Tangent orbital rendezvous using linear relative motion with J 2 perturbations

The tangent-impulse coplanar orbit rendezvous problem is studied based on the linear relative motion for J 2 -perturbed elliptic orbits. There are three cases: (1) only the first impulse is tangent; (2) only the second impulse is tangent; (3) both impulses are tangent. For a given initial impulse point, the first two problems can be transformed into finding all roots of a single variable function about the transfer time, which can be done by the secant method. The bitangent rendezvous problem requires the same solution for the first two problems. By considering the initial coasting time, the bitangent rendezvous solution is obtained with a difference function. A numerical example for two coplanar elliptic orbits with J 2 perturbations is given to verify the efficiency of these proposed techniques.