Harmonic Gravity Research Articles

Comprehensive mass modeling of the Moon from spectrally correlated free‐air and terrain gravity data

A lunar crust‐to‐core mass model for the region ±64° latitude was developed using gravity components evaluated from available spherical harmonic gravity and topographic field models that include Lunar Prospector, Clementine, and earlier satellite observations. Terrain gravity effects were computed at 100‐km altitude in spherical coordinates from 1° topography (GLTM 2) by Gauss‐Legendre quadrature integration. Corresponding free‐air gravity anomalies (LP75G) were spectrally correlated with the terrain effects to differentiate the terrain‐correlated and terrain‐decorrelated free‐air components. The absence of correlation between these free‐air components was interpreted for a Moho that may involve over 120 km of relief, assuming the lunar crust was mainly compensated by its thickness variations. Lacking the strong regional gravity effects of the terrain, the terrain‐decorrelated anomalies may be interpreted for their subcrustal components on the basis of their correlation spectrum with the free‐air anomalies. Inversions of the subcrustal anomalies inferred boundary undulations for the core‐mantle, asthenosphere‐lithosphere, and middle‐upper mantle that are remarkably correlated with surface impacts. The elevated core topography revealed beneath the Procellarum basin is consistent with the uplifting effects of the Imbrium impact and the development of the great lunar hotspot. Topographic undulations inferred for the lower and middle mantle reflect the dichotomized thermal evolution of the lunar near and far sides during bombardment time. On the nearside the results support the development of relatively thinner and hotter lithosphere by mantle convection that facilitated the diapiric rise of magma and mare flooding of the basins. For the farside the results favor the development of thicker and cooler lithosphere by viscous entrainment of lower density material into the lower mantle that limited basin flooding.

A Global Solution for the Gravity Field, Rotation, Landmarks, and Ephemeris of Eros

As part of the NEAR Radio Science investigation, a global solution that includes both spherical and ellipsoidal harmonic gravity fields of Eros, Eros pole and rotation rate, Eros ephemeris, and landmark positions from the optical data was generated. This solution uses the entire one-year in orbit collection of X-band radiometric tracking (Doppler and range) from the Deep Space Network and landmark tracking observations generated from the NEAR spacecraft images of Eros. When compared to a constant density shape model, the gravity field shows a nearly homogeneous Eros. The Eros landmark solutions are in good agreement with the Eros shape model, and they reduce the center-of-mass and center-of-figure offset in the z direction to 13 m. Most of the NEAR spacecraft orbits are determined in all directions to an accuracy of several meters. The solution for the ephemeris of Eros constrains the mass of Vesta to 18.2±0.4 km 3/s 2 and reduces the uncertainty in the Earth–Moon mass ratio.

Optimal space manoeuvres in a non-Keplerian force field

In this work the problem of a spacecraft bi-impulsive transfer between two given non coplanar elliptical orbits, with minimum fuel consumption, is solved considering a non-Keplerian force field (the perturbing forces include Earth gravity harmonics and atmospheric drag). The problem is transformed in the Two Point Boundary Value Problem. It is developed and implemented a new algorithm, that uses the analytical expressions developed here. A dynamics that considered a Keplerian force field was used to produce an initial guess to solve the Two Point Boundary Value Problem. Several simulations were performed to observe the spacecraft orbital behaviour by different kind of perturbations and constraints, on a fuel consumption optimization point of view.

Transformation of spherical harmonic coefficients to ellipsoidal harmonic coefficients

Analytical expressions linking spherical harmonics gravity field expansions with ellipsoidal harmonics gravity field expansions are developed. Certain symmetries and simplifications for the transformation between the two are noted. Using the expressions, a numerical approach is developed and applied for the computation of ellipsoidal harmonic gravity coefficients using spherical harmonics coefficients as inputs. This method can be used to transform a measured spherical harmonic gravity field into an ellipsoidal harmonic gravity field for use within the Brillouin sphere of the original body. This would allow for the computation of spacecraft and natural trajectories close to the surface of an asteroid or comet using a measured gravity field.

