical Weather Prediction at NASA/GSFC

NASA Technical Reports Server (NTRS)

Atlas, Robert

2004-01-01

The lack of adequate observational data continues to be recognized as a major factor limiting both atmospheric research and numerical prediction on a variety of temporal and spatial scales. Since the advent of meteorological satellites in the 1960's, a considerable research effort has been directed toward the design of space-borne meteorological sensors, the development of optimal methods for the utilization of these data, (and an assessment of the influence of existing satellite data and the potential influence of future satellite observations on numerical weather prediction. This has included both Observing System Experiments (OSEs) and Observing System Simulation Experiments (OSSEs). OSEs are conducted to evaluate the impact of specific observations or classes of observations on analyses and forecasts. While OSEs are performed with existing data, OSSEs are conducted to evaluate the potential for future observing systems to improve-NWP, as well as to evaluate trade-offs in observing system design, and to develop and test improved methods for data assimilation. At the conference, results from OSEs to evaluate satellite data sets that have recently become available to the global observing system, such as AIRS and Seawinds, and results from OSSEs to determine the potential impact of space-based lidar winds will be presented.

A spacecraft's own ambient environment: The role of simulation-based research

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

Ketsdever, Andrew D.; Gimelshein, Sergey

2014-12-09

Spacecraft contamination has long been a subject of study in the rarefied gas dynamics community. Professor Mikhail Ivanov coined the term a spacecraft's 'own ambient environment' to describe the effects of natural and satellite driven processes on the conditions encountered by a spacecraft in orbit. Outgassing, thruster firings, and gas and liquid dumps all contribute to the spacecraft's contamination environment. Rarefied gas dynamic modeling techniques, such as Direct Simulation Monte Carlo, are well suited to investigate these spacebased environments. However, many advances were necessary to fully characterize the extent of this problem. A better understanding of modeling flows over largemore » pressure ranges, for example hybrid continuum and rarefied numerical schemes, were required. Two-phase flow modeling under rarefied conditions was necessary. And the ability to model plasma flows for a new era of propulsion systems was also required. Through the work of Professor Ivanov and his team, we now have a better understanding of processes that create a spacecraft's own ambient environment and are able to better characterize these environments. Advances in numerical simulation have also spurred on the development of experimental facilities to study these effects. The relationship between numerical results and experimental advances will be explored in this manuscript.« less

Assessment Study of Small Space Debris Removal by Laser Satellites

NASA Technical Reports Server (NTRS)

Choi, Sang H.; Papa, Richard S.

2011-01-01

Space debris in Earth orbit poses significant danger to satellites, humans in space, and future space exploration activities. In particular, the increasing number of unidentifiable objects, smaller than 10 cm, presents a serious hazard. Numerous technologies have been studied for removing unwanted objects in space. Our approach uses a short wavelength laser stationed in orbit to vaporize these small objects. This paper discusses the power requirements for space debris removal using lasers. A short wavelength laser pumped directly or indirectly by solar energy can scan, identify, position, and illuminate the target, which will then be vaporized or slow down the orbital speed of debris by laser detonation until it re-enters the atmosphere. The laser-induced plasma plume has a dispersive motion of approximately 105 m/sec with a Lambertian profile in the direction of the incoming beam [1-2]. The resulting fast ejecting jet plume of vaporized material should prevent matter recombination and condensation. If it allows any condensation of vaporized material, the size of condensed material will be no more than a nanoscale level [3]. Lasers for this purpose can be indirectly pumped by power from an array of solar cells or directly pumped by the solar spectrum [4]. The energy required for vaporization and ionization of a 10 cm cube ( 2700 gm) of aluminum is 87,160 kJ. To remove this amount of aluminum in 3 minutes requires a continuous laser beam power of at least 5.38 MW under the consideration of 9% laser absorption by aluminum [5] and 5% laser pumping efficiency. The power needed for pumping 5.38 MW laser is approximately 108 MW, which can be obtained from a large solar array with 40% efficiency solar cells and a minimal area of 450 meters by 450 meters. This solar array would collect approximately 108 MW. The power required for system operation and maneuvering can be obtained by increasing solar panel size. This feasibility assessment covers roughly the power requirement, laser system, and a potential operational scenario.

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.

