The Solution of Optimal Two-Impulse Transfer between Elliptical Orbits with Plane Change

Abstract

The optimizing total velocity increment v ∆ needed for orbital maneuver between two elliptic orbits with plane change is investigated. Two-impulse orbital transfer is used based on a changing of transfer velocities concept due to the changing in the energy. The transferring has been made between two elliptic orbits having a common centre of attraction with changing in their planes in standard Hohmann transfer with the terminal orbit which is elliptic orbit and not circular. We develop a treatment based on the elements of elliptic orbits 1 1 , a e , 2 2 , a e and , programming code of MATHEMATICA V10, with no condition on the eccentricity or the semi-major axis of the initial, transformed, and the final orbits. We find that there are constrains on the transfer angles 1 θ and α . For α it must be between 40˚ and 160˚, and there is no solution if α is less than 40˚ and bigger than 160˚ and 1 θ takes the values less than 40˚. The minimum total velocity increments obtained at the value of 1 θ less than 25 o and α equal to 160˚. This is an interesting result in orbital transfer problem in which the change of orbital plane is necessary for the transferring.