Lunar capture in the planar restricted three-body problem |
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Authors: | Yi Qi Shijie Xu |
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Institution: | 1. School of Astronautics, Beihang University, Beijing, 100191, China
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Abstract: | The capture dynamics is an important field in Astronomy and Astronautics. In this paper, the near-optimal lunar capture in the Earth–Moon transfer is investigated under the frame of the planar circular restricted three-body problem. We try to work out how to achieve the permanent lunar capture with the minimum maneuver consumption. This problem is decomposed into two parts: the pre-maneuver part and the post-maneuver part. In the pre-maneuver part, considering the criteria of the gravitational capture, we obtain the minimum pre-maneuver velocity