Estimation of gravity field harmonics in the presence of spin-axis direction error using radio tracking data.
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Lorell, J.↗
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Converting gravity bins to spherical harmonic coefficients
The gravity bin technique as originally formulated recovers the local gravity field from the bin parameters by finite differencing. The spherical harmonic coefficients of the gravity field are then computed by an orthogonal transformation of the local gravity field. The result differs from that of the traditional method. This paper discusses the difference and proposes a new algorithm to convert the bin parameters to spherical harmonic coefficients. It is shown that the new method produces the same gravity field as the traditional method and maintains the high computational efficiency of the basic gravity bin technique.
Wu, J. T.↗
Documentation of photogrammetric mission simulator program. Volume 5: Gravity recovery module
Electronic modules used to simulate lunar gravity potential recovery based on spherical harmonics gravity model
Source record↗
Venus gravity and topography: 60th degree and order model
We have combined the most recent Pioneer Venus Orbiter (PVO) and Magellan (MGN) data with the earlier 1978-1982 PVO data set to obtain a new 60th degree and order spherical harmonic gravity model and a 120th degree and order spherical harmonic topography model. Free-air gravity maps are shown over regions where the most marked improvement has been obtained (Ishtar-Terra, Alpha, Bell and Artemis). Gravity versus topography relationships are presented as correlations per degree and axes orientation.
Konopliv, A. S.↗
The implementation of two satellite programs in a microcomputer environment
This paper describes the implementation of two computer programs that predict the motion of artificial satellites. The two programs are developed in a microcomputer environment. The particular microcomputer used is an IBM AT system. The programs can predict the orbital behavior of artificial satellites under the influence of gravity harmonics up to a 21 by 21 field, luni-solar gravity, drag, and solar radiation pressure. One program uses Cowell's method and the other uses variation of parameters with a singly averaging technique. Both programs use commercially available software to post-process trajectory information and to generate graphics display. The programs reside on floppy disks and are available to the general public through NASA's Computer Software Management and Information Center (COSMIC).
Kwok, J. H.↗
The mass, gravity field, and ephemeris of Mercury
In the present gravity analysis of Mariner 10/Deep Space Network radio Doppler and range data for Mercury encounters in March 1974 and March 1975, a combined least-squares fit to the Doppler data has determined two second-degree gravity harmonics that are referred to a 2439-km equatorial radius. It is noted that the 1-sigma error limits on the gravity results encompass the possibility that harmonics other than J2 and C22 significantly differ from zero. The Deep Space Network radio range data obtained with Mariner 10 are primarily applicable to such improvements of Mercury's ephemeris as the more precise determination of perihelion precession.
Anderson, John D.↗
Estimating lithospheric properties at Atla Regio, Venus
Magellan spehrical harmonic gravity and topography models are used to estimate lithospheric properties at Alta Regio, Venus, a proposed hotspot with dynamic support from mantle plume(s). Global spherical harmonic and local representations of the gravity field share common properties in the Atla region interms of their spectral behavior over a wavelength band from approximately 2100 to approximately 700 km. The estimated free-air admittance spectrum displays a rather featureless long-wavelength portion followed by a sharp rise at wavelengths shorter than about 1000 km. This sharp rise requires significant flexural support of short-wavelength structures. The Bouguer coherence also displays a sharp drop in this wavelength band, indicating a finite flexural rigidity of the lithosphere. A simple model for lithospheric loading from above and below is introduced (D. W. Forsyth, 1985) with four parameters: f, the ratio of bottom loading to top loading; z(sub m), crustal thickness; z(sub l) depth to bottom loading source; and T(sub e) elastic lithosphere thickness. A dual-mode compensation model is introduced in which the shorter wavelengths (lambda approximately less than 1000 km) might be explained best by a predominance of top loading by the large shield volcanoes Maat Mons, Ozza Mons, and Sapas Mons, and the longer wavelengths (lambda approximately greater than 1500 km) might be explained best by a deep depth of compensation, possibly representing bottom loading by a dynamic source. A Monte Carlo inversion technique is introduced to thoroughly search out the four-space of the model parameters and to examine parameter correlation in the solutions. Venus either is a considerabe deficient in heat sources relative to Earth, or the thermal lithosphere is overthickened in response to an earlier episode of significant heat loss from the planet.
