The Comparison of Optimal and Locally-Optimal Heliocentric Flyby Trajectories of the Solar-Sail Spacecraft, the Investigation of Simplified Model

The method of locally optimal control for weakly controllable systems is applied to calculation of the flybys transfer trajectories to asteroids by the solar-sail spacecraft. The earlier developed method of time of flyby minimization from the circle orbit to the asteroids or comets allows comparing of the locally-optimal and optimal flyby trajectories of solar-sail spacecraft. For to explain the obtained results, the simplified model of control of the position of a single mass point by the restricted force was investigated. The analytical results, obtained by this investigation, were used for qualitative analysis of the optimal and locally-optimal transfer trajectories between the Earth and Mars.