Two-impulse transfer between coplanar elliptic orbits using along-track thrust

The two-body two-impulse orbit transfer problem between two coplanar elliptic orbits using only along-track thrust is studied in this paper. Both impulse vectors are constrained to be on the along-track directions at the impulse points. First, the relationship between transfer angle and final true anomaly is derived. For a given final true anomaly, the range of the transfer angle is obtained for different cases. Then, the transfer angle is solved by the secant method in its feasible range. With the transfer angle and the transfer semilatus rectum, the velocity vectors of the transfer orbit at impulse points are obtained. Two impulse points and the corresponding impulse magnitudes for a 180 transfer are also analyzed. Finally, the minimum-energy and minimum-transit-time solutions are obtained by optimizing the final true anomaly. Numerical tests demonstrate the effectiveness of the proposed method for two-impulse along-track orbit transfers. The results show that the minimum-energy transfer with two along-track impulses is close to the "true" minimum-energy transfer with two free-direction impulses.