Abstract
The tangent-impulse coplanar orbit rendezvous problem is studied based on the linear relative motion forJ2-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 withJ2perturbations is given to verify the efficiency of these proposed techniques.
Highlights
The orbital rendezvous problem is a fundamental one in aerospace engineering for human space activities
This paper studies the tangent-impulse orbital rendezvous problem between two coplanar elliptic orbits with the J2 perturbation
For the first and the second tangent impulse problems, the numerical solutions are obtained by the secant method for a single variable function
Summary
The orbital rendezvous problem is a fundamental one in aerospace engineering for human space activities. If the transfer time is assigned, the required initial velocity for the chaser can be obtained by solving Lambert’s problem [1,2,3,4]. For the orbit rendezvous problem, the flight time of the chaser and that of the target are required to be equal For this purpose, Zhang et al [10, 11] solved the tangent orbit rendezvous problem with the same terminal velocity direction and the two-impulse bitangent rendezvous problem, respectively. Based on the STM in the elliptic target orbit with the influence of the J2 perturbation [16], the required initial relative velocity vector can be obtained. The bitangent orbit indicates that it is the same solution for the tangent to initial orbit problem and the tangent to final orbit problem
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