Some Numerical Comparisons of Three-body Trajectories with Patched Two-body Trajectories for Low Thrust Rockets

The n-body problem for low-thrust vehicles with optimal thrust control is formulated for the case of constant thrust with coast. A successive two-body approximation to the n-body problem is also developed under the assumption of tangential thrust during the planetocentric leg. This approximation involves one arbitrary parameter the planetocentric radius at the patch point whose best value can be determined by comparison with n-body solutions. Numerical solutions of several three-body problems indicate that the patch radius should be about 300 Earth radii for either a circular or a parabolic initial Earth orbit.