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

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

“…The trajectory structure is determined based on the previous studies [1,[8][9][10]. The main advantage of the given-structure trajectory approach is that it yields Pontryagin extremals: under a "good" computational scheme for the shooting method and a "good" initial approximation, the modified Newton's method converges in a few iterations.…”

“…The initial approximation to the values of the phase and conjugate variables in the shooting parameter vector is chosen using the solution obtained previously in the modified pulse statement [1] in accordance with [12]: at the thrust activation time instants they correspond to the values of the phase and conjugate variables before the impulse action; at the thrust deactivation time instants, to the values of the phase and conjugate variables after the impulse action. The duration of active segments is estimated based on fuel consumption for a given engine activation; the duration of passive segments is equal to the corresponding duration of passive segments between the impulse actions.…”

“…After performing the second series of maneuvers, the spacecraft is in a target orbit from which the characteristic velocity of final ascent maneuvers to the GEO is bounded by a given value. According to the earlier studies [1,[8][9][10], the cost of releasing is small for the bi-elliptical final ascent scheme. In the target orbit, the satellite is separated from the CB.…”

“…The approaches to solving this problem can be divided into two large groups: prevention and cleaning. A detailed literature review on the topic was presented in [1]. In addition, we mention the works [2,3], covering the monitoring issues of man-made space debris, and [4][5][6][7], describing different means of capture and removal of large-size space debris.…”

“…It was established that in the problem with a phase constraint on the maximum possible distance between the spacecraft and the Earth and an unlimited transfer time, the solution is apsidal and coincides with that obtained in the previous step. The need to solve the problem in a modified pulse statement (considering the release of the AFT and CB) [1], representing the third step of the problem hierarchy methodology, was due to the difficulty of a direct transition to the problem with a high limited thrust: the modified Newton's method did not converge when using the solution of the second-step problem as an initial approximation.…”