Phillips, Roger J.↗
Analysis of crustal structure of Venus utilizing residual Line-of-Sight (LOS) gravity acceleration and surface topography data. A trial of global modeling of Venus gravity field using harmonic spline method
To construct Venus' gravity disturbance field (or gravity anomaly) with the spacecraft-observer line of site (LOS) acceleration perturbation data, both a global and a local approach can be used. The global approach, e.g., spherical harmonic coefficients, and the local approach, e.g., the integral operator method, based on geodetic techniques are generally not the same, so that they must be used separately for mapping long wavelength features and short wavelength features. Harmonic spline, as an interpolation and extrapolation technique, is intrinsically flexible to both global and local mapping of a potential field. Theoretically, it preserves the information of the potential field up to the bound by sampling theorem regardless of whether it is global or local mapping, and is never bothered with truncation errors. The improvement of harmonic spline methodology for global mapping is reported. New basis functions, a singular value decomposition (SVD) based modification to Parker & Shure's numerical procedure, and preliminary results are presented.
Fang, Ming↗
An improved lunar moment of inertia determination - A proposed strategy
A strategy for determining an improved lunar moment of inertia is proposed. An improved uncertainty in the lunar inhomogeneity parameter could reduce the core density error from 4.20 gr/cu cm to 0.1 gm/cu cm for the case of a lunar density model having a 300 km core radius. The current error of 0.0025 for the lunar inhomogeneity parameter is mostly due to the uncertainties in the C20 and C22 gravity harmonics. An optimum reduction strategy for obtaining an order of magnitude improvement in the gravity estimates is based on covariance analyses of Doppler data. The long-arc reduction method is shown to provide better results than the short-arc technique, and the use of an orbit with a 7000 km semimajor axis along with certain terms of up to degree and order eight is recommended.
Ananda, M. P.↗
Gravity field improvement using global positioning system data from TOPEX/Poseidon - A covariance analysis
The TOPEX/Poseidon satellite data can be used to improve the knowledge of the earth's gravitational field. The GPS data are especially useful for improving the gravity field over the world's oceans, where the current tracking data are sparse. Using realistic scenario for processing 10 days of GPS data, a covariance analysis is performed to obtain the expected improvement to the GEM-T2 gravity field. The large amount of GPS data and the large number of parameters (1979 parameters for the gravity field, plus carrier-phase biases, etc.) required special filtering techniques for efficient solution. The gravity-bin technique is used to compute the covariance matrix associated with the spherical harmonic gravity field. The covariance analysis shows that the GPS data from one 10-day arc of TOPEX/Poseidon with no a priori constraints can resolve medium degree and order (3-26) parameters with sigmas (standard deviations) that are an order of magnitude smaller than the corresponding sigmas of GEM-T2. When the information from GEM-T2 is combined with the TOPEX/Poseidon GPS measurements, an order-of-magnitude improvement is observed in low- and medium-degree terms with significant improvements spread over a wide range of degree and order.
Bertiger, Willy I.↗
Gravity field improvement using GPS data from Topex/Poseidon - A covariance analysis
A covariance analysis is performed using a realistic scenario for processing 10 days of GPS data, to obtain the expected improvement to the GEM-T2 gravity field. The gravity bin technique has been refined to compute the covariance matrix associated with the spherical harmonic gravity field. It is shown that the GPS data from one ten-day arc of Topex/Poseidon with no a priori can improve medium degree and order (3-26) sigmas for the parameters in the GEM-T2 gravity field by more than an order of magnitude.
