Orbit and attitude dynamics and the Goddard Trajectory Determination System
Goddard trajectory determination system, discussing attitude dynamics, data preparation, differential correction and orbit information
Siry, J. W.↗
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Nuclear charge densities in spherical and deformed nuclei: Toward precise calculations of charge radii
Precise measurements of atomic transitions affected by electron-nucleus hyperfine interactions offer sensitivity to explore basic properties of the atomic nucleus and study fundamental symmetries, including the search for new physics beyond the standard model of particle physics. Specifically, such measurements, augmented by atomic and nuclear calculations, will enable extraction of the higher-order radial moments of the charge-density distribution in spherical and deformed nuclei. The new data impose higher precision requirements on a theoretical description. The nuclear charge density is composed of the proton point distribution folded with the nucleonic charge distributions. The latter induce subtle relativistic corrections due to the coupling of nucleon magnetic moments with the nuclear spin-orbit density. Additional corrections come from the effect of center-of-mass projection. We assess the precision of nuclear charge density calculations by studying the behavior of relativistic and center-of-mass motion corrections to the second and fourth charge radial moments. Special attention has been paid to the magnetic spin-orbit density associated with the local variations of the spin-orbit current. The calculations for semimagic and open-shell nuclei are performed in the framework of self-consistent mean-field theory using quantified energy density functionals and density-dependent pairing forces. We used the general expression for the spin-orbit form factor that is valid for spherical and deformed nuclei. We studied the impact of various correction terms on the charge radii, fourth radial moments, diffraction radii, and surface thickness of spherical and deformed nuclei. The spin-orbit corrections to charge radial moments and surface thickness show strong shell fluctuations which can make an appreciable effect when aiming at high-precision predictions of isotopic shifts. The inclusion of relativistic and center-of-mass corrections impacts the quality of energy density functionals optimized to charge radii data. To establish reliable constraints on the existence of new forces from isotope shift measurements, precise calculations of nuclear charge densities of deformed nuclei are needed. The proper inclusion of the spin-orbit charge density and other correction terms is essential when aiming at extraction of subtle effects which become particularly visible in isotopic trends. It is also important when developing high-quality nuclear energy density functionals optimized using heterogeneous datasets involving absolute charge radii, differential charge radii, and charge form factor properties deduced from electron-scattering data.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Approximating Quasiparticle and Excitation Energies from Ground State Generalized Kohn–Sham Calculations
Quasiparticle energies and fundamental band gaps specifically are critical properties of molecules and materials. It was rigorously established that the generalized Kohn–Sham HOMO and LUMO orbital energies are the chemical potentials of electron removal and addition and thus good approximations to band edges and fundamental gaps from a density functional approximation (DFA) with minimal delocalization error. For other quasiparticle energies, their connection to the generalized Kohn–Sham orbital energies has not been established but remains highly interesting. We provide the comparison of experimental quasiparticle energies for many finite systems with calculations from the GW Green function and localized orbitals scaling correction (LOSC), a recently developed correction to semilocal DFAs, which has minimal delocalization error. Extensive results with over 40 systems clearly show that LOSC orbital energies achieve slightly better accuracy than the GW calculations with little dependence on the semilocal DFA, supporting the use of LOSC DFA orbital energies to predict quasiparticle energies. This also leads to the calculations of excitation energies of the N-electron systems from the ground state DFA calculations of the (N – 1)-electron systems. Findings show good performance with accuracy similar to TDDFT and the delta SCF approach for valence excitations with commonly used DFAs with or without LOSC. For Rydberg states, good accuracy was obtained only with the use of LOSC DFA. Our report highlights the pathway to quasiparticle and excitation energies from ground density functional calculations.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Evaluation of the use of occultation data in differential correction procedures for determination of the lunar orbit
Earth and sun occultation data evaluation for use in differential correction of lunar satellite orbit
OCCULTATION↗
Application of altitude control techniques for low altitude earth satellites
The applications sensors of many low altitude earth satellites designed for recording surface or atmospheric data require near zero orbital eccentricities for maximum usefulness. Coverage patterns and altitude profiles require specified values of orbit semimajor axis. Certain initial combinations of semimajor axis, eccentricity, and argument of perigee can produce a so called 'frozen orbit' and minimum altitude variation which enhances sensor coverage. This paper develops information on frozen orbits and minimum altitude variation for all inclinations, generalizing previous results. In the altitude regions where most of these satellites function (between 200 and 1000 kilometers) strong atmospheric drag effects influence the evolution of the initial orbits. Active orbital maneuver control techniques to correct evolution of orbit parameters while minimizing the frequency of maneuvers are presented. The paper presents the application of theoretical techniques for control of near frozen orbits and expands upon the methods useful for simultaneously targeting several inplane orbital parameters. The applications of these techniques are illustrated by performance results from the Atmosphere Explorer (AE-3 and -5) missions and in preflight maneuver analysis and plans for the Seasat Oceanographic Satellite.
