Orbit design for a future geodetic satellite and gravity field recovery

Spherical geodetic satellites tracked by satellite laser ranging (SLR) stations provide indispensable scientific products that cannot be replaced by other sources. For studying the time-variable gravity field, two low-degree coefficients C₂₀ and C₃₀ derived from GRACE and GRACE Follow-On missions are replaced by the values derived from SLR tracking of geodetic satellites, such as LAGEOS-1/2, LARES-1/2, Starlette, Stella, and Ajisai. The subset of these satellites is used to derive the geocenter motion which is fundamental in the realization of the origin of the terrestrial reference frames. LAGEOS satellites provide the most accurate standard gravitational product GM of the Earth. In this study, we use the Kaula theorem of gravitational perturbations to find the best possible satellite height, inclination, and eccentricity for a future geodetic satellite to maximize orbit sensitivity in terms of the recovery of low-degree gravity field coefficients, geocenter, and GM. We also derive the common station-satellite visibility-coverability coefficient as a function of the inclination angle and satellite height. We found that the best inclination for a future geodetic satellite is 35°–45° or 135°–145° with a height of about 1500–1700 km to support future GRACE/MAGIC missions with C₂₀ and C₃₀. For a better geocenter recovery and derivation of the standard gravitational product, the preferable height is 2300–3500 km. Unfortunately, none of the existing geodetic satellites has the optimum height and inclination angle for deriving GM, geocenter, and C₂₀ because there are no spherical geodetic satellites at the heights between 1500 (Ajisai and LARES-1) and 5800 km (LAGEOS-1/2, LARES-2).