Boundary conditions in linearized harmonic gravity

We investigate the initial-boundary value problem for linearized gravitational theory in harmonic coordinates. Rigorous techniques for hyperbolic systems are applied to establish well-posedness for various reductions of the system into a set of six wave equations. The results are used to formulate computational algorithms for Cauchy evolution in a 3-dimensional bounded domain. Numerical codes based upon these algorithms are shown to satisfy tests of robust stability for random constraint violating initial data and random boundary data; and shown to give excellent performance for the evolution of typical physical data. The results are obtained for plane boundaries as well as piecewise cubic spherical boundaries cut out of a Cartesian grid.

Determination of Shape, Gravity, and Rotational State of Asteroid 433 Eros

Prior to the Near Earth Asteroid Rendezvous (NEAR) mission, little was known about Eros except for its orbit, spin rate, and pole orientation, which could be determined from ground-based telescope observations. Radar bounce data provided a rough estimate of the shape of Eros. On December 23, 1998, after an engine misfire, the NEAR-Shoemaker spacecraft flew by Eros on a high-velocity trajectory that provided a brief glimpse of Eros and allowed for an estimate of the asteroid's pole, prime meridian, and mass. This new information, when combined with the ground-based observations, provided good a priori estimates for processing data in the orbit phase.After a one-year delay, NEAR orbit operations began when the spacecraft was successfully inserted into a 320×360 km orbit about Eros on February 14, 2000. Since that time, the NEAR spacecraft was in many different types of orbits where radiometric tracking data, optical images, and NEAR laser rangefinder (NLR) data allowed a determination of the shape, gravity, and rotational state of Eros. The NLR data, collected predominantly from the 50-km orbit, together with landmark tracking from the optical data, have been processed to determine a 24th degree and order shape model. Radiometric tracking data and optical landmark data were used in a separate orbit determination process. As part of this latter process, the spherical harmonic gravity field of Eros was primarily determined from the 10 days in the 35-km orbit. Estimates for the gravity field of Eros were made as high as degree and order 15, but the coefficients are determined relative to their uncertainty only up to degree and order 10. The differences between the measured gravity field and one determined from a constant density shape model are detected relative to their uncertainty only to degree and order 6. The offset between the center of figure and the center of mass is only about 30 m, indicating that Eros has a very uniform density (1% variation) on a large scale (35 km). Variations to degree and order 6 (about 6 km) may be partly explained by the existence of a 100-m, regolith or by small internal density variations. The best estimates for the J2000 right ascension and declination of the pole of Eros are α=11.3692±0.003° and δ=17.2273±0.006°. The rotation rate of Eros is 1639.38922±0.00015°/day, which gives a rotation period of 5.27025547 h. No wobble greater than 0.02° has been detected. Solar gravity gradient torques would introduce a wobble of at most 0.001°.

Lunar Laser Ranging: Glorious Past And A Bright Future

Lunar Laser Ranging (LLR), a part of the NASA Apollo program, has beenon-going for more than 30 years. It provides the grist for a multi-disciplinarydata analysis mill. Results exist for solid Earth sciences, geodesy and geodynamics,solar system ephemerides, terrestrial and celestial reference frames, lunar physics,general relativity and gravitational theory. Combined with other data, it treatsprecession of the Earth's spin axis, lunar induced nutation, polar motion/Earthrotation, Earth orbit obliquity to the ecliptic, intersection of the celestial equatorwith the ecliptic, luni-solar solid body tides, lunar tidal deceleration, lunar physicaland free librations, structure of the moon and energy dissipation in the lunar interior.LLR provides input to lunar surface cartography and surveying, Earth station and lunar retroreflector location and motion, mass of the Earth-moon system, lunar and terrestrial gravity harmonics and Love numbers, relativistic geodesic precession, and the equivalence principle of general relativity. With the passive nature of the reflectors and steady improvement in observing equipment and data analysis, LLR continues to provide state-of-the-art results. Gains are steady as the data-base expands. After more than 30 years, LLR remains the only active Apollo experiment. It is important to recognize examples of efficient and cost effective progress of research. LLR is just such an example.