Nickerson, K. G.↗
Improved Orbit Determination of the Cygnss Satellites and its Application to Gnss-R Ocean Altimetry
The accuracy of spaceborne ocean surface altimetry depends on precise knowledge of the altimeter satellite orbit. Previous studies of the potential utility of CYGNSS GNSS Reflectometry (GNSS-R) measurements for ocean altimetry have identified its orbit error as a limiting factor. To address this, a recent firmware upgrade to the CYGNSS satellites have enabled the downlink of additional GPS raw measurements from its navigation receiver and increased numerical precision in open-loop GNSS-R tracking information. In this paper, we present improvements to the accuracy of both the orbit determination and the ocean surface height retrievals as a result of these recent upgrades. JPL’s GipsyX software is used to process 120 days of GPS navigation measurements for one of the 8 CYGNSS satellites. Incorporating high fidelity dynamic models and antenna group delay correction, daily orbit overlaps throughout the period show mean RMS differences of 3 cm in height, 7 cm in cross-track, and 10 cm in along-track. Applying these new orbits reduced the standard deviation of retrieved surface height anomalies. When spatially averaged, the sea surface height anomalies were reduced from 1.0 m to 0.8 m. Further improvements are expected using new ionospheric corrections and re-tracking methods currently in development.
Conrad, Alex↗
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.↗
Energy Frontier Research Centers: Center for the Computational Design of Functional Layered Materials (CCDM) August 1, 2014 - July 31, 2018; Center for Complex Materials from First Principles (CCM) August 1, 2018 - July 31, 2021 (Final Report)
The mission of the DOE Energy Frontier Research Centers CCDM (2014-2018) and CCM (2018-2021) was to theoretically develop, computationally apply, and experimentally validate electronic structure methods for all materials, with a focus on the complex materials, especially layered and two-dimensional materials, strongly-correlated materials, and liquid water. This was achieved by over 200 published journal articles authored by about 17 senior investigators from physics and chemistry and from theory, computation, and experiment, plus their collaborators. In particular, the Centers confirmed the predictive power of the SCAN (strongly constrained and appropriately normed) density functional, which was constructed to satisfy 17 known exact constraints and several appropriate norms. Without being fitted to real bonded systems, and at a modest computational cost, SCAN correctly predicted covalent, ionic, metallic, hydrogen, and van der Waals bonds in many challenging materials. SCAN gave an improved description of defects in semiconductors, surface properties of metals, seven phases of ice, liquid water, liquid and supercooled silicon, subtle structural distortions in ferroelectrics, formation energies and structural predictions for solids, and critical pressures for structural phase transitions. Perhaps most remarkably, SCAN correctly described some strongly-correlated materials that were previously believed to be beyond the reach of density-functional approximations. SCAN is the only density functional that correctly predicts the band gap closing under chemical doping of the cuprate high-temperature superconducting materials. SCAN also predicts a landscape of competing stripe and magnetic phases in the cuprates. For some materials with some codes, SCAN has convergence problems that are greatly reduced by the CCM-developed r 2 SCAN, without loss of accuracy or rigor. SCAN and r 2 SCAN still make some self-interaction error, which is greatly reduced by the CCDM/ CCM-developed local orbital scaling correction (LOSC). These Centers further proved that the fundamental energy gaps of a solid from an orbital energy difference and from total energy differences are the same for a large class of generalized Kohn-Sham (GKS) functionals, including SCAN and standard hybrid functionals, and that symmetry breaking arises when a dynamic density fluctuation drops to zero frequency. The Centers identified new mechanisms for catalysis in layered materials with ions intercalated between the layers, investigated charge density waves both in model systems and in real layered materials, studied changes of band gap with the number of layers, and explored topological ultrathin films, bent nanoribbons, and defects.