Electrical valley filtering in transition metal dichalcogenides

NASA Astrophysics Data System (ADS)

Hsieh, Tzu-Chi; Chou, Mei-Yin; Wu, Yu-Shu

2018-03-01

This work investigates the feasibility of electrical valley filtering for holes in transition metal dichalcogenides. We look specifically into the scheme that utilizes a potential barrier to produce valley-dependent tunneling rates, and perform the study with both a k .p -based analytic method and a recursive Green's function-based numerical method. The study yields the transmission coefficient as a function of incident energy and transverse wave vector, for holes going through lateral quantum barriers oriented in either armchair or zigzag directions, in both homogeneous and heterogeneous systems. The main findings are the following: (1) The tunneling current valley polarization increases with increasing barrier width or height; (2) both the valley-orbit interaction and band structure warping contribute to valley-dependent tunneling, with the former contribution being manifest in structures with asymmetric potential barriers, and the latter being orientation dependent and reaching maximum for transmission in the armchair direction; and (3) for transmission ˜0.1 , a tunneling current valley polarization of the order of 10 % can be achieved.

Improvements to NASA's Debris Assessment Software

NASA Technical Reports Server (NTRS)

Opiela, J.; Johnson, Nicholas L.

2007-01-01

NASA's Debris Assessment Software (DAS) has been substantially revised and expanded. DAS is designed to assist NASA programs in performing orbital debris assessments, as described in NASA s Guidelines and Assessment Procedures for Limiting Orbital Debris. The extensive upgrade of DAS was undertaken to reflect changes in the debris mitigation guidelines, to incorporate recommendations from DAS users, and to take advantage of recent software capabilities for greater user utility. DAS 2.0 includes an updated environment model and enhanced orbital propagators and reentry-survivability models. The ORDEM96 debris environment model has been replaced by ORDEM2000 in DAS 2.0, which is also designed to accept anticipated revisions to the environment definition. Numerous upgrades have also been applied to the assessment of human casualty potential due to reentering debris. Routines derived from the Object Reentry Survival Analysis Tool, Version 6 (ORSAT 6), determine which objects are assessed to survive reentry, and the resulting risk of human casualty is calculated directly based upon the orbital inclination and a future world population database. When evaluating reentry risks, the user may enter up to 200 unique hardware components for each launched object, in up to four nested levels. This last feature allows the software to more accurately model components that are exposed below the initial breakup altitude. The new DAS 2.0 provides an updated set of tools for users to assess their mission s compliance with the NASA Safety Standard and does so with a clear and easy-to-understand interface. The new native Microsoft Windows graphical user interface (GUI) is a vast improvement over the previous DOS-based interface. In the new version, functions are more-clearly laid out, and the GUI includes the standard Windows-style Help functions. The underlying routines within the DAS code are also improved.

Mapping the Substellar Mass-Luminosity Relation Down to the L/T Transition

NASA Astrophysics Data System (ADS)

Dupuy, Trent

2016-10-01

Substellar models underpin our theoretical understanding of brown dwarfs and gas-giant exoplanets, so assessing their accuracy is paramount. The past several years have seen progress in testing models thanks to a growing number of dynamical (total) masses for brown dwarf binaries determined via (relative) orbit monitoring from ground-based AO. However, the strongest tests of models require individual masses, particularly for calibrating the mass-luminosity relation. This is poorly constrained over the range of spectral types most influenced by clouds (mid-L to early-T). Given the observed prevalence of clouds in the atmospheres of directly imaged planets, testing models at such temperatures is crucial.We propose a 3-year program to obtain individual masses for a sample of 11 substellar binaries. Our proposal builds on nearly a decade of orbital monitoring from the ground to measure dynamical total masses. Our goal is thus to measure precise mass ratios, utilizing HST's unique wide-field, high-angular resolution astrometric capabilities. We will obtain WFC3-UVIS images capturing our targets and numerous reference stars so that we can measure the relative amount of orbital motion in each component to determine mass ratios. Three of our targets have I-band photocenter orbits measured at USNO and VLT and thus only require one epoch of resolved I-band imaging to unlock individual masses. We will use this first large sample of substellar individual masses to map out the mass-luminosity relation over a wide range of temperatures (1000-2000 K) including the L/T transition. This will become a touchstone sample for tests of ultracool atmospheric models in the era of JWST.

