On the recovery of geopotential coefficients using satellite-to-satellite range-rate data on a sphere

If satellite range-rate information is given continuously on an extra terrestrial sphere (S), the spherical harmonic coefficients of the gravitational potential of the Earth can be determined by direct integration of the data. An exact solution is given in the case when circular satellite orbits crosses S in all directions. A simpler acquisition of the data is achieved when the observations are restricted to polar satellite orbits. However, in this case the solutions become more complex due to attenuation. A solution to order sin Δ, where Δ is the separation angle of the two satellites, is given for the zonal harmonics. For tesseral hamonics a zero-order solution is derived. Corrections are given for observations out of S. Finally, the along track configuration of the satellite pair is compared with a radially designed satellite system (one above the other). The former is found most favourable for the recovery of geopotential coefficients.