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At least 469 records · Page 26

Algorithms for the Computation of Debris Risks

Determining the risks from space debris involve a number of statistical calculations. These calculations inevitably involve assumptions about geometry - including the physical geometry of orbits and the geometry of non-spherical satellites. A number of tools have been developed in NASA's Orbital Debris Program Office to handle these calculations; many of which have never been published before. These include algorithms that are used in NASA's Orbital Debris Engineering Model ORDEM 3.0, as well as other tools useful for computing orbital collision rates and ground casualty risks. This paper will present an introduction to these algorithms and the assumptions upon which they are based.

Matney, Mark↗

Algorithms for the Computation of Debris Risk

Determining the risks from space debris involve a number of statistical calculations. These calculations inevitably involve assumptions about geometry - including the physical geometry of orbits and the geometry of satellites. A number of tools have been developed in NASA’s Orbital Debris Program Office to handle these calculations; many of which have never been published before. These include algorithms that are used in NASA’s Orbital Debris Engineering Model ORDEM 3.0, as well as other tools useful for computing orbital collision rates and ground casualty risks. This paper presents an introduction to these algorithms and the assumptions upon which they are based.

Matney, Mark J.↗

Orbit Transfer Programs

Collection of computer programs developed that solve problem of transfer between noncoplanar circular orbits for spacecraft with chemical propulsion systems. Two basic programs given. First, referred to as "exact solution," gives complete, exact time histories of transfers. Second, or "approximate solution," program gives approximate information on transfer time and fuel cost but provides no detail of trajectory.

Breakwell, J. V.↗

A computer graphics system for visualizing spacecraft in orbit

To carry out unanticipated operations with resources already in space is part of the rationale for a permanently manned space station in Earth orbit. The astronauts aboard a space station will require an on-board, spatial display tool to assist the planning and rehearsal of upcoming operations. Such a tool can also help astronauts to monitor and control such operations as they occur, especially in cases where first-hand visibility is not possible. A computer graphics visualization system designed for such an application and currently implemented as part of a ground-based simulation is described. The visualization system presents to the user the spatial information available in the spacecraft's computers by drawing a dynamic picture containing the planet Earth, the Sun, a star field, and up to two spacecraft. The point of view within the picture can be controlled by the user to obtain a number of specific visualization functions. The elements of the display, the methods used to control the display's point of view, and some of the ways in which the system can be used are described.

Eyles, Don E.↗

Comparison theorems, numerical integration and satellite orbits

A comparison theorem estimating the difference between solutions of a perturbed and unperturbed equation is obtained. This is then applied to obtain error estimates in numerical integration problems, in particular, those problems involving computation of satellite orbits. The main result is a proof of the intuitive notion that the error in numerically integrating a stable equation grows less rapidly than for an unstable equation.

Stokes, A.↗

Estimating Baselines From Constrained Data On GPS Orbits

Method of processing measurements of signals received at terrestrial stations from satellites in Global Positioning System (GPS) increases precision of estimates of both orbits of GPS satellites and locations of stations, computed from measurement and orbital data. Involves network of fiducial GPS stations collocated with very-long-baseline-interferometry (VLBI) stations, for which independent VLBI determinations of baselines available. Locations of stations used to establish baselines for geodesy. Potential applications include measurements of seismic and volcanic displacements and movements of tectonic plates.

Lindqwister, Ulf J.↗

Dark matter energy exchange in stars orbiting supermassive black holes

Stars on tight orbits around the supermassive black hole at the Galactic Center pass through regions where the dark matter~(DM) density may be strongly enhanced. We compute the orbit-averaged DM-induced energy exchange for S4714 as an example. It is a star on an exceptionally close and relativistic orbit around Sagittarius~A*. For a spiked dark matter profile, the exchange reaches the stellar luminosity at $σ_{χp} \sim 10^{-36}~\mathrm{cm}^2$ for MeV-GeV masses and $σ_{χe} \sim 5\times10^{-38}~\mathrm{cm}^2$ for sub-MeV masses, opening a new annihilation-free route toward dark-star phases. These cross sections lie within the range predicted by freeze-in scenarios and are consistent with cosmic-ray--boosted and solar-reflection dark matter constraints.

