Analytical Framework for Precise Relative Motion in Low Earth Orbits

摘要

This work presents a practical and efficient analytical framework for the precise modeling of the relative motion inlow Earth orbits. Developed to support the design and verification of relative guidance navigation and controlalgorithms devoted to spacecraft rendezvous for active debris removal applications, only the orbital perturbation dueto nonspherically symmetric mass distribution is considered. The relative motion is modeled in mean relative orbitalelements, revisiting the available formulations to include the first-order expansion of the effects due to any even zonalharmonics and the second-order expansion of the unperturbed and J2 terms. Mean/osculating orbital elementconversions are obtained by merging a second-order Hamiltonian approach applied to the J2 problem with theKaula linear perturbation method for the remaining terms of the geopotential. The paper describes the main buildingblocks of the framework as well as their interfaces because the key aspect to achieve precision is to set up a fullyconsistent environment. The results show the achievable accuracy under realistic operational conditions for possibleguidance and navigation applications.