In this chapter the basic equations for the calculation of orbits and trajectories are given, and the properties of the most important types of trajectories used in rendezvous missions are discussed. In sections 3.1 and 3.2 the reference frames are defined and the laws of motion in elliptic and circular orbits in the ‘orbital plane’ coordinate frame are addressed. Equations of motion, expressed in this frame, are conveniently used during launch and phasing operations. In sections 3.3 and 3.4, the trajectories between chaser and target vehicle which are used in the far and close range rendezvous approaches are discussed. They are treated as relative trajectories in the ‘local orbital frame’ of the target. Only the ideal undisturbed trajectories are looked at in this chapter, and the necessary velocity changes, or continuous forces to be applied and the resulting position changes, are derived for ideal cases. The major sources of trajectory disturbances are addressed in chapter 4.

Reference frames

The purpose of this section is to define the coordinate frames used in this book for the description of the orbital motion, for absolute and relative trajectory and attitude motions and for the relations of these motions to geometric features on the spacecraft. Each frame Fi is defined by its origin Oi and a set of three orthogonal vectors a1, a2, a3.