Modeling Issues Concerning Motion of the Saturnian Satellites

A study is performed to find the minimum-order model that can achieve an accuracy of 1 km in the dynamic propagation of the Saturnian satellites over a period of four years. The need for such an investigation has risen out of recent advances in the accuracy of orbit determination techniques that are to be used in the Cassini mission. Effects such as Saturn’s rings, tides on Saturn and the satellites, gravity harmonics on Saturn and the satellites, other solar system bodies, small Saturnian satellites, coupling of the satellite attitudes with translational dynamics, and general relativity are considered. A conservative assessment of the effects that must be modeled is obtained with numerical simulation using a fixed set of initial conditions for the satellites. This simple method is shown to exaggerate the impact of new modeling effects, so a second method is employed where the initial conditions are adjusted in order to minimize the perturbations of new effects. The second method suggests that, in addition to the point mass interactions of the eight major Saturnian satellites, the minimum order model includes zonal harmonics of Saturn up through eighth order, Saturn’s rings, Janus, the asphericities of Mimas and Enceladus, and the point mass effects of the Sun and Jupiter.

An Improved 360 Degree and Order Model of Venus Topography

We present an improved 360 degree and order spherical harmonic solution for Venus' topography. The new model uses the most recent set of Venus altimetry data with spacecraft positions derived from a recent high resolution gravity model. Geometric analysis indicates that the offset between the center of mass and center of figure of Venus is about 10 times smaller than that for the Earth, the Moon, or Mars. Statistical analyses confirm that the RMS topography follows a power law over the central part of the spectrum. Compared to the previous topography model, the new model is more highly correlated with Venus' harmonic gravity field.

The sensitivity of glacial isostatic adjustment predictions to a low-viscosity layer at the base of the upper mantle

Recent inferences of mantle viscosity based on convection-related observables (long-wavelength nonhydrostatic geoid and free-air gravity harmonics) indicate the presence of a relatively thin low-viscosity region at the base of the upper mantle. We explore the sensitivity of observables associated with glacial isostatic adjustment (GIA) to the viscosity and thickness of this region. These observables include post-glacial relative sea-level (RSL) variations within previously glaciated areas and in the “far field” of the Late Pleistocene ice sheets, as well as anomalies associated with the rotational state of the planet. The latter include present-day secular variations in the geopotential harmonic J 2 (or, equivalently, variations in the rotation rate) and polar wander speed. We find, in contrast to previous suggestions, that the GIA observables (with the exception of polar wander speed) are sensitive to fine-scale low-viscosity structure at the base of the upper mantle. For example, J ̇ 2 predictions can be altered by as much as 2×10 −11 yr −1 by the inclusion of a low-viscosity zone. This signal is sufficient to significantly affect both inferences of mantle viscosity and constraints on the present-day melting of large polar ice sheets (Antarctic, Greenland) that are derived using this observable. Indeed, if a low-viscosity region exists, then models that do not include it can overestimate recent polar melting events by as much as 0.5 mm/yr of equivalent eustatic sea-level rise.

Elastic Thickness Estimates for Venus from Line of Sight Accelerations

A new method of obtaining the transfer function, or admittance,Zf, between the Fourier transforms of topography and gravity of a planet is proposed that uses the line of sight (LOS) Doppler velocities directly. The expected LOS accelerations are first calculated from the spherical harmonic coefficients of the topography, the latitude, longitude, and height of the spacecraft, and the direction of Earth viewed from the planet. The admittance can then be obtained using standard signal processing methods, by comparing the LOS acceleration calculated from the topography with the time derivative of the observed LOS Doppler velocities. This method is applied to the Magellan data from cycle 4 for Atla and shows that the short wavelength behavior of the admittance is that expected from an elastic layer whose thicknessTeis 30 ± 5 km. The main contribution to the short wavelength gravity field comes from the large volcanoes Ozza, Maat, and Sapas Montes. Comparison with admittance estimates from spherical harmonic gravity fields and from local inversions shows that these methods produce estimates ofZf(k) that do not fit those expected from a simple flexural model. TheTevalues from Beta and Ulfrun of 27.5 and 33 km are similar to that of Atla, whereas Dali (12 km) gives a smaller value. No reliable value can yet be estimated from Aphrodite, probably because the topography is poorly determined. These estimates ofTecover the same range as those from flexural modeling of topography associated with coronae.

