Spacecraft Transfer Optimization with Releasing the Additional Fuel Tank and the Booster to the Earth Atmosphere

This paper considers the idea of reducing the debris of near-Earth space by releasing the spent parts of a spacecraft on orbits touching the conditional boundary of the Earth's atmosphere. We optimize the spacecraft transfer trajectory from a circular reference orbit of an artificial Earth satellite to a target elliptical orbit in a modified pulse problem statement. The convergence of Newton's method is improved by introducing a series of auxiliary coordinate systems at each point of applying an impulse action. The derivatives in the transversality conditions are calculated using a special numerical-analytical differentiation technique.