We consider the problem proposed on the 4th Global Trajectory Optimization Competition (GTOC4).

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The paper considers the reducing of the near-Earth space debris due to the stages discharge into the Earth’s atmosphere, introduces the solution for optimizing the impulse transfer between the artificial Earth satellite reference circular orbit and the target elliptical orbit with a phase constraint on the maximum distance of the spacecraft from the Earth. A specially developed numerical-analytical differentiation technology allows us to calculate derivatives under the transversality of Lagrange principle. The paper proposes the transversality and stationarity conditions analysis, which results in the conclusion that the Beletsky — Egorov — Pines integral, and the Hamiltonian are continuous in the moments of all intermediate impulse actions application, including the stage discharge moments. The paper shows that the problem solution for various flight schemes coincides with a similar one without a priori assumption about the impulse effects apsidal nature.

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