The Use of Resonant Orbits in Satellite Geodesy: A Review

Abstract

Dynamic resonance, arising from commensurate (orbital or rotational) periods of satellites or planets with each other, has been a strong force in the development of the solar system. The repetition of conditions over the commensurate periods can result in amplified long-term changes in the positions of the bodies involved. Such resonant phenomena driven by the commensurability between the mean motion of certain artificial Earth satellites and the Earth’s rotation originally contributed to the evaluation and assessment of the Stokes parameters (harmonic geopotential coefficients) that specify the Earth’s gravitational field. The technique constrains linear combinations of the harmonic coefficients that are of relevant resonant order (lumped coefficients). The attraction of the method eventually dwindled, but the very accurate orbits of CHAMP and GRACE have recently led to more general insights for commensurate orbits applied to satellite geodesy involving the best resolution for all coefficients, not just resonant ones. From the GRACE mission, we learnt how to explain and predict temporary decreases in the resolution and accuracy of derived geopotential parameters, due to passages through low-order commensurabilities, which lead to low-density ground-track patterns. For GOCE we suggest how to change a repeat orbit height slightly, to achieve the best feasible recovery of the field parameters derived from on-board gradiometric measurements by direct inversion from the measurements to the harmonic geopotential coefficients, not by the way of lumped coefficients. For orbiters of Mars, we have suggestions which orbits should be avoided. The slow rotation of Venus results in dense ground-tracks and excellent gravitational recovery for almost all orbiters.