Mapping the Substellar Mass-Luminosity Relation Down to the L/T Transition

NASA Astrophysics Data System (ADS)

Dupuy, Trent

2017-08-01

Substellar models underpin our theoretical understanding of brown dwarfs and gas-giant exoplanets, so assessing their accuracy is paramount. The past several years have seen progress in testing models thanks to a growing number of dynamical (total) masses for brown dwarf binaries determined via (relative) orbit monitoring from ground-based AO. However, the strongest tests of models require individual masses, particularly for calibrating the mass-luminosity relation. This is poorly constrained over the range of spectral types most influenced by clouds (mid-L to early-T). Given the observed prevalence of clouds in the atmospheres of directly imaged planets, testing models at such temperatures is crucial.We propose a 3-year program to obtain individual masses for a sample of 11 substellar binaries. Our proposal builds on nearly a decade of orbital monitoring from the ground to measure dynamical total masses. Our goal is thus to measure precise mass ratios, utilizing HST's unique wide-field, high-angular resolution astrometric capabilities. We will obtain WFC3-UVIS images capturing our targets and numerous reference stars so that we can measure the relative amount of orbital motion in each component to determine mass ratios. Three of our targets have I-band photocenter orbits measured at USNO and VLT and thus only require one epoch of resolved I-band imaging to unlock individual masses. We will use this first large sample of substellar individual masses to map out the mass-luminosity relation over a wide range of temperatures (1000-2000 K) including the L/T transition. This will become a touchstone sample for tests of ultracool atmospheric models in the era of JWST.

Dynamics of a satellite and normalization around lagrangian points in the Neptune-Triton system

NASA Astrophysics Data System (ADS)

Yokoyama, T.; Stuchi, T. J.; Solórzano, C. R. H.; Corria, A. A.; Prado, A. F. B.; Winter, O. C.; Winter, S. M. G.; Sanchez, D. M.

Since a mission to Pluto-Charon is in progress a similar mission to Neptune-Triton system probably is just a matter of time Besides the interesting items listed in the Hammel s proposal to explore Neptune Hammel et al 2002 there are others very interesting points Triton is a very large satellite with M T M N approx 2 09 times 10 -4 where M T and M N are the masses of Triton and Neptune respectively Its current inclination with respect to Neptune s equator is about 157 345 0 This unusual high and retrograde inclination for a very large inner satellite makes this problem unique in our solar system Hammel et al 2002 also propose that a top priority in this mission should be a Neptune-Triton orbiter not just a flyby tour Therefore assuming a massless spacecraft orbiting Neptune-Triton system basically the system can be stated in terms of the classical restricted three body problem The new ingredient is the Neptune oblateness and the retrograde motion of Triton With some slight displacements the lagrangian equilibria points still exist as well as many of the properties of the classical problem In this work we first give an extensive numerical exploration in the case when the spacecraft orbits Triton considering Sun Neptune and its oblateness as disturbers In the plane bf a times bf I where bf a is the semi major axis and bf I is the inclination of the orbiter we give a plot of the stable regions where the massless can survive for thousand of years Retrograde and direct inclinations were

Velocity-gauge real-time TDDFT within a numerical atomic orbital basis set

NASA Astrophysics Data System (ADS)

Pemmaraju, C. D.; Vila, F. D.; Kas, J. J.; Sato, S. A.; Rehr, J. J.; Yabana, K.; Prendergast, David

2018-05-01

The interaction of laser fields with solid-state systems can be modeled efficiently within the velocity-gauge formalism of real-time time dependent density functional theory (RT-TDDFT). In this article, we discuss the implementation of the velocity-gauge RT-TDDFT equations for electron dynamics within a linear combination of atomic orbitals (LCAO) basis set framework. Numerical results obtained from our LCAO implementation, for the electronic response of periodic systems to both weak and intense laser fields, are compared to those obtained from established real-space grid and Full-Potential Linearized Augmented Planewave approaches. Potential applications of the LCAO based scheme in the context of extreme ultra-violet and soft X-ray spectroscopies involving core-electronic excitations are discussed.

Closed-Form and Numerically-Stable Solutions to Problems Related to the Optimal Two-Impulse Transfer Between Specified Terminal States of Keplerian Orbits

NASA Technical Reports Server (NTRS)

Senent, Juan

2011-01-01

The first part of the paper presents some closed-form solutions to the optimal two-impulse transfer between fixed position and velocity vectors on Keplerian orbits when some constraints are imposed on the magnitude of the initial and final impulses. Additionally, a numerically-stable gradient-free algorithm with guaranteed convergence is presented for the minimum delta-v two-impulse transfer. In the second part of the paper, cooperative bargaining theory is used to solve some two-impulse transfer problems when the initial and final impulses are carried by different vehicles or when the goal is to minimize the delta-v and the time-of-flight at the same time.

Numerical solution of Space Shuttle Orbiter flow field including real gas effects

NASA Technical Reports Server (NTRS)

Prabhu, D. K.; Tannehill, J. C.

