Analytical spacecraft formation dynamics in eccentric orbits 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 achieves an accurate analytical solution of relative motion between two spacecrafts using each spacecraft’s 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