Hybrid optimization method for space flight with low thrust and its use for flight from Earth to asteroid Apophis

The purpose of this study is optimization of spacecraft flight to the Near-Earth asteroid Apophis under condition of maximizing the spacecraft mass in the asteroid’s satellite orbit. Presented data allow choosing optimal launch dates and duration of heliocentric part of the interplanetary transfer for the cases of “ideal” and piecewise-constant thrust. The results were obtained using hybrid method of space trajectories optimization. This method combines some direct and indirect computational procedures. The initial approximation was obtained using global search method and then improved by “traveling tube” and local variations algorithms. The Pontryagin method with parametric continuation of solution was used to obtain the final result.
The study was supported by Russian Foundation For Basic Research (grant N 09-01-00710) and by Scientific Schools Support Program (grant NSh-6700.2010.1).