1984-01-01

The hypersonic, laminar flow around the Space Shuttle Orbiter has been computed for both an ideal gas (gamma = 1.2) and equilibrium air using a real-gas, parabolized Navier-Stokes code. This code employs a generalized coordinate transformation; hence, it places no restrictions on the orientation of the solution surfaces. The initial solution in the nose region was computed using a 3-D, real-gas, time-dependent Navier-Stokes code. The thermodynamic and transport properties of equilibrium air were obtained from either approximate curve fits or a table look-up procedure. Numerical results are presented for flight conditions corresponding to the STS-3 trajectory. The computed surface pressures and convective heating rates are compared with data from the STS-3 flight.

Long term evolution of planetary systems with a terrestrial planet and a giant planet.

NASA Astrophysics Data System (ADS)

Georgakarakos, Nikolaos; Dobbs-Dixon, Ian; Way, Michael J.

2017-06-01

We study the long term orbital evolution of a terrestrial planet under the gravitational perturbations of a giant planet. In particular, we are interested in situations where the two planets are in the same plane and are relatively close. We examine both possible configurations: the giant planet orbit being either outside or inside the orbit of the smaller planet. The perturbing potential is expanded to high orders and an analytical solution of the terrestrial planetary orbit is derived. The analytical estimates are then compared against results from the numerical integration of the full equations of motion and we find that the analytical solution works reasonably well. An interesting finding is that the new analytical estimates improve greatly the predictions for the timescales of the orbital evolution of the terrestrial planet compared to an octupole order expansion.

Modeling of the Orbital Debris Environment Risks in the Past, Present, and Future

NASA Technical Reports Server (NTRS)

Matney, Mark

2016-01-01

Despite of the tireless work by space surveillance assets, much of the Earth debris environment is not easily measured or tracked. For every object that is in an orbit we can track, there are hundreds of small debris that are too small to be tracked but still large enough to damage spacecraft. In addition, even if we knew today's environment with perfect knowledge, the debris environment is dynamic and would change tomorrow. Therefore, orbital debris scientists rely on numerical modeling to understand the nature of the debris environment and its risk to space operations throughout Earth orbit and into the future. This talk will summarize the ways in which modeling complements measurements to help give us a better picture of what is occurring in Earth orbit, and helps us to better conduct current and future space operations.

Theoretical treatment of the spin-orbit coupling in the rare gas oxides NeO, ArO, KrO, and XeO

NASA Technical Reports Server (NTRS)

Langhoff, S. R.

1980-01-01

Off-diagonal spin-orbit matrix elements are calculated as a function of internuclear distance for the rare gas oxides NeO, ArO, KrO, and XeO using the full microscopic spin-orbit Hamiltonian, including all one- and two-electron integrals, and POL-CI wave functions comparable to those of Dunning and Hay (1977). A good agreement was found when comparing these results in detail with the calculations of Cohen, Wadt and Hay (1979) that utilize an effective one-electron one-center spin-orbit operator. For the rare gas oxide molecules, it is suggested that the numerical results are a more sensitive test of the wave functions (particularly to the extent of charge transfer) than the exact evaluation of all terms in the full spin-orbit operator.

Impacts of the Angular Dependence of the Solar Diffuser BRDF Degradation Factor on the SNPP VIIRS Reflective Solar Band On-Orbit Radiometric Calibration

NASA Technical Reports Server (NTRS)

Lei, Ning; Xiong, Xiaoxiong

2016-01-01

Using an onboard sunlit solar diffuser (SD) as the primary radiance source, the visible infrared imaging radiometer suite (VIIRS) on the Suomi National Polar-orbiting Partnership satellite regularly performs radiometric calibration of its reflective solar bands (RSBs). The SD bidirectional reflectance distribution function (BRDF) value decreases over time. A numerical degradation factor is used to quantify the degradation and is determined by an onboard SD stability monitor (SDSM), which observes the sun and the sunlit SD at almost the same time. We had shown previously that the BRDF degradation factor was angle-dependent. Consequently, due to that the SDSM and the RSB view the SD at very different angles relative to both the solar and the SD surface normal vectors, directly applying the BRDF degradation factor determined by the SDSM to the VIIRS RSB calibration can result in large systematic errors. We develop a phenomenological model to calculate the BRDF degradation factor for the RSB SD view from the degradation factor for the SDSM SD view. Using the yearly undulations observed in the VIIRS detector gains for the M1-M4 bands calculated with the SD BRDF degradation factor for the SDSM SD view and the difference between the VIIRS detector gains calculated from the SD and the lunar observations, we obtain the model parameter values and thus establish the relation between the BRDF degradation factors for the RSB and the SDSM SD view directions.