Bertiger, Willy I.↗
Planetary geodesy
The current known geodetic parameters of the planets and their moons are reviewed. A 3:2 spin-orbit resonance has been calculated for Mercury, a planet for which previous mass estimates are suggested to be inaccurate by 30 pct. The Pioneer Venus Orbiter data indicated a Venus diameter of 6051 km, a geoid surface highly-correlated with the surface topography, and regional gravity anomalies. Reflective mirrors on the surface and data from the Lunar Orbiter 4 have produced values for the principal polar moment of inertia homogeneity factor, the earth-moon mass ratio, a fifth degree and order spherical harmonic gravity model, the lunar acceleration, and the lunar potential Love number. The Mars gravity field is now estimated up to 12th degree and order spherical harmonics from Mariner 9 and Viking Orbiters 1 and 2, which also obtained new topographical data. New gravity fields and mass are being calculated for the Jovian and Saturnian moons. The outer planets' radii and rotational periods have recently been revised to greater accuracy. New data will be forthcoming from the Space Telescope and the planned Venus Radar Mapper.
Sjogren, W. L.↗
Flexure and the role of inplane force around coronae on Venus
Large coronae on Venus, such as Artemis and Latona, are rimmed by conspicuous trenches and associated outer rises. Sandwell and Schubert have observed that these systems resemble terrestrial subduction zones in planform and have succeeded in fitting an elastic plate bending equation to the inferred flexural topography. However, the first zero crossing bending moments required are -2.5 x 10(exp 17) N for Artemis and -5.0 x 10(exp 16) N for Latona. Since these moments are similar in magnitude to those of subducting slabs on Earth, a rollback subduction mechanism was proposed to explain the flexure around the largest coronae, although a differential thermal subsidence model is sufficient to account for the topography around some coronae. The purpose is to investigate the effect of inplane force as a possible alternative to large applied moments in producing flexure at Artemis and Latona. The close correlation of gravity to topography on Venus implies the absence of a low viscosity zone and the strong coupling of the lithosphere to mantle convection. If coronae are the surface manifestations of mantle plumes, they may be the sites of active convective stress coupling. As the upwelling reaches the lithosphere, it spreads radially outward, inducing shear tractions on the base of the plate. In addition, the hot, expanding corona may load the surrounding plate horizonally. Both the basal shear stresses and radial loading can be treated as an equivalent compressive inplane force in the mechanical lithosphere, which contributes to the bending of the outlying plate. Using a model that relates inplane force to the measured gravity anomalies, a rough value of the inplane force at Artemis was calculated. Recent Pioneer Venus spherical harmonic gravity models indicate a geoid anomaly of about 75 m over Artemis, which corresponds to an estimated inplane force on the order of -1x10(exp 13) N/m. The gravity model is unable to resolve Latona, but an inplane force of similar dimensions is assumed. The maximum possible inplane force based on the expected rheology can be constrained by using the approximate 5 K/km thermal gradient inferred from the best fit 30 km elastic plate at Artemis and Latona. For a dry olivine flow law in the upper mantle, the compressional load limit of the 60 km thick mechanical lithosphere is -4 x 10(exp 13) N/m. This value is equivalent to a load of -8 x 10(exp 13) N/m on a 30 km thick elastic plate.
Brown, C. David↗
The Mystery of the Mars North Polar Gravity-Topography Correlation(Or Lack Thereof)
Maps of moderately high resolution gravity data obtained from the Mars Global Surveyor (MGS) gravity calibration orbit campaign and high precision topography obtained from the Mars Orbiter Laser Altimeter (MOLA) experiment reveal relationships between gravity and topography in high northern latitudes of Mars. Figure 1 shows the results of a JPL spherical harmonic gravity model bandpass filtered between degrees 6 and 50 contoured over a MOLA topographic image. A positive gravity anomaly exists over the main North Polar cap, but there are at least six additional positive gravity anomalies, as well as a number of smaller negative anomalies, with no obvious correlation to topography. Additional information is contained in the original extended abstract.
