Mathematical Procedures for the Non-Coplanar Tangential Transfers between Circular Orbits

To transfer a satellite or a spacecraft from a low parking orbit to another orbit requires one of the many orbital transfers. These orbital transfers need to determine some orbital elements of the initial and final orbits as perigee and apogee distances. The transfers compete to achieve the transition with minimal consumption of energy, transfer time, as well as the highest accuracy of transition. In the present research, certain mathematical procedures implementable with the help of computers will be employed to investigate the two important non-coplanar tangential transfers between circular orbits called the Hohmann and bi-elliptic transfers. Also, a comparative study between Hohmann and bi-elliptic transfers will be established. At the end of present study, we will be able to determine the lowest value of the velocity change and the best transfer between the Hohmann and bi-elliptic transfers with minimal fuel consumption.