Relative motion of orbiting bodies

Abstract. A problem of relative motion of orbiting bodies is investigated on the example of the free motion of any body ejected from the orbital station that stays in a circular orbit around the earth. An elementary approach is illustrated by a simulation computer program and supported by a mathematical treatment based on approximate differential equations of the relative orbital motion. 1. Relative motion of bodies in space orbits—an introductory approach Let two satellites orbit the earth. We know that their passive orbital motion obeys Kepler’s laws. But how does one of them move relative to the other? This relative motion is important, say, for the spacecraft docking in orbit. If two satellites are brought together but have a (small) nonzero relative velocity, they will drift apart nonrectilinearly. In unusual conditions of the orbital flight, navigation is quite different from what we are used to here on the earth, and our intuition fails us. The study of the relative motion of the spacecraft reveals many extraordinary features that are hard to reconcile with common sense and our everyday experience. In this paper we discuss the problem of passive relative motion of orbiting bodie