08 HYDROGEN↗
Spin density and orbital optimization in open shell systems: A rational and computationally efficient proposal
The present work describes a new method to compute accurate spin densities for open shell systems. The proposed approach follows two steps: first, it provides molecular orbitals which correctly take into account the spin delocalization; second, a proper CI treatment allows to account for the spin polarization effect while keeping a restricted formalism and avoiding spin contamination. The main idea of the optimization procedure is based on the orbital relaxation of the various charge transfer determinants responsible for the spin delocalization. The algorithm is tested and compared to other existing methods on a series of organic and inorganic open shell systems. The results reported here show that the new approach (almost black-box) provides accurate spin densities at a reasonable computational cost making it suitable for a systematic study of open shell systems.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Comparison of state-interaction and spinor-representation calculations of spin-orbit coupling within exact two-component coupled-cluster theories
Here a benchmark study of state-interaction and spinor-representation calculations of spin-orbit coupling using the exact two-component Hamiltonians with atomic mean-field integrals (the X2CAMF schemes) at the equation-of-motion coupled-cluster singles and doubles level is reported. We adopt a version of the X2CAMF scheme with spin-orbit integrals correct to first order for the state-interaction calculations and a version correct to infinite order for the spinor-representation calculations. The differences between the state-interaction calculations with minimum active spaces to account for (quasi-)degeneracy and the spinor-representation calculations thus correspond to higher-order spin-orbit contributions. This state-interaction approach with scalar-relativistic effects accurately included in the reference functions and in the spin-orbit integrals is shown to exhibit robust performance for elements across the periodic table. On the other hand, the more rigorous spinor representation shows more rapid convergence with respect to the number of correlated electrons and is the preferred choice for accurate calculations for heavy elements.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Self-interaction corrections applied to Mg-porphyrin, C{sub 60}, and pentacene molecules
We have applied a recently developed method to incorporate the self-interaction correction through Fermi orbitals to Mg-porphyrin, C{sub 60}, and pentacene molecules. The Fermi-Löwdin orbitals are localized and unitarily invariant to the Kohn-Sham orbitals from which they are constructed. The self-interaction-corrected energy is obtained variationally leading to an optimum set of Fermi-Löwdin orbitals (orthonormalized Fermi orbitals) that gives the minimum energy. A Fermi orbital, by definition, is dependent on a certain point which is referred to as the descriptor position. The degree to which the initial choice of descriptor positions influences the variational approach to the minimum and the complexity of the energy landscape as a function of Fermi-orbital descriptors is examined in detail for Mg-porphyrin. The applications presented here also demonstrate that the method can be applied to larger molecular systems containing a few hundred electrons. The atomization energy of the C{sub 60} molecule within the Fermi-Löwdin-orbital self-interaction-correction approach is significantly improved compared to local density approximation in the Perdew-Wang 92 functional and generalized gradient approximation of Perdew-Burke-Ernzerhof functionals. The eigenvalues of the highest occupied molecular orbitals show qualitative improvement.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Zero CTE Glass in the Hubble Space Telescope