Phillips, R. J.↗
Time-Variable Gravity Signal due to Extratropic Pacific Water Mass Redistribution
Using the satellite-laser-ranging (SLR) data, Cox and Chao [2002] reported the detection of a large post-1998 anomaly (in the form of a positive jump) in the time series of Earth s lowest-degree gravity harmonic 52, or the dynamic oblateness. Among several groups now examining the mass redistribution in the global geophysical fluids in search of the cause(s), we report here a temporally coinciding anomalies found in the extratropic north + south Pacific basins. Clearly seen in the leading EOFPC mode for extratropic Pacific, these anomalies occurred in sea-surface height, sea-surface temperature, and temperature- and salinity-depth profiles. We based our analysis on two different data sources: TOPEX/Poseidon altimetry, and the ECCO ocean general circulation model output assimilating T/P data. The magnitude of these changes, when converted to equivalent J2 change, appears to be a few times too small to explain the observed J2 directly. These findings, and the fact that the anomalies occurred following the strong 1997-98 El Nino, suggest strong geophysical connection of the interannual-to-decadal variation of 52 with the Pacific Decadal Oscillation (PDO) and the ultimate global-change processes that cause PDO. More work is underway, and additional independent data sources are examined, paying close attention to the fact that the J2 anomaly has been reversing back to normal since 2001. These include: (1) cryospheric contributions (melting of glaciers and ice sheets); (2) land hydrological contributions; (3) polar sea influences ( e g , via deep flow); (4) fluid flow in Earth's core; (5) time-variable gravity signals from SLR in higher harmonic degree/order, including J3,J4, (2,1), and (2,2) coefficients, considering their lower signal-to-noise ratios; (6) Earth rotation data in terms of length-of-day and polar motion.
Chao, B. F.↗
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.↗
Lunar gravitational field estimation and the effects of mismodeling upon lunar satellite orbit prediction
Lunar spherical harmonic gravity coefficients are estimated from simulated observations of a near-circular low altitude polar orbiter disturbed by lunar mascons. Lunar gravity sensing missions using earth-based nearside observations with and without satellite-based far-side observations are simulated and least squares maximum likelihood estimates are developed for spherical harmonic expansion fit models. Simulations and parameter estimations are performed by a modified version of the Smithsonian Astrophysical Observatory's Planetary Ephemeris Program. Two different lunar spacecraft mission phases are simulated to evaluate the estimated fit models. Results for predicting state covariances one orbit ahead are presented along with the state errors resulting from the mismodeled gravity field. The position errors from planning a lunar landing maneuver with a mismodeled gravity field are also presented. These simulations clearly demonstrate the need to include observations of satellite motion over the far side in estimating the lunar gravity field. The simulations also illustrate that the eighth degree and order expansions used in the simulated fits were unable to adequately model lunar mascons.
Davis, John H.↗
Repeat Ground Track Lunar Orbits in the Full-Potential Plus Third-Body Problem
A high degree and order Lunar gravitational field is superimposed on the Earth-Moon Restricted Three Body model to capture the dominating forces on a spacecraft in the vicinity of the Moon. For the synchronously rotating Moon, periodic orbits in this model map repeat ground tracks and represent higher order solutions to the frozen orbit problem. The near-circular, stable or near-stable solutions are found over a wide range of defining characteristics making them suitable for long-lifetime parking applications such as science orbits, crew exploration vehicle parking orbits, and global coverage constellation orbits. A full ephemeris is considered for selected orbits to evaluate the validity of the time-invariant, simplified model. Of the most promising results are the low-altitude families of near-circular, inclined orbits that maintain long-term stability despite the highly non-spherical Lunar gravity. The method is systematic and enables rapid design and analysis of long-life orbits around any tidally-locked celestial body with an arbitrarily high degree and order spherical harmonic gravity field. .
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