Geometric Theory of Optimum Disorbit Problems

This paper presents the general solutions of the problem of optimally disorbiting a vehicle initially in an elliptical orbit. A vehicle is initially moving along an elliptical orbit about a spherical planet with center at. The problem is to bring the vehicle along an optimal trajectory (in the sense of minimum fuel consumption) which finally intersects the top of the sensible atmosphere of the central planet. The top of the sensible atmosphere is assumed to form a sphere of radius R and center 0, enclosing the planet, and the motion is assumed to be planar. Several sub-classes of the problem will be considered, namely when the entry angle is given, or the entry speed is given or both the entry angle and the entry speed are pre-assigned, etc. These constraints are dictated by the safe recovery of the vehicle since the heating and deceleration during the re-entry portion of the trajectory depends on the entry angle and the entry speed.