Stress and Flexural Modeling of the Martian Lithospheric Response to Alba Patera

The martian volcano Alba Patera is surrounded by a system of graben which appears to be the result of an extensional stress applied to the region after the construction of the volcano. These faults provide a map of the stress field that created them. We used this information, as well as the recent Goddard spherical harmonic gravity model (GMM-1) and a spherical harmonic representation of the Mars Digital Elevation Model, to constrain models of: (1) the lithospheric flexure under the load of the volcano, (2) the gravitational anomaly due to the volcano, and (3) the magnitude of the extensional stress in the region. We found that elastic lithospheric thicknesses between 10 and 50 km resulted in statistically acceptable fits to the gravity and topography data. We also found that a 1.5–2 kilobar extensional regional stress in conjunction with the axisymmetric stress field of the volcanic load produced a stress field that is consistent with the observed trends of the graben.

A height‐ and time‐dependent model of polar mesosphere summer echoes

The generation of VHF radar echoes in the polar summer mesosphere is studied with a height‐ and time‐dependent model including three mechanisms: electron scavenging by microscopic ice particles created by heterogeneous nucleation on meteoric dust, formation of steep gradients in the ice particle and electron concentrations by the Kelvin effect, and reduction of the electron diffusivity by the presence of negatively charged particles. Then turbulent mixing produces a viscous convective subrange in the variance spectrum of the electron concentration, which in turn, can give rise to strong radar echoes. Based on a gravity‐wave‐perturbed model and many sensitivity tests, several conclusions are reached. Taking into account the high variability of relevant parameters, the model can predict the wide range of reflectivities measured on the northern hemisphere and indicates that the virtual absence of detectable radar echoes on the southern hemisphere is probably due to the annual variation of the meteoric mass influx and relatively high mesopause temperatures. The frequently occurring double‐layer structure of the reflectivity is characteristic of almost unperturbed rnesospheric conditions. In the presence of weak harmonic gravity waves, the inherently strong nonlinearity of the model yields steepened and breaking reflectivity structures. In agreement with observational results, the model further predicts a positive (negative) correlation between the vertical velocity variance and the reflectivity of spectrally broad (narrow) echoes. It is suggested that the frequently measured aspect sensitivity of spectrally narrow echoes results from anisotropic turbulence in the electron gas occurring if the inertial subrange is small or absent and the viscous‐convective subrange virtually adjoins the buoyancy subrange. Even under extremely favorable conditions, the calculated reflectivities at radar frequencies near 1 GHz are much weaker than measured ones, confirming an earlier result that in the UHF range, polar mesosphwre summer echoes originate from modified Thomson scattering.

Radial profile of mantle viscosity: Results from the joint inversion of convection and postglacial rebound observables

We present new inferences of the radial profile of mantle viscosity that simultaneously fit long‐wavelength free‐air gravity harmonics associated with mantle convection and a large set of decay times estimated from the postglacial uplift of sites within previously glaciated regions (Hudson Bay, Arctic Canada, and Fennoscandia). The relative sea level variation at these latter sites is constrained by age‐height pairs obtained by geological survey, rather than the subjective trends which are commonly used in glacial isostatic adjustment (GIA) studies. Our viscosity inferences are generated using two approaches. First, we adopt a relative viscosity profile which is known to provide a good fit to the free‐air gravity harmonics and determine an absolute scaling which yields a best fit to the GIA decay time constraints. Second, we perform an iterative, nonlinear, joint inversion of the two data sets. In both cases our inferred profiles are characterized by a significant increase of viscosity (∼2 orders of magnitude), with depth, to values of ∼1022 Pa s in the bottom half of the lower mantle. The new viscosity profiles are shown to satisfy constraints based on the postglacial uplift of both Fennoscandia (the classic Haskell [1935] number) and Hudson Bay which have commonly been invoked to argue for an isoviscous mantle. Furthermore, the models are used to predict a set of long‐wavelength signatures of the GIA process. These include predictions of GIA‐induced variations in (1) the length‐of‐day over the late Holocene period; (2) the Earth's precession constant and obliquity over the last 2.6 Myr; and (3) the present‐day zonal harmonics of the geopotential, Jl(l≤7). The predictions (1) and (3) bound the late Holocene (and ongoing) mass flux between the large polar ice sheets (Greenland and Antarctic) and the global oceans to small values (≤0.4 mm/yr equivalent eustatic sea level rise).