Orbiting high above the turbulence of the Earth's atmosphere, the Hubble Space Telescope (HST) has provided breathtaking views of astronomical objects never before seen in such detail. The steady diffraction-limited images allow this medium-size telescope to reach faint galaxies fainter than 30th stellar magnitude. Some of these galaxies are seen as early as 2 billion years after the Big Bang in a 13.7 billion year old universe. Up until recently, astronomers assumed that all of the laws of physics and astronomy applied back then as they do today. Now, using the discovery that certain supernovae are "standard candles," astronomers have found that the universe is expanding faster today than it was back then: the universe is accelerating in its expansion. The Hubble Space Telescope is a two-mirror Ritchey-Chretien telescope of 2.4m aperture in low earth orbit. The mirrors are made of Ultra Low Expansion (ULE) glass by Corning Glass Works. This material allows rapid figuring and outstanding performance in space astronomy applications. The paper describes how the primary mirror was mis-figured in manufacturing and later corrected in orbit. Outstanding astronomical images taken over the last 17 years show how the application of this new technology has advanced our knowledge of the universe. Not only has the acceleration of the expansion been discovered, the excellent imaging capability of HST has allowed gravitational lensing to become a tool to study the distribution of dark matter and dark energy in distant clusters of galaxies. The HST has touched practically every field of astronomy enabling astronomers to solve many long-standing puzzles. It will be a long time until the end of the universe when the density is near zero and all of the stars have long since evaporated. It is remarkable that humankind has found the technology and developed the ability to interpret the measurements in order to understand this dramatic age we live in.
Wood, H. John↗
The Mars Observer laser altimeter investigation
The primary objective of the Mars Observer laser altimeter (MOLA) investigation is to determine globally the topography of Mars at a level suitable for addressing problems in geology and geophysics. Secondary objectives are to characterize the 1064-nm wavelength surface reflectivity of Mars to contribute to analyses of global surface mineralogy and seasonal albedo changes, to assist in addressing problems in atmospheric circulation, and to provide geodetic control and topographic context for the assessment of possible future Mars landing sites. The principal components of MOLA are a diode-pumped, neodymium-doped yttrium aluminum garnet laser transmitter that emits 1064-nm wavelength laser pulses, a 0.5-m-diameter telescope, a silicon avalanche photodiode detector, and a time interval unit with 10-ns resolution. MOLA will provide measurements of the topography of Mars within approximately 160-m footprints and a center-to-center along-track foot print spacing of 300 m along the Mars Observer subspacecraft ground track. The elevation measurements will be quantized with 1.5 m vertical resolution before correction for orbit- and pointing induced errors. MOLA profiles will be assembled into a global 0.2 deg x 0.2 deg grid that will be referenced to Mars' center of mass with an absolute accuracy of approximately 30 m. Other data products will include a global grid of topographic gradients, corrected individual profiles, and a global 0.2 deg x 0.2 deg grid of 1064-nm surface reflectivity.
Zuber, M. T.↗
Optimized Trajectory Correction Burn Placement for NRHO Orbit Maintenance
NASA's future Artemis missions plan to utilize a near rectilinear halo orbit (NRHO) in the lunar vicinity to facilitate access to the lunar surface and place other critical assets to support human exploration. This exploration architecture requires a vehicle to remain in the NRHO for long periods of time ranging from several days, to weeks, to months, and even years. Consequently, periodic orbit maintenance burns become essential to ensure the spacecraft follows the desired reference trajectory in an efficient yet effective manner despite crew activity, navigation uncertainty, maneuver execution errors, disturbance accelerations, orbit insertion dispersions, and other system limitations. This work introduces a targeting algorithm that can be utilized to analyze a variety of targeting constraints and parameters that maximizes overall performance. Techniques associated with robust trajectory optimization are used to identify the optimized number and placement for NRHO trajectory correction (NTC) burns that accounts for the mission schedule, both a primary and backup navigation system, targeting strategies and burn plan configurations, vehicle venting, thruster selection, and integrated GN\&C performance. A notional scenario extracted from the NASA Artemis III mission is used to motivate and demonstrate these concepts and performance results.
