Averaged Relative Motion and Applications to Formation Flight Near Perturbed Orbits

DOI: 10.2514/1.30620 This paper presents expressions for describing averaged relative motion between two satellites in neighboring orbits around an oblate planet. The theory assumes small relative distances between the satellites, but is uniformly valid for all elliptic orbits as well as the special case of a circular reference orbit by the use of nonsingular orbital elements. These expressions are useful when the short-periodic variations in relative position and velocity are of limited interest and, instead, the time-averaged behavior of the states is sought. The averaged expressions also provide insight into the effects of an oblate planet on bounded relative motion. For example, a bias term due to oblateness effects, hitherto unreported, has been identified in the radial position, which can be accounted for in the reference trajectory. Application of these expressions is shown in the derivation of an analytical filter that removes short-periodic variations in relative states without the use of tuned numerical filters, one for each frequency of interest,whicharenormallyusedfordisturbanceaccommodationincontrolsystemdesign.Theuseofthisanalytical filter is demonstrated for formation keeping on a prescribed relative trajectory.