Saturn's Central Flash from the 3 July 1989 Occultation of 28 Sgr

We present observations of Saturn's central flash obtained from Palomar and McDonald Observatories during the 3 July 1989 occultation of 28 Sgr. As the star passed close to the geometric center of Saturn's shadow, the focusing of the incident starlight by the planet's atmosphere formed multiple stellar images along the limb which were detected in infrared images obtained at wavelengths of 3.9 (Palomar) and 2.1 μm (McDonald). These are the first reported observations of a central flash due to Saturn, and the first for any planet in which the signal from each stellar image could be determined separately, permitting a comparison of both intensity and position for each image with model predictions. The starlight forming the central flash was strongly modulated by passage through Saturn's rings. Four separate flashes were observed from each observatory, corresponding to the points on the limb where the starlight passed through the Cassini Division and the relatively transparent C Ring, with maximum brightnesses reaching 1-2% of the unocculted stellar intensity. The more usual brightening seen during previous central flashes as the observer crossed the caustic formed by the planet's oblate limb was not detectable in this event due to strong attenuation by the B Ring. The timing of the flashes is quite sensitive to the shape of Saturn's limb, which depends in turn on the planet's zonal gravity harmonics and on the zonal wind profile in the lower stratosphere, near the 2.5-mbar pressure level. The locations of the images along the limb, as well as the timing, shapes, and amplitudes of the individual flash light curves, are well matched by a smoothed model based on a tropospheric zonal wind profile obtained from tracking cloud features in Voyager images and the Saturn ring optical depth profile obtained from the Voyager Photopolarimeter experiment. The smoothing required to give the best match to the data exceeds that attributable to the finite angular extent of the occulted star and may be due to refractive scattering by turbulence or wave structure in Saturn's atmosphere. The detailed agreement of the models and observations is improved by assuming a uniform zonal wind speed of 40 msec -1 at 25-70° north latitude in the stratosphere, suggesting that midlatitude zonal winds on Saturn decay with height above the troposphere to the nonzero mean of local tropospheric winds. There is no evidence of significant atmospheric absorption at the observed wavelengths, which correspond to spectral regions of weak methane absorption.

