Optimization of the interplanetary flight to Mars with three-pulse approach to Phobos based on Lagrange principle

Abstract

The problem of optimal control of the spacecraft interplanetary flight from the Earth to Mars with a three-pulse approach to the Phobos tracking orbit is considered. The departure of the spacecraft from the Earth is also approximated by pulses. The attraction of the Earth and Mars is taken into account. The problem is solved numerically on the basis of Lagrange principle. The results are compared with the scheme of a full turn free approach to Phobos. The initial approximation is carried out based on a combination of Lambert problems solutions. The software package is developed. Ephemerides are taken into account in the calculations, and the NASA SPICE package is used.