Meighen-Berger, Stephan A. [Iowa U.] (ORCID:000000↗

Guidance and Control System for a Satellite Constellation

A distributed guidance and control algorithm was developed for a constellation of satellites. The system repositions satellites as required, regulates satellites to desired orbits, and prevents collisions. 1. Optimal methods are used to compute nominal transfers from orbit to orbit. 2. Satellites are regulated to maintain the desired orbits once the transfers are complete. 3. A simulator is used to predict potential collisions or near-misses. 4. Each satellite computes perturbations to its controls so as to increase any unacceptable distances of nearest approach to other objects. a. The avoidance problem is recast in a distributed and locally-linear form to arrive at a tractable solution. b. Plant matrix values are approximated via simulation at each time step. c. The Linear Quadratic Gaussian (LQG) method is used to compute perturbations to the controls that will result in increased miss distances. 5. Once all danger is passed, the satellites return to their original orbits, all the while avoiding each other as above. 6. The delta-Vs are reasonable. The controller begins maneuvers as soon as practical to minimize delta-V. 7. Despite the inclusion of trajectory simulations within the control loop, the algorithm is sufficiently fast for available satellite computer hardware. 8. The required measurement accuracies are within the capabilities of modern inertial measurement devices and modern positioning devices.

Bryson, Jonathan Lamar↗

An improved model of the Earth's gravity field - GEM-T3

An improved model of the Earth's gravitational field is developed from a combination of conventional satellite tracking, satellite altimeter measurements, and surface gravimetric data (GEM-T3). This model gives improved performance for the computation of satellite orbital effects as well as a superior representation of the geoid from that achieved in any previous Goddard Earth Model. The GEM-T3 model uses altimeter data directly to define the orbits, geoid, and dynamic height fields. Altimeter data acquired during the GEOS-3 (1975-1976), SEASAT (1978), and GEOSAT (1986-1987) missions were used to compute GEM-T3. In order to accommodate the non-gravitational signal mapped by these altimeters, spherical harmonic models of the dynamic height of the ocean surface were recovered for each mission simultaneously with the gravitational field. The tracking data utilized in the solution includes more than 1300 arcs of data encompassing 31 different satellites. The observational data base is highly dependent on SLR, but also includes TRANET Doppler, optical, S-Band average range-rate and satellite-to-satellite tracking acquired between ATS-6 and GEOS-3. The GEM-T3 model has undergone extensive error calibration.

Nerem, R. S.↗

SEAHT: A computer program for the use of intersecting arcs of altimeter data for sea surface height refinement

The SEAHT program is designed to process multiple passes of altimeter data with intersecting ground tracks, with the estimation of corrections for orbital errors to each pass such that the data has the best overall agreement at the crossover points. Orbit error for each pass is modeled as a polynomial in time, with optional orders of 0, 1, or 2. One or more passes may be constrained in the adjustment process, thus allowing passes with the best orbits to provide the overall level and orientation of the estimated sea surface heights. Intersections which disagree by more than an input edit level are not used in the error parameter estimation. In the program implementation, passes are grouped into South-North passes and North-South passes, with the North-South passes partitioned out for the estimation of orbit error parameters. Computer core utilization is thus dependent on the number of parameters estimated for the set of South-North arcs, but is independent on the number of North-South passes. Estimated corrections for each pass are applied to the data at its input data rate and an output tape is written which contains the corrected data.

Allen, C. P.↗

Efficient computation of optimal low thrust gravity perturbed orbit transfers

We have developed a new method for solving low-thrust fuel-optimal orbit transfer problems in the vicinity of a large body (planet or asteroid), considering a high-fidelity spherical harmonic gravity model. The algorithm is formulated via the indirect optimization method, leading to a two-point boundary value problem (TPBVP). We make use of a hyperbolic tangent smoothing law for performing continuation on the thrust magnitude to reduce the sharpness of the control switches in early iterations and thus promote convergence. The TPBVP is solved using the method of particular solutions (MPS) shooting method and Picard-Chebyshev numerical integration. Application of Picard-Chebyshev integration affords an avenue for increased efficiency that is not available with step-by-step integrators. We demonstrate that computing the particular solutions with only a low-fidelity force model greatly increases the efficiency of the algorithm while ultimately achieving near machine precision accuracy. A salient feature of the MPS is that it is parallelizable, and thus further speedups are available. It is also shown that, for near Earth orbits and over a small number of en-route revolutions around the Earth, only the zonal perturbation terms are required in the costate equations to obtain a solution that is accurate to machine precision and optimal to engineering precision. The proposed framework can be used for trajectory design around small asteroids and also for orbit debris rendezvous and removal tasks.

