Modeling and Analysis of the Bounds of Periodical Satellite Relative Motion

Abstract

The precise analytic bounds of periodical satellite relative motion are obtained in this paper. To explore the bounds easily, a set of algebraic relative motion equations are applied. In these newly developed equations, the tangent value of half the true anomaly is regarded as a restated independent variable. The upper and lower bounds of the coordinates in the leader local-vertical/local-horizontal frame are found by solving the partial derivatives of the coordinates with respect to the restated independent variable. These bounds are expressed as functions of the leader’s orbital elements and the orbital element differences of the follower with respect to the leader. The bounds’ variation with differential orbital elements is further analyzed, in which some interesting phenomena are discussed. The bounds of the intersatellite separation are also studied. It has been found that there are at most four extreme value points in the intersatellite separation in most cases. In some degenerate cases, there may be two or zero extreme value points for the intersatellite separation. A few of examples are also given to test the theoretical analysis. Some potential applications, like formation configuration design and optimal control, are discussed too. It shows that the bounds theory in this paper can be used effectively in many real applications.