Linear Covariance Analysis↗
A method of gravity release compensation in the optical alignment of orbiting meteorological sounding and imaging instruments
This paper describes a method developed for precompensating the front-end (telescope) optical alignment of the Imager and Sounder radiometric instruments, which will be launched as components of the GOES I - M series of meteorological satellites. To satisfy the severe pointing accuracy requirements on these instruments, their alignments must be offset in the one - G field of the laboratory, in order that they will be correct in orbit. A method was developed to make the necessary alignment offset, using a counterweight mechanism; autocollimation returns from reference mirrors on the instrument structure and supporting fixturing provided feedback for adjusting the counterweight mechanism. A series of experiments was performed to verify that these autocollimation return measurements were a good predictor of telescope line-of-sight changes; these experiments are described and their results summarized.
Wetzel, James C.↗
Improved band gaps and structural properties from Wannier–Fermi–Löwdin self-interaction corrections for periodic systems
The accurate prediction of band gaps and structural properties in periodic systems continues to be one of the central goals of electronic structure theory. However, band gaps obtained from popular exchange–correlation (XC) functionals (such as LDA and PBE) are severely underestimated partly due to the spurious self-interaction error (SIE) inherent to these functionals. In this work, we present a new formulation and implementation of Wannier function-derived Fermi–Löwdin (WFL) orbitals for correcting the SIE in periodic systems. Since our approach utilizes a variational minimization of the self-interaction energy with respect to the Wannier charge centers (WCC), it is computationally more efficient than the HSE hybrid functional and other self-interaction corrections that require a large number of transformation matrix elements. Here, calculations on several (17 in total) prototypical molecular solids, semiconductors, and wide-bandgap materials show that our WFL self-interaction correction approach gives better band gaps and bulk moduli compared to semilocal functionals, largely due to the partial removal of self-interaction errors.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Ground control points refresh for MODIS and VIIRS geolocation monitoring
The Control Point Matching (CPM) program and a set of over 1200 globally distributed ground control points (GCPs ) have been successfully used to develop more than 20 years of MODIS geolocation products. In this research, we refresh current GCP library with more than 2500 new GCPs using the latest Landsat 8 Collection 2 images. The refreshed GCPs are distributed from 56 S to 80 N latitude, with more than 2000 shoreline and 500 inland GCP chips. The size of these GCPs are extended from800*800 to 1400*1400 Landsat pixels and the CPM program correspondingly increase s t h e searching distance from 0.8 pixels to 2.5 pixels, which also extends the geolocation error measurement from +/-45 to the edge of scan at +/-55 degree in scan angle. This will allow the algorithm to catch geolocation errors that are larger than one MODIS pixel. The geolocation errors measured with the refreshed GCP library are comparable to the previous results, yet with 2-3more times of matched GCPs. The daytime Aqua ascending orbits and Terra descending orbits enable us to identify a few GCP outliers which might be due to the quality of the original Landsat images. Most importantly, the refreshed GCP library will include images from both Landsat band 4 to match with VIIRS I1, and Landsat band 6 to match with VIIRS I3. This will allow us to measure and correct on orbit band-to-band registration at both track and scan directions, which will help understanding and improving future JPSS mission’s prelaunch geometric performance.
VIIRS↗
Development of the propulsion subsystem for the Viking 75 Orbiter
The development of the Viking 75 Orbiter propulsion subsystem has been completed and qualification is under way. This development required an extension of the Mariner Mars 1971 propulsion subsystem technology to meet the Viking 75 requirements of three times the burn time and five times the number of burns. Modifications have been incorporated into the rocket engine to increase the cooling margin for the 2700-second Mars orbit insertion burn. This capability has been demonstrated in both engine firings and subsystem tests. A new surface tension device has been developed to position the propellants (N2O4 and MMH) over the tank outlets during zero-g flight. Extensive scale model testing has been conducted to prove this propellant management concept. This subsystem will provide midcourse corrections, an orbit insertion burn and 20 orbit trims for the Viking 75 Spacecraft. The Viking Project is managed by the Langley Research Center, National Aeronautics and Space Administration.
Vote, F. C.↗