Capture of near-Earth objects with low-thrust propulsion and invariant manifolds

NASA Astrophysics Data System (ADS)

Tang, Gao; Jiang, Fanghua

2016-01-01

In this paper, a mission incorporating low-thrust propulsion and invariant manifolds to capture near-Earth objects (NEOs) is investigated. The initial condition has the spacecraft rendezvousing with the NEO. The mission terminates once it is inserted into a libration point orbit (LPO). The spacecraft takes advantage of stable invariant manifolds for low-energy ballistic capture. Low-thrust propulsion is employed to retrieve the joint spacecraft-asteroid system. Global optimization methods are proposed for the preliminary design. Local direct and indirect methods are applied to optimize the two-impulse transfers. Indirect methods are implemented to optimize the low-thrust trajectory and estimate the largest retrievable mass. To overcome the difficulty that arises from bang-bang control, a homotopic approach is applied to find an approximate solution. By detecting the switching moments of the bang-bang control the efficiency and accuracy of numerical integration are guaranteed. By using the homotopic approach as the initial guess the shooting function is easy to solve. The relationship between the maximum thrust and the retrieval mass is investigated. We find that both numerically and theoretically a larger thrust is preferred.

Asteroidal versus cometary meteoroid impacts on the Long Duration Exposure Facility (LDEF)

NASA Technical Reports Server (NTRS)

Zook, Herbert A.

1993-01-01

Meteoroids that enter the Earth's atmosphere at low velocities will tend to impact the apex side (that surface facing the spacecraft direction of motion) of a spacecraft at a very high rate compared to the rate with which they will impact an antapex-facing surface. This ratio--apex to antapex impact rates--will become less as meteoroid entry velocities increase. The measured ration, apex to antapex, for 500 micron diameter impact craters in 6061-T6 aluminum on LDEF seems to be about 20 from the work of the meteoroid SIG group and others, that was presented at the first LDEF symposium. Such a ratio is more consistent with the meteoroid velocity distributions derived by Erickson and by Kessler, than it is with others that have been tested. These meteoroid velocity distributions have mean entry velocities into the Earth's atmosphere of 16.5 to 16.9 km/s. Others have numerically simulated the orbital evolution of small dust grains emitted from asteroids and comets. For those asteroidal grains small enough (below about 100 microns diameter) to drift from the asteroid belt to the orbit of the Earth, under P-R and solar wind drag, without suffering collisional destruction, the following results are found: as the ascending or descending nodes cross the Earth's orbit, their orbital eccentricities and inclinations are quite low (e less than 0.3, i less than 20 deg), and their mean velocity with respect to the Earth is about 5 or 6 km/s. When gravitational acceleration of the Earth is taken into account, the corresponding mean velocities relative to the top of the Earth's atmosphere are 12 to 13 km/s. This means that, at best, these small asteroidal particles cannot comprise more than 50 percent of the particles entering the Earth's atmosphere. When gravitational focusing is considered, they cannot comprise more than a few percent of those in heliocentric orbit at 1 AU. The rest are presumably of cometary origin.

The effect of the hot oxygen corona on the interaction of the solar wind with Venus

NASA Technical Reports Server (NTRS)

Belotserkovskii, O. M.; Mitnitskii, V. IA.; Breus, T. K.; Krymskii, A. M.; Nagy, A. F.

1987-01-01

A numerical gasdynamic model, which includes the effects of mass loading of the shocked solar wind, was used to calculate the density and magnetic field variations in the magnetosheath of Venus. These calculations were carried out for conditions corresponding to a specific orbit of the Pioneer Venus Orbiter (PVO orbit 582). A comparison of the model predictions and the measured shock position, density and magnetic field values showed a reasonable agreement, indicating that a gasdynamic model that includes the effects of mass loading can be used to predict these parameters.

Space Shuttle orbiter entry heating and TPS response: STS-1 predictions and flight data

NASA Technical Reports Server (NTRS)

Ried, R. C.; Goodrich, W. D.; Li, C. P.; Scott, C. D.; Derry, S. M.; Maraia, R. J.

1982-01-01

Aerothermodynamic development flight test data from the first orbital flight test of the Space Transportation System (STS) transmitted after entry blackout is given. Engineering predictions of boundary layer transition and numerical simulations of the orbiter flow field were confirmed. The data tended to substantiate preflight predictions of surface catalysis phenomena. The thermal response of the thermal protection system was as expected. The only exception is that internal free convection was found to be significant in limiting the peak temperature of the structure in areas which do not have internal insulation.

