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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Contributions of Spherical Harmonics to Magnetic and Gravitational Fields

Gravitational forces are of cardinal importance in the dynamics of spacecraft; magnetic attractions sometime play a significant role also, as was the case with the Long Duration Exposure Facility, and as is now true for the first segment of Space Station Freedom. Both satellites depend on gravitational moment and a device known as a magnetic damper to stabilize their orientation. Magnetic fields are mathematically similar to gravitational fields in one important respect: each can be regarded as a gradient of a potential function that, in turn, can be described as an infinite series of spherical harmonics. Consequently, the two fields can be computed, in part, with quantities that need only be evaluated once, resulting in a savings of time when both fields are needed. The objective of this material is to present magnetic field and gravitational force expressions, and point out the terms that belong to both this is accomplished in Section 1 and 2. Section 3 contains the deductive reasoning with which one obtains the expressions of interest. Finally, examples in Section 4 show these equations can be used to reproduce others that arise in connection with special cases such as the magnetic field produced by a tilted dipole, and gravitational force exerted by an oblate spheroid. The mathematics are discussed in the context of terrestrial fields; however, by substituting appropriate constants, the results can be made applicable to fields belonging to other celestial bodies. The expressions presented here share the characteristics of algorithms set forth for computing gravitational force. In particular, computation is performed speedily by means of recursion formulae, and the expressions do not suffer from the shortcoming of a singularity when evaluated at points that lie on the polar axis.

Roithmayr, Carlos M.↗
NASA NTRS2019

A Joint Analysis of GPS Displacement and GRACE Geopotential Data for Simultaneous Estimation of Geocenter Motion and Gravitational Field

Gravitational potential data from GRACE are being used to study mass redistribution within and between the atmosphere, hydrosphere, cryosphere, and solid Earth. The GRACE data are made available in a reference frame with its origin at the center of mass of the Earth system (geocenter) while many other geophysical models and data sets refer to a reference frame attached to the Earth's surface. Changes in the offset between these reference frames (geocenter motion) must be accounted for when GRACE data are used to quantify surface mass changes. In this study, we developed a technique for co‐estimation of geocenter motion and gravitational potential field seamlessly from degree 1 to 90 by simultaneously inverting a set of globally‐distributed GPS displacement time series and the temporally‐varying GRACE gravity data. We found that the effect of geocenter motion was evident particularly in the GPS time series of horizontal displacements. Our estimates of geocenter motion are most consistent with the Satellite Laser Ranging (SLR) results within 1 mm in X and Z components and a submillimeter in Y component, when compared to monthly variability averaged over the period of 2003–2016. The overall magnitude of the degree‐1 (l = 1) surface mass load is estimated to be ~3 cm in equivalent water height annually migrating south‐westward from Europe (December–January) to the South Pacific (June–July). Our results also show that dense GPS network data improve water storage recovery in major river basins in the United States and Europe by contributing significantly to the recovery of higher‐degree (l ≥ ~20) geopotential coefficients.

Razeghi, Mahdiyeh↗
NASA NTRS1993

Statistics of Experiments on Cluster Formation and Transport in a Gravitational Field

Metastable state relaxation in a gravitational field is investigated in the case of non-critical binary solutions. A relaxation description is presented in terms of the time-dependent Ginzburg-Landau formalism for a non-conserved order parameter. A new ansatz for solution of the corresponding partial nonlinear stochastic differential equation is discussed. It is proved that, for the supersaturated solution under consideration, the metastable state relaxation in a gravitational field leads to formation of solute concentration gradients due to the sedimentation of subcritical solute clusters. The pure discussion of the possible methods to compare theoretical results and experimental data related to solute sedimentation in a gravitational field is presented. It is shown that in order to describe these experiments it is necessary to deal both with the value of the solute concentration gradient and with its formation rate. The stochastic nature of the sedimentation process is shown.

Izmailov, Alexander F.↗
NASA NTRS1993

GMM-1: A 50 degree and order gravitational field model for Mars

Knowledge of the gravitational field, in combination with surface topography, provides one of the principal means of inferring the internal structure of a planetary body. The highest resolution gravitational field for Mars published thus far was derived from Doppler tracking data from the Mariner 9 and Viking 1 and 2 spacecraft and is complete to degree and order 18 corresponding to a half wavelength resolution of approximately 600 km. This field, which is characterized by a spatial resolution that is slightly better than that of the highest resolution (16x16) topographic model, has been utilized extensively in analyses of the state of stress and isostatic compensation of the Martian lithosphere. However, the resolution and quality of current gravity and topographic fields are such that the origin and evolution of even the major physiographic features on Mars, such as the hemispheric dichotomy and Tharsis rise, are not well understood. We have re-analyzed the Viking and Mariner data sets and have derived a new gravitational field, which we designated GMM-1 (Goddard Mars Model-1). This model is complete to spherical harmonic degree and order 50 with a corresponding (half wavelength) spatial resolution of 200-300 km where the data permit. In contrast to previous models, GMM-1 was solved to as high degree and order as necessary to nearly exhaust the attenuated gravitational signal contained in the tracking data.

Smith, D. E.↗
NASA NTRS1995

Seasonal Variations of the Earth's Gravitational Field: An Analysis of Atmospheric Pressure, Ocean Tidal, and Surface Water Excitation

Seasonal variations in the Earth's gravitational field are investigated through the analysis of LAGEOS I satellite laser ranging measurements spanning 1984 to 1992. Global surface pressure data are analyzed; a self-consistent equilibrium ocean tide model is used to compute the effect of the gravitational field on tides. Laser ranging measurements are used to model gravitational field effects.

Laser↗
NASA NTRS1989

The gravitational field of Phobos

The external gravitational field produced by a rigid body of uniform density but irregular shape is formulated in terms of spherical harmonics. The formalism is applied to the Martian satellite Phobos. Based on a three-dimensional shape model of Phobos by Duxbury (1989), the gravitational coefficients up to degree and order 4 for a homogeneous Phobos are computed. In particular, J2 is found to be 0.105. The in-plane libration amplitude of a homogeneous Phobos is predicted to be 0.97 deg, within the rather large uncertainty of the observed value of 0.78 + or - 0.4 deg.

Chao, B. Fong↗
NASA NTRS2005

Computing Gravitational Fields of Finite-Sized Bodies

A computer program utilizes the classical theory of gravitation, implemented by means of the finite-element method, to calculate the near gravitational fields of bodies of arbitrary size, shape, and mass distribution. The program was developed for application to a spacecraft and to floating proof masses and associated equipment carried by the spacecraft for detecting gravitational waves. The program can calculate steady or time-dependent gravitational forces, moments, and gradients thereof. Bodies external to a proof mass can be moving around the proof mass and/or deformed under thermoelastic loads. An arbitrarily shaped proof mass is represented by a collection of parallelepiped elements. The gravitational force and moment acting on each parallelepiped element of a proof mass, including those attributable to the self-gravitational field of the proof mass, are computed exactly from the closed-form equation for the gravitational potential of a parallelepiped. The gravitational field of an arbitrary distribution of mass external to a proof mass can be calculated either by summing the fields of suitably many point masses or by higher-order Gauss-Legendre integration over all elements surrounding the proof mass that are part of a finite-element mesh. This computer program is compatible with more general finite-element codes, such as NASTRAN, because it is configured to read a generic input data file, containing the detailed description of the finiteelement mesh.

Quadrelli, Marco↗