519.6 Modeling and optimization of the transfer of a small spacecraft from Earth orbit to Jupiter orbit under a solar sail

Mozzhorina T. Y. (Bauman Moscow State Technical University), Nasybullina K. R. (Bauman Moscow State Technical University)

SOLAR SAIL, THE SHOOTING METHOD, BOUNDARY VALUE PROBLEMS OF ORDINARY DIFFERENTIAL EQUATIONS, OPTIMAL CONTROL, PONTRYAGIN'S MAXIMUM PRINCIPLE, FLIGHT BETWEEN THE ORBITS OF THE EARTH AND JUPITER


doi: 10.18698/2309-3684-2025-3-4766


This paper examines the optimization of the transfer of a low-mass spacecraft from Earth’s orbit to Jupiter’s orbit using a solar sail, under the assumptions that both orbits lie in the same plane and that the solar sail possesses ideal properties. The optimization of the sail’s orientation angle is performed using Pontryagin’s maximum principle in solving a minimum-time problem. The resulting boundary-value problem derived from the maximum principle is solved by the shooting method. The computational program was implemented in C++. The paper provides a detailed mathematical derivation of the optimal control laws for two possible independent controls: the sail orientation angle and the acceleration imparted to the spacecraft by the solar sail. The influence of terminal boundary conditions on the numerical solution is investigated, considering cases corresponding to Jupiter’s mean orbit, as well as its aphelion and perihelion distances. The effect of solar sail acceleration on the interorbital transfer time is also analyzed. An assessment of the accuracy of the obtained results is presented, demonstrating the feasibility of applying the shooting method to similar problems. A comparison with previously published results is also provided.


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