High precision dynamic orbit integration for spaceborne gravimetry in view of GRACE Follow-on

Future gravity missions like GRACE Follow-on and beyond will deliver low-low satellite-to-satellite ranging measurements of a much increased precision on the order of nanometers. This necessitates a re-evaluation of the processes used in gravity field determination with an eye to numerical stability and computational precision. This study investigates the computation of dynamic orbits, which are used for multiple purposes in gravity recovery. They are, for example, used in computing linearized observations for the low-low satellite-to-satellite tracking instruments. The precision at which the dynamic orbits are determined thus must surpass the precision of the ranging observations.

Dynamic orbits for GRACE were computed both in a simple simulation, where the force model was reduced to a static potential of degree and order 60, and for real observational data. Encke’s method was employed while using a novel reference trajectory determined through rigorous optimization. This reference trajectory was parametrized with equinoctial elements to minimize errors resulting from imprecision in the reference motion.

The differences in coordinates between successive iterations of orbit determination were used as a benchmark for the quality of the orbit solution. Using Encke’s method with equinoctial elements, the coordinate difference between iterations was reduced from on the order of tens of micrometers to some nanometers in the spectral range relevant to GRACE satellite-to-satellite tracking observations. The resulting dynamic orbits are self-consistent to below the expected precision of the GRACE Follow-on ranging instruments.