Precise determination of the geopotential with a low-low satellite-to-satellite tracking mission

A detailed analytical and numerical study has been performed of a low-low satellite-to-satellite tracking (SST) mission for the precise determination of the Earth's geopotential. An analytical description of perturbations on range and range rate between two low satellites due to the geopotential was developed. An analytical expression was then utilized to characterize the amplitudes and frequencies of perturbations on SST range rate. The results showed that a significant number of perturbations occurred at identical frequencies, which were linearly combined to form lumped harmonic perturbations. The number of lumped harmonic perturbations with amplitudes greater than a specified value was then compared to the number of coefficients for each order, and this comparison was used to define the information content of the SST signal. This definition was used to quantitatively compare SST range and range rate measurement types, the sensitivity to the size of the geopotential perturbations, and the effect of satellite separation. This analysis showed that SST range measurements were more sensitive to geopotential perturbations than SST range rate measurements, and the sensitivity to geopotential perturbations increased as the satellite separation was increased up to five degrees.; Extensive numerical simulations of the gravity recovery were performed using the Global Positioning System (GPS) for the orbit determination of both low satellites. GPS tracking of a single low satellite was also used to perform an initial estimate of the geopotential. The GPS gravity information was combined with gravity information derived from SST range rate and range measurements with a precision of 1 {dollar}mu{dollar}m/s and 10 {dollar}mu{dollar}m, respectively. These numerical simulations verified the results from the analytical approach and were used to explore the effect of atmospheric model errors. The effect of short period atmospheric density variations on the gravity recovery was also studied.; Numerical simulations were performed to estimate a complete geopotential to degree and order 70. The results of these simulations showed that the absolute cumulative geoid error could be reduced to less than 4 cm at degree 70. A geoid with this accuracy would allow the calculation of a sea surface topography model out to degree and order 70, without being significantly corrupted by geoid errors.