Determination of Initial Conditions for Satellite Formation Flying in Elliptical Orbits

Abstract

The initial conditions that generate bounded motion in eccentric reference orbit are determined for satellite formation flying. Because Hill's equations cannot describe the relative motion between two satellites in eccentric orbit, a new relative dynamics utilizing the nonlinearity and eccentricity correction for Hill's initial conditions is implemented. The constraint that matches angular rates of chief and deputy satellites is used to obtain the bounded motion between them. The constraint can be applied to satellite formation motions in eccentric orbit, since it implicates J2 perturbation due to the central body's aspherical gravitational forces. The periodic bounded motions are analyzed for the orbit with the eccentricity of less than 0.05 and about 0.5 km relative distance between chief and deputy satellites. It is mainly illustrated that the satellite formations in small eccentric orbits can have bounded motions; consequently, the formation can be kept by matching angular rates of the satellites. These results demonstrate an useful method that reduces the cost for operating satellites by providing effective initial conditions for satellite formation flying in eccentric orbit.

Keywords

• satellite formation flying
• relative bounded motion