Development and analysis of a high fidelity linearized J(2) model for satellite formation flying

Abstract

With the recent flurry of research on satellite formation flying, a need has become apparent for a set of linearized equations of relative motion that capture the effect of the J2 geopotential disturbance force. Typically, Hill's linearized equations of relative motion have been used for this analysis, but they fail to capture the effect of the J2 disturbance force on a satellite cluster. In this paper, a new set of constant coefficient, linearized differential equations of motion is derived. These equations are similar in form to Hill's equations, but they capture the effects of the J2 disturbance force. A numerical simulator is employed to check the fidelity of the equations. It is shown that with the appropriate initial conditions, the new lin earized equations of motion have periodic errors (on the order of centimeters) that do not grow in time. The new linearized equations of motion also allow for insight into the effects of the J2 disturbance on a satellite cluster. This includes 'tumbling', the period of the relative orbit, and satellite separation due to differential J2 effects. Overall, a new high fidelity set of linearized equations are produced that are well suited to model satellite relative motion in the presence of the J2 disturbance force.