The effect of the hot oxygen corona on the interaction of the solar wind with Venus

NASA Astrophysics Data System (ADS)

Belotserkovskii, O. M.; Breus, T. K.; Krymskii, A. M.; Mitnitskii, V. Ya.; Nagey, A. F.; Gombosi, T. I.

1987-05-01

A numerical gas dynamic model, which includes the effects of mass loading of the shocked solar wind, was used to calculate the density and magnetic field variations in the magnetosheath of Venus. These calculations were carried out for conditions corresponding to a specific orbit of the Pioneer Venus Orbiter (PVO orbit 582). A comparison of the model predictions and the measured shock position, density and magnetic field values showed a reasonable agreement, indicating that a gas dynamic model that includes the effects of mass loading can be used to predict these parameters.

Spacecraft Orbit Design in the Circular Restricted Three-Body Problem Using Higher-Dimensional Poincare Maps

DTIC Science & Technology

2013-12-01

the plane of the primary bodies. That is, motion is possible only in the x and y directions. For example, in the ...Earth-Moon planar CR3BP, the S/C path remains in the same plane as the Moon’s orbit about the Earth—more precisely, the orbit of both the Earth and...travels out of the plane of the massive primaries, in the z direction as well. Importantly, there is added complexity in the spatial

Assembly vs. direct launch of transfer vehicles

NASA Technical Reports Server (NTRS)

Katzberg, Stephen J.; Pritchard, E. Brian

1990-01-01

A top level assessment is performed of the relative impacts of on-orbit assembly of the lunar or Mars transfer vehicles versus direct launch. The objective is to identify the major option paths for the Earth-to-orbit, ETO, transportation systems. Heavy lift launch vehicles, if large enough, could reduce or eliminate on-orbit assembly. However, with every new approach, there are always counter-balancing considerations and it is the objective to begin the delineation of the necessary follow-on trade study issues.

Numerical modeling of multidimensional flow in seals and bearings used in rotating machinery

NASA Technical Reports Server (NTRS)

Hendricks, R. C.; Tam, L. T.; Przekwas, A.; Muszynska, A.; Braun, M. J.; Mullen, R. L.

1988-01-01

The rotordynamic behavior of turbomachinery is critically dependent on fluid dynamic rotor forces developed by various types of seals and bearings. The occurrence of self-excited vibrations often depends on the rotor speed and load. Misalignment and rotor wobbling motion associated with differential clearance were often attributed to stability problems. In general, the rotative character of the flowfield is a complex three dimensional system with secondary flow patterns that significantly alter the average fluid circumferential velocity. A multidimensional, nonorthogonal, body-fitted-grid fluid flow model is presented that describes the fluid dynamic forces and the secondary flow pattern development in seals and bearings. Several numerical experiments were carried out to demonstrate the characteristics of this complex flowfield. Analyses were performed by solving a conservation form of the three dimensional Navier-Stokes equations transformed to those for a rotating observer and using the general-purpose computer code PHOENICS with the assumptions that the rotor orbit is circular and that static eccentricity is zero. These assumptions have enabled a precise steady-state analysis to be used. Fluid injection from ports near the seal or bearing center increased fluid-film direct dynamic stiffness and, in some cases, significantly increased quadrature dynamic stiffness. Injection angle and velocity could be used for active rotordynamic control; for example, injection, when compared with no injection, increased direct dynamic stiffness, which is an important factor for hydrostatic bearings.

Comparison of precise orbit determination methods of zero-difference kinematic, dynamic and reduced-dynamic of GRACE-A satellite using SHORDE software

NASA Astrophysics Data System (ADS)

