Reducing inter-satellite drift of low Earth orbit constellations using short-periodic corrections

Constellation design theory has been studied extensively. However, analysis of longitude-dependent perturbation effects on inter-satellite distance drift has not received much attention. In addition to oblateness-related perturbations, sectoral and tesseral perturbations are non-negligible for low Earth orbits, due to their effect on inter-satellite distance evolution. This paper introduces the idea of reducing the tesseral/sectoral relative drift by including these perturbations in the short-periodic correction of the mean elements. An analytical expression of the correction is derived based on the Lie transform theory. Different from previous works, the ratio between the Earth rotation rate and the satellite’s mean motion is chosen as the small parameter in the Lie theory formulation. The independent variables of the generating-function-related partial differential equations can be reduced to a single variable when using this small parameter. Numerical simulations validate that the sectoral and tesseral effects on the inter-satellite distance drift in satellite constellations can be mitigated by using the proposed correction of the mean elements.