M.Sc Thesis

M.Sc StudentGalperin Aleander
SubjectAnalytic Solutions for Optimal Orbital Transfers around
Oblate Planets
DepartmentDepartment of Aerospace Engineering
Supervisor PROF. Pinchas Gurfil
Full Thesis textFull thesis text - English Version


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 transfer between coplanar circular orbits. Three such well-known transfers are the Hohmann transfer, which is an optimal bi-impulsive transfer, the bi-elliptic tri-impulsive transfer, and the bi-parabolic transfer, which results from optimizing the bi-elliptic transfer.

These solutions were developed based on the Keplerian restricted two-body problem. They do not take into account any perturbation effects, and assume a gravitational model of a homogenous spherical planet. The omission of the perturbation effects results in a deviated target orbit, and the use of an inaccurate mathematical model results in maneuvers that are not optimized in terms of fuel cost.

In this research, the well-known Hohmann, bi-elliptic, and bi-parabolic transfers are analytically modified and extended in order to accommodate the J2 zonal harmonic, and new solutions for the optimal maneuvers are presented. The 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 orbital simulations.