Inserting a maximum-mass spacecraft into a target orbit using a limited-thrust engine with releasing the separable part of its launch vehicle into the Earth's atmosphere

Space debris is an urgent problem of our time. This paper considers the idea of reducing near-Earth space debris by releasing the spent additional fuel tank (AFT) and the booster's central block (CB) into the Earth's atmosphere. The spacecraft transfer from a reference circular orbit of an artificial Earth satellite to a target elliptical orbit is optimized. The transition maneuvers are carried out using a booster with a high limited-thrust engine and the AFT. The second zonal harmonic of the Earth's gravitational field is taken into account. The optimal control problem is solved based on Pontryagin's maximum principle. Bulky derivatives are calculated using a specially developed numerical-analytical differentiation technique. The Pontryagin extremals obtained below are the next step in implementing the problem hierarchy methodology.