Relative Motion Dynamics with Arbitrary Perturbations in the Local-Vertical Local-Horizon Reference Frame

Abstract

Accurate models for spacecraft relative dynamics are essential to the design of high-precision control and long-term estimation. In the literature, numerous analytical models have been proposed that describe, with different degrees of accuracy, the relative dynamics in presence of specific perturbations. These models however may be limited for future missions, like long-baseline formation flying, that will require analytical formulations capable of considering the influence of different perturbations at the same time, in order to meet the high-demanding mission requirements. The aim of this Note is to provide a general and flexible framework for the inclusion of arbitrary perturbations into the equations of relative motion. The framework decouples the perturbations influence from the Keplerian component of the motion, so that designers can include the perturbations of interest according to the mission scenario. In the future, the proposed framework might be used by autonomous spacecraft for real-time reconfiguration of the guidance system in response to a changed operating scenario. The inclusion of arbitrary zonal harmonics perturbations and atmospheric drag into our framework is discussed.