Space Trajectories. Orbital Transfer

Artificial satellites are used for a wide range of missions: telecommunications, navigation, Earth and space observation... To carry out its mission, the satellite must be placed in a specific orbit, chosen according to its objectives and equipment (antennas, solar panels, optical instruments, etc.). It must then maintain a precise orbit throughout its operational life. The maneuvers to be performed are formulated as orbital transfer problems. The aim is to reach the target orbit from an initial orbit, while minimizing propellant consumption. A transfer problem can be approached in two different ways, depending on the type of engine used.

Impulse modeling assumes that speed changes are instantaneous. This assumption is well suited to the high thrust levels produced by chemical propulsion. The transfer problem then consists in finding out when and in which direction the impulses should be delivered. Analytical solutions exist for the simplest cases, such as Hohmann transfer between circular orbits.

Continuous thrust modeling becomes necessary as soon as the duration of propulsive phases (or boosts) becomes significant in relation to the orbital period. In this case, an optimal control problem must be solved to determine engine ignition and extinction times, as well as thrust orientation during each propulsive phase. These problems generally have no analytical solution, with the exception of Edelbaum transfer between circular orbits. They have to be solved by direct or indirect numerical optimization methods.

This article presents the impulse and continuous orbital transfer models, the elementary analytical solutions, and the numerical resolution methods used for space applications.