Formation flying: Accommodating non-linearity and eccentricity perturbations

Understanding the dynamics of spacecraft relative motion is of importance for rendezvous and formation flying. Bounded relative motion is of interest to the formation flying problem. In particular, the circular projection relative orbit and the circular orbit have been identified suitable for various missions. Both these circular orbit solutions are natural to the unperturbed linearized relative orbit dynamics, for a circular reference orbit. In the presence of non-linearity and eccentricity of the reference orbit, the initial conditions have to be corrected to obtain bounded relative motion. The objective of this paper is to study the effect of non-linearity and eccentricity on the breakdown of Hill's solutions. The paper further relates these initial condition corrections to the period matching constraint required for bounded relative motion. It also studies the effect of non-linearity and eccentricity on various satellites in a constellation as a function of their phase angle. A perturbation solution is presented for bounded relative motion, using eccentricity of the reference orbit and another small parameter, characterizing the quadratic gravitational effects.

Formation flying: Accommodating non-linearity and eccentricity perturbations Conference Paper