Optimization of Orbital Parameters of Spacecraft in the Task of Measuring the Gravitational Field of the Earth

An analytical method has been developed for the optimization of the orbital parameters of a spacecraft constellation for measuring the Earth’s gravitational field (EGF). The method is based on identifying the repeatability cycles of subsatellite tracks under unperturbed Keplerian motion, subject to the condition of an integer multiple of satellite revolutions over an integer number of nodal days. By comparing the results of the analytical and numerical approaches, a functional dependence has been obtained that allows determining the spacecraft orbit altitude for perturbed motion with an accuracy of up to 30 m. The paper considers two time scales of orbit integration in the work: a full coverage cycle (30 days) and a subcycle (7 days). For the obtained optimal configurations, full-scale integration of the orbital motion and subsequent recovery of the EGF have been performed, which made it possible to assess the influence of the orbital parameters on the accuracy of the recovered field.