Junkins, John L.↗

Effective bond orders from two-step spin–orbit coupling approaches: The I{sub 2}, At{sub 2}, IO{sup +}, and AtO{sup +} case studies

The nature of chemical bonds in heavy main-group diatomics is discussed from the viewpoint of effective bond orders, which are computed from spin–orbit wave functions resulting from spin–orbit configuration interaction calculations. The reliability of the relativistic correlated wave functions obtained in such two-step spin–orbit coupling frameworks is assessed by benchmark studies of the spectroscopic constants with respect to either experimental data, or state-of-the-art fully relativistic correlated calculations. The I{sub 2}, At{sub 2}, IO{sup +}, and AtO{sup +} species are considered, and differences and similarities between the astatine and iodine elements are highlighted. In particular, we demonstrate that spin–orbit coupling weakens the covalent character of the bond in At{sub 2} even more than electron correlation, making the consideration of spin–orbit coupling compulsory for discussing chemical bonding in heavy (6p) main group element systems.

74 ATOMIC AND MOLECULAR PHYSICS↗

Equation of state of dense plasmas: Orbital-free molecular dynamics as the limit of quantum molecular dynamics for high-Z elements

The applicability of quantum molecular dynamics to the calculation of the equation of state of a dense plasma is limited at high temperature by computational cost. Orbital-free molecular dynamics, based on a semiclassical approximation and possibly on a gradient correction, is a simulation method available at high temperature. For a high-Z element such as lutetium, we examine how orbital-free molecular dynamics applied to the equation of state of a dense plasma can be regarded as the limit of quantum molecular dynamics at high temperature. For the normal mass density and twice the normal mass density, we show that the pressures calculated with the quantum approach converge monotonically towards those calculated with the orbital-free approach; we observe a faster convergence when the orbital-free approach includes the gradient correction. We propose a method to obtain an equation of state reproducing quantum molecular dynamics results up to high temperatures where this approach cannot be directly implemented. With the results already obtained for low-Z plasmas, the present study opens the way for reproducing the quantum molecular dynamics pressure for all elements up to high temperatures.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Trade-Space Analysis Tool for Constellations (TAT-C)

Traditionally, space missions have relied on relatively large and monolithic satellites, but in the past few years, under a changing technological and economic environment, including instrument and spacecraft miniaturization, scalable launchers, secondary launches as well as hosted payloads, there is growing interest in implementing future NASA missions as Distributed Spacecraft Missions (DSM). The objective of our project is to provide a framework that facilitates DSM Pre-Phase A investigations and optimizes DSM designs with respect to a-priori Science goals. In this first version of our Trade-space Analysis Tool for Constellations (TAT-C), we are investigating questions such as: How many spacecraft should be included in the constellation? Which design has the best costrisk value? The main goals of TAT-C are to: Handle multiple spacecraft sharing a mission objective, from SmallSats up through flagships, Explore the variables trade space for pre-defined science, cost and risk goals, and pre-defined metrics Optimize cost and performance across multiple instruments and platforms vs. one at a time.This paper describes the overall architecture of TAT-C including: a User Interface (UI) interacting with multiple users - scientists, missions designers or program managers; an Executive Driver gathering requirements from UI, then formulating Trade-space Search Requests for the Trade-space Search Iterator first with inputs from the Knowledge Base, then, in collaboration with the Orbit Coverage, Reduction Metrics, and Cost Risk modules, generating multiple potential architectures and their associated characteristics. TAT-C leverages the use of the Goddard Mission Analysis Tool (GMAT) to compute coverage and ancillary data, streamlining the computations by modeling orbits in a way that balances accuracy and performance.TAT-C current version includes uniform Walker constellations as well as Ad-Hoc constellations, and its cost model represents an aggregate model consisting of Cost Estimating Relationships (CERs) from widely accepted models. The Knowledge Base supports both analysis and exploration, and the current GUI prototype automatically generates graphics representing metrics such as average revisit time or coverage as a function of cost.

Science Data Processing↗