Estimating Lithospheric Properties at Atla Regio, Venus

Magellan spherical harmonic gravity and topography models are used to estimate lithospheric properties at Atla 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 in terms of their spectral behavior over a wavelength band from ∼2100 to ∼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, J. Geophys. Res. 90, 12,623-12,632) with four parameters: f, the ratio of bottom loading to top loading; Z m , crustal thickness; Z l, depth to bottom loading source; and T e, elastic lithosphere thickness. No model is found that fits simultaneously the estimated free-air admittance and Bouguer coherence across the entire spectrum. A dual-mode compensation model is introduced in which the shorter wavelengths (λ ⪉ 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 (λ ⪊ 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 correlations in the solutions. It is shown that simultaneous inversion on admittance and Bouguer coherence in the short-wavelength band constrains the elastic thickness to a range of approximately 40 to 50 km. Introduction of the free-air coherence as an observable in the inversion narrows the estimates of the other three parameters ( f = 0.10 ± 0.01, Z m = 30 ± 13 km, Z l = 7 ± 5 km) and provides a solution T e = 45 ± 3 km. In the long-wavelength band, Z l is found to be about 150 km, and this is the only parameter that can be estimated robustly. Crustal thickness, Z m , is unbounded, and the solutions are degenerate in that there is no discrimination between top and bottom loading. Acceptable elastic thicknesses range from 0 to 140 km. The elastic thickness results from both wavelength bands are corroborated in the spatial domain by examining residual standard deviations for a range of T e values. The results found here are consistent with the results of Smrekar (1994) for wavelengths longer than 600 km. Values of Z l are consistent with other analyses that exclude wavelengths longer than about 2,000 km. Inclusion of wavelengths longer than about 3000 km leads to compensation depths of approximately 200 km. Moment-curvature relationships based on yield strength envelopes are used to constrain temperature gradient. Average curvature is obtained from the flexurally deformed Moho surface by Fourier transform techniques. Surface temperature gradients are obtained in the range 7-10 K km -1, depending on the strain rate adopted. The relationship between elastic thickness and temperature gradient is calibrated by comparing elastic thickness estimates of two East African hotspots with measured heat flow. The excess heat flow at the East African hotspots over the African continental mean, if applicable to Venus, can be used to show that the globally averaged heat flow on Venus must be much lower than the Earth-scaled value predicts. A thick (∼350-km) ambient thermal lithosphere, as proposed by A. B. Kucinskas and D. L. Turcotte in this issue, and interpretable from the long-wavelength depth of compensation at Atla Regio, provides an acceptable background temperature gradient. When it is added to the excess heat flow or temperature gradient, the predicted heat flow at Atla Regio is consistent with the moment-curvature results. The thermal lithosphere beneath Atla Regio may be about 100 km thick and this answer can be obtained by two independent methods: from the ambient thermal lithosphere thickness and simple elevation scaling (result dependent on long gravity wavelengths) and from the elastic thickness estimate converted to temperature gradient (result dependent on short gravity wavelengths). Either Venus is considerably 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.

Venus Spherical Harmonic Gravity Model to Degree and Order 60

The Magellan and Pioneer Venus Orbiter radiometric tracking data sets have been combined to produce a 60th degree and order spherical harmonic gravity field. The Magellan data include the high-precision X-band gravity tracking from September 1992 to May 1993 and post-aerobraking data up to January 5, 1994. Gravity models are presented from the application of Kaula's power rule for Venus and an alternative a priori method using surface accelerations. Results are given as vertical gravity acceleration at the reference surface, geoid, vertical Bouguer, and vertical isostatic maps with errors for the vertical gravity and geoid maps included. Correlation of the gravity with topography for the different models is also discussed.

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.

Study of the Lunar Core by VLBI Observations of Artificial Radio Sources on the Moon

Differential VLBI technique can measure the variation in the angular distance between two artificial radio transmitters on the Moon with an accuracy of a few centimeters. We can observe the physical librations of the Moon through this technique since rotation of the Moon changes the angular distance. The gravitational field of the Moon can also be determined by observations of the angular distance between the radio source on the Moon and that on a lunar orbiter. Calculations show that this technique can determine the amplitude of the physical librations with an accuracy of 10-5 which are one or two orders higher than those obtained by using the Apollo Lunar Surface Experiments Package in 1970's. We can estimate the density and the radius of the lunar core through accurate amplitude and period of the librations together with seismic observations. The accuracy of determination of the lunar gravity harmonics of degree 2 derivable from the VLBI observations are in the range from 10-4 to 10-6. We are developing radio transmitters which will be put on the lunar surface by hard landing from the lunar orbiter.

Gravity field improvement using global positioning system data from TOPEX/Poseidon: A covariance analysis

The TOPEX/Poseidon satellite (inclination 65°, period 113 min) is scheduled for launch in 1992 to study the world's ocean topography through precise altimetric measurements. It will also carry an experimental Global Positioning System (GPS) receiver to demonstrate precise orbit determination with GPS. Data for the GPS experiment will be collected by the on‐board receiver and a worldwide network of ground receivers. These data may also 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 a realistic scenario for processing 10 days of GPS data, we perform a covariance analysis 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.) require special filtering techniques for efficient solution. We have used the gravity bin technique introduced earlier 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.