Gravity estimation from STAGE, a Satellite‐to‐Satellite Tracking Mission

Abstract

An analysis was performed to determine the accuracy of estimating gravity anomalies using satellite-to-satellite tracking between the Space Transportation System (NASA's space shuttle) and the constellation of GPS satellites (STAGE: Shuttle-GPS Tracking for Anomalous Gravitation Estimation). Second time derivatives of the observed ranges, obtained from carrier phase measurements, between the low and high satellites provide in situ line-of-sight components of gravitation, as long as on-board accelerometers are used to correct for the nongravitational signals. Absolute (nondifferential), single-difference, and double-difference modes of tracking the GPS satellites were considered in the analysis, which showed that the last yields the highest gravity estimation accuracy. With instrumentation already (or soon to be) available, it is anticipated that the gravitational acceleration at altitude can be measured to an accuracy of about 0.3 mGal (1 mGA1 = 10-Sm/s 2 -• 1 tag) for an integration time of 60 s. Double-difference acceleration data collected by the shuttle at 300 km altitude could, depending on mission duration and data processing techniques, yield estimates of 2ø-mean gravity anomalies on the Earth's surface to an accuracy of about 5 mGal. Accuracy in lø-mean anomalies of about 4-5 mGal would be achievable using a free-flyer at 160 km altitude and assuming a potentially feasible measurement accuracy of 0.1 mGal (30 s integration time). Paper number 90JB00573. 0148-0227/90/90JB-00573505.00 mode [Kaula, 1970] where one satellite in high orbit tracks a low-altitude satellite. Compared to the low-low mode, it has the disadvantage that global coverage of high resolution requires up to twice as much time on account of the data gaps created when the Earth prevents intervisibility of the two satellites. The advantages of this concept are that the high satellite is virtually (atmospheric) drag free and tracking can be done with fewer ground stations. Tracking the low satellite is still a problem unless it can be tracked by a satellite navigation system (see below). The European Space Agency (ESA) recently studied the possibility of tracking a GRM-type satellite with the positioning satellite, called POPSAT [Reigber et al., 1987]. The apparent demise of GRM has created a temporary vacuum in efforts to map the gravity field globally. Satellite gravity gradiometer missions are being initiated (ESA's Aristoteles [Benz et al., 1988] and NASA's Superconducting Gravity Gradiometer Mission (SGGM) [Morgan and Paik, 1988]), but the technology required to achieve the necessary high precision (10 -• to 10 -13 S -2) in gravity gradient measurements at satellite altitude is still unproven. To fill the void, the U.S. Air Force has begun an earnest investigation of using the Global Position System (GPS) for high-low satellite-to-satellite tracking [Upadhyay et al., 1989] where the motivation was the possibility of obtaining reasonable accuracies for gravity model improvement with minimal cost. High-low tracking using GPS was also sugge...

Gravimetry and Gravity Field Models

“…Upadhyay et al [1989b] expanded this feasibility study with analyses of on‐orbit calibration of accelerometers and the on‐orbit transfer of alignment between experiment IMU (inertial measurement unit) and Shuttle IMU. Jekeli and Upadhyay [1990] performed a thorough analysis to predict the accuracy obtainable from such a satellite‐to‐satellite tracking mission. It was estimated that 2°x2° mean gravity anomalies can be recovered to an accuracy of 5 mgal.…”

“… Parker and Zumberge [1989] used ideal‐body analyses to show that results from the various geophysical experiments could be explained by unmodeled crustal densities; results of the tower experiment were thought to be due to unmodeled densities within 2 km of tower. However, a reanalysis of the experiment by Jekeli et al [1990] showed that the discrepancy was attributable to neglected topography mostly beyond 2 km from the tower and concluded that gravity behaves according to Newtonian law to an accuracy of several tens of microgals. Other tower experiments followed.…”

Satellite Positioning

“…Moreover, this combination permits (at least in a post‐mission analysis) the separation of the full gravity vector from inertial and rotational accelerations, making a practical proposition of vector gravimetry: the simultaneous determination of gravity anomalies and deflections of the vertical, which in turn can be used to calculate geoid profiles by simple integration along the line traversed by a vehicle thus instrumented [Colombo, 1990c]. In space applications, Jekeli [1988], Upadhyay et al [1989], and Jekeli and Upadhyay [1990] describe the proposed STAGE experiment, where a GPS receiver would be installed in the Space Shuttle to map gravity from low altitudes, and in which an inertial navigation unit would be needed to separate gravitation from the forces of aerodynamic drag and solar radiation pressure.…”

Position and velocity perturbations for the determination of geopotential from space geodetic measurements

“…Although the orbit energy-based approach was first proposed by Wolff (1969) for direct measurement of the Earth's gravity field and has since been substantially investigated (see, e.g., Douglas et al 1980;Ilk 1983Ilk , 1986Jekeli and Upadhyay 1990;Rowlands et al 2002), Jekeli (1999) demonstrated that the naive version of Wolff's SST scheme is too simplified and can hardly be applicable to process real SST data. Jekeli (1999) then proposed a fully functional version of SST to recover the Earth's gravity field.…”