Bounded Satellite Relative Motion in Coplanar Three-Body Systems

What is it about?

Initializing the satellite orbit to be coplanar with a third-body's orbit renders the mean inclination and mean right ascension of the ascending node (RAAN) fixed. Applying this observation to formation flying missions, when the chief satellite orbit and the third-body orbit are coplanar, the relative dynamics have analytical solutions. In this scenario, the differential argument of perigee and differential mean anomaly do not affect long-term variations of the relative motion. However, the differential semimajor axis and differential eccentricity can induce secular drifts in the along-track direction. The differential inclination can cause secular changes in the cross-track direction, and the differential RAAN can generate periodic cross-track variations. Based on these findings, the newly-proposed boundedness condition can mitigate the growth of the along-track and the cross-track position components. Comparing to previous boundedness conditions, the newly-proposed boundedness condition, designed for the case wherein the chief satellite and the third-body orbits are coplanar, yields two additional degrees-of-freedom in the formation design. Simulation results indicate that this new boundedness condition is efficient for mitigating the increase of the averaged distance between satellites, even when the chief and the third body are not precisely coplanar.

Featured Image