Analytical spacecraft relative dynamics with gravitational, drag and third-body perturbations.

There has been a growing interest in spacecraft formation flying for space science applications. Such missions will require an accurate and efficient dynamics model, on-board the flight computer, to calculate and control the desired relative motion. Hence, an analytical dynamics model which can be applied to eccentric orbits and includes perturbations can provide an increase in accuracy and efficiency. This paper develops an accurate analytical solution of relative motion between two spacecraft using classical orbital elements. The analytical solution is obtained by propagating the orbital elements forward in time, while taking into account gravitational field up to the fifth harmonic, third-body and drag secular and periodic perturbations, and calculating the relative motion in the local-vertical–local-horizontal reference frame at each time-step. The analytical solution was observed to accurately describe the relative motion when compared with a numerical simulator, yielding errors on the order of meters for separation distances on the order of hundreds of meters. • Analytical spacecraft relative dynamics • Gravitational, drag, and third-body LuniSolar perturbations • Effects of perturbations on spacecraft relative motion in LEO and HEO • Effects of Long and short periodic variations due to J 2 on spacecraft relative motion [ABSTRACT FROM AUTHOR]