Minimum-fuel station-change for geostationary satellites using low-thrust considering perturbations

The objective of this paper is to find the minimum-fuel station change for geostationary satellites with low-thrust while considering significant perturbation forces for geostationary Earth orbit (GEO). The effect of Earth's triaxiality, lunisolar perturbations, and solar radiation pressure on the terminal conditions of a long duration GEO transfer is derived and used for establishing the station change model with consideration of significant perturbation forces. A method is presented for analytically evaluating the effect of Earth's triaxiality on the semimajor axis and longitude during a station change. The minimum-fuel problem is solved by the indirect optimization method. The easier and related minimum-energy problem is first addressed and then the energy-to-fuel homotopy is employed to finally obtain the solution of the minimum-fuel problem. Several effective techniques are employed in solving the two-point boundary-value problem with a shooting method to overcome the problem of the small convergence radius and the sensitivity of the initial costate variables. These methods include normalization of the initial costate vector, computation of the analytic Jacobians matrix, and switching detection. The simulation results show that the solution of the minimum-fuel station change with low-thrust considering significant perturbation forces can be obtained by applying these preceding techniques.