Li, Kai; Zhou, Xuhua; Guo, Nannan; Zhao, Gang; Xu, Kexin; Lei, Weiwei

2017-09-01

Zero-difference kinematic, dynamic and reduced-dynamic precise orbit determination (POD) are three methods to obtain the precise orbits of Low Earth Orbit satellites (LEOs) by using the on-board GPS observations. Comparing the differences between those methods have great significance to establish the mathematical model and is usefull for us to select a suitable method to determine the orbit of the satellite. Based on the zero-difference GPS carrier-phase measurements, Shanghai Astronomical Observatory (SHAO) has improved the early version of SHORDE and then developed it as an integrated software system, which can perform the POD of LEOs by using the above three methods. In order to introduce the function of the software, we take the Gravity Recovery And Climate Experiment (GRACE) on-board GPS observations in January 2008 as example, then we compute the corresponding orbits of GRACE by using the SHORDE software. In order to evaluate the accuracy, we compare the orbits with the precise orbits provided by Jet Propulsion Laboratory (JPL). The results show that: (1) If we use the dynamic POD method, and the force models are used to represent the non-conservative forces, the average accuracy of the GRACE orbit is 2.40cm, 3.91cm, 2.34cm and 5.17cm in radial (R), along-track (T), cross-track (N) and 3D directions respectively; If we use the accelerometer observation instead of non-conservative perturbation model, the average accuracy of the orbit is 1.82cm, 2.51cm, 3.48cm and 4.68cm in R, T, N and 3D directions respectively. The result shows that if we use accelerometer observation instead of the non-conservative perturbation model, the accuracy of orbit is better. (2) When we use the reduced-dynamic POD method to get the orbits, the average accuracy of the orbit is 0.80cm, 1.36cm, 2.38cm and 2.87cm in R, T, N and 3D directions respectively. This method is carried out by setting up the pseudo-stochastic pulses to absorb the errors of atmospheric drag and other perturbations. (3) If we use the kinematic POD method, the accuracy of the GRACE orbit is 2.92cm, 2.48cm, 2.76cm and 4.75cm in R, T, N and 3D directions respectively. In conclusion, it can be seen that the POD of GRACE satellite is practicable by using different strategies and methods. The orbit solution is well and stable, they all can obtain the GRACE orbits with centimeter-level precision.

Burn Delay Analysis of the Lunar Orbit Insertion for Korea Pathfinder Lunar Orbiter

NASA Astrophysics Data System (ADS)

Bae, Jonghee; Song, Young-Joo; Kim, Young-Rok; Kim, Bangyeop

2017-12-01

The first Korea lunar orbiter, Korea Pathfinder Lunar Orbiter (KPLO), has been in development since 2016. After launch, the KPLO will execute several maneuvers to enter into the lunar mission orbit, and will then perform lunar science missions for one year. Among these maneuvers, the lunar orbit insertion (LOI) is the most critical maneuver because the KPLO will experience an extreme velocity change in the presence of the Moon’s gravitational pull. However, the lunar orbiter may have a delayed LOI burn during operation due to hardware limitations and telemetry delays. This delayed burn could occur in different captured lunar orbits; in the worst case, the KPLO could fly away from the Moon. Therefore, in this study, the burn delay for the first LOI maneuver is analyzed to successfully enter the desired lunar orbit. Numerical simulations are performed to evaluate the difference between the desired and delayed lunar orbits due to a burn delay in the LOI maneuver. Based on this analysis, critical factors in the LOI maneuver, the periselene altitude and orbit period, are significantly changed and an additional delta-V in the second LOI maneuver is required as the delay burn interval increases to 10 min from the planned maneuver epoch.

Spin–orbit DFT with Analytic Gradients and Applications to Heavy Element Compounds

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

Zhang, Zhiyong

We have implemented the unrestricted DFT approach with one-electron spin–orbit operators in the massively parallel NWChem program. Also implemented is the analytic gradient in the DFT approach with spin–orbit interactions. The current capabilities include single-point calculations and geometry optimization. Vibrational frequencies can be calculated numerically from the analytically calculated gradients. The implementation is based on the spin–orbit interaction operator derived from the effective core potential approach. The exchange functionals used in the implementation are functionals derived for non-spin–orbit calculations, including GGA as well as hybrid functionals. Spin–orbit Hartree–Fock calculations can also be carried out. We have applied the spin–orbit DFTmore » methods to the Uranyl aqua complexes. We have optimized the structures and calculated the vibrational frequencies of both (UO2 2+)aq and (UO2 +)aq with and without spin–orbit effects. The effects of the spin–orbit interaction on the structures and frequencies of these two complexes are discussed. We also carried out calculations for Th2, and several low-lying electronic states are calculated. Our results indicate that, for open-shell systems, there are significant effects due to the spin–orbit effects and the electronic configurations with and without spin–orbit interactions could change due to the occupation of orbitals of larger spin–orbit interactions.« less

Earth observations taken from shuttle orbiter Columbia

NASA Image and Video Library

1995-10-26

STS073-708-089 (26 October 1995) --- As evidenced by this 70mm photograph from the Earth-orbiting Space Shuttle Columbia, international borders have become easier to see from space in recent decades. This, according to NASA scientists studying the STS-73 photo collection, is particularly true in arid and semi-arid environments. The scientists go on to cite this example of the razor-sharp vegetation boundary between southern Israel and Gaza and the Sinai. The nomadic grazing practices to the south (the lighter areas of the Sinai and Gaza, top left) have removed most of the vegetation from the desert surface. On the north side of the border, Israel uses advanced irrigation techniques in Israel, mainly "trickle irrigation" by which small amounts of water are delivered directly to plant roots. These water-saving techniques have allowed precious supplies from the Jordan River to be used on farms throughout the country. Numerous fields of dark green can be seen in this detailed view. Scientists say this redistribution of the Jordan River waters has increased the Israeli vegetation cover to densities that approach those that may have been common throughout the Mid-East in wetter early Biblical times. A small portion of the Mediterranean Sea appears top right.

Orbitals for classical arbitrary anisotropic colloidal potentials

NASA Astrophysics Data System (ADS)

Girard, Martin; Nguyen, Trung Dac; de la Cruz, Monica Olvera

2017-11-01

Coarse-grained potentials are ubiquitous in mesoscale simulations. While various methods to compute effective interactions for spherically symmetric particles exist, anisotropic interactions are seldom used, due to their complexity. Here we describe a general formulation, based on a spatial decomposition of the density fields around the particles, akin to atomic orbitals. We show that anisotropic potentials can be efficiently computed in numerical simulations using Fourier-based methods. We validate the field formulation and characterize its computational efficiency with a system of colloids that have Gaussian surface charge distributions. We also investigate the phase behavior of charged Janus colloids immersed in screened media, with screening lengths comparable to the colloid size. The system shows rich behaviors, exhibiting vapor, liquid, gel, and crystalline morphologies, depending on temperature and screening length. The crystalline phase only appears for symmetric Janus particles. For very short screening lengths, the system undergoes a direct transition from a vapor to a crystal on cooling; while, for longer screening lengths, a vapor-liquid-crystal transition is observed. The proposed formulation can be extended to model force fields that are time or orientation dependent, such as those in systems of polymer-grafted particles and magnetic colloids.

Magnitude of finite-nucleus-size effects in relativistic density functional computations of indirect NMR nuclear spin-spin coupling constants.

PubMed

Autschbach, Jochen

2009-09-14

A spherical Gaussian nuclear charge distribution model has been implemented for spin-free (scalar) and two-component (spin-orbit) relativistic density functional calculations of indirect NMR nuclear spin-spin coupling (J-coupling) constants. The finite nuclear volume effects on the hyperfine integrals are quite pronounced and as a consequence they noticeably alter coupling constants involving heavy NMR nuclei such as W, Pt, Hg, Tl, and Pb. Typically, the isotropic J-couplings are reduced in magnitude by about 10 to 15 % for couplings between one of the heaviest NMR nuclei and a light atomic ligand, and even more so for couplings between two heavy atoms. For a subset of the systems studied, viz. the Hg atom, Hg(2) (2+), and Tl--X where X=Br, I, the basis set convergence of the hyperfine integrals and the coupling constants was monitored. For the Hg atom, numerical and basis set calculations of the electron density and the 1s and 6s orbital hyperfine integrals are directly compared. The coupling anisotropies of TlBr and TlI increase by about 2 % due to finite-nucleus effects.

76 FR 61356 - Information Collection Being Submitted for Review and Approval to the Office of Management and...

Federal Register 2010, 2011, 2012, 2013, 2014

2011-10-04

... geostationary orbital arc with the positive direction pointing east, i.e., in the direction of travel of the... information: (1) In the X-Z plane, i.e., the plane of the geostationary orbit, over a range of 30 Degrees from...

Analysis of the Conformally Flat Approximation for Binary Neutron Star Initial Conditions

DOE PAGES

Suh, In-Saeng; Mathews, Grant J.; Haywood, J. Reese; ...

2017-01-09

The spatially conformally flat approximation (CFA) is a viable method to deduce initial conditions for the subsequent evolution of binary neutron stars employing the full Einstein equations. Here in this paper, we analyze the viability of the CFA for the general relativistic hydrodynamic initial conditions of binary neutron stars. We illustrate the stability of the conformally flat condition on the hydrodynamics by numerically evolving ~100 quasicircular orbits. We illustrate the use of this approximation for orbiting neutron stars in the quasicircular orbit approximation to demonstrate the equation of state dependence of these initial conditions and how they might affect themore » emergent gravitational wave frequency as the stars approach the innermost stable circular orbit.« less