Linear time-varying state transition matrix for spacecraft relative dynamics on highly elliptical orbits

Abstract

Space exploration is a topic of great interest in the space community and worldwide. For instance, the race to the Lunar surface now includes not only government agencies, but also commercial entities and organizations. Such missions will require robotic spacecraft to perform formation flying, rendezvous and docking to reduce costs of the overall mission and establish space stations within Lunar orbits. Therefore, an accurate and computationally efficient dynamics model, to be used within a spacecraft’s guidance, navigation and control system, to calculate and control the desired relative motion will be required. This paper presents a new, linear time-varying, solution to spacecraft relative motion on Lunar orbits that includes solar radiation pressure, third-body, and J2 perturbations. The solution is obtained by using Hamiltonian dynamics in combination with the Peano–Baker solution for linear time-varying systems, which allows for the inclusion of short and long periodic variations of each perturbation within the dynamical model. The solution resulted in a 75% decrease in computational time when compared to a numerical simulator with the same perturbing effects.