Analysis of Relative Motion in Along-Track Formation of Spacecraft

Abstract

In this paper, precise position keeping of a deputy spacecraft with respect to a chief spacecraft is considered in the formation flight. Especially, the case where the deputy spacecraft is located at the certain distance from the chief spacecraft in the tangential direction is analyzed under the J2 perturbation. The relative position between the two spacecraft is affected by the J2 perturbation, and the state transition matrix of the relative position and velocity including the effects of J2 is derived. With the state transition matrix, the variation of the relative motion during the orbit period is evaluated. The initial velocity of the deputy spacecraft in terms of the Hill coordinates and the small eccentricity of the chief spacecraft orbit that alleviate the effects of J2 are obtained. Numerical studies are executed to validate the analytical results. µ R J 2 2 (J 2 = 1.0826 × 10 −3) r r (r = |r|) a e i ω Ω M E ν θ (θ = ν + ω) q 1 , q 2 (q 1 = e cos ω, q 2 = e sin ω) n c d 0 * 1 C