Closed-form solutions for optimal orbital transfers around oblate planets

Optimal spacecraft orbit control has been the subject of extensive research, which resulted in solutions for optimal orbit transfers. A common orbital maneuver problem is the fuel-optimal impulsive transfer between coplanar circular orbits. Three such well-known transfers are the Hohmann transfer, which is an optimal biimpulsive transfer, the bi-elliptic tri-impulsive transfer, and the bi-parabolic transfer. These solutions were developed based on the Keplerian restricted two-body problem. However, the omission of perturbations results in deviated target orbits and leads to maneuvers that are not actually fuel-optimal. In this paper, the well-known Hohmann, bi-elliptic, and bi-parabolic transfers are modified to accommodate the J₂ zonal harmonic, and new closed-form solutions for the optimal maneuvers are presented. An improvement in maneuver precision is obtained by using an analytical model based on closed-form solutions of motion in the equatorial plane under the effect of J₂. The performance improvement is validated using high-fidelity simulations, which include a myriad of orbital perturbations.