Abstract
By exploiting a direct geometrical approach, an exact and efficient analytic formulation of relative motion was presented. Using the orbital elements without imposing any particular conditions on the base or the target satellites trajectories, exact expressions for the relative motion are obtained in a closed form. This solution allows the parameterization of the relative motion manifold and offers new methods to study its geometrical and topological properties. The study is complete and it maintains a high degree of accuracy even in the presence of J2 perturbations. It is adequate for long-term prediction of bounded relative orbits.
Highlights
Due to the importance of rendezvous and docking maneuvers application between spacecrafts in presence of primary perturbing body like Earth, the study of the relative motion had concerned by many studies in the recent decades
The first use of the relative motion was by Hill[7] in the late 19th century who was studying the motion of the Moon
This paper aims to find an exact solution for the relative motion problem under the J2 perturbations
Summary
Due to the importance of rendezvous and docking maneuvers application between spacecrafts in presence of primary perturbing body like Earth, the study of the relative motion had concerned by many studies in the recent decades. The intercept problem is one in which a chase vehicle is forced in such a way that its path intersects the path of a target point (which may be occupied by another vehicle) This problem was studied by Clohessy and Wiltshire[3] in the interest of developing a guidance scheme for the rendezvous problem assuming that the target vehicle was in a circular orbit. Kelly[9] developed an optimal solution to the two impulse rendezvous problem using relative motion equations and includes the effects of eccentric orbits and gravity perturbations. This paper aims to find an exact solution for the relative motion problem under the J2 perturbations. The relative satellite motion without any restriction as to the plane of the satellite orbits as well as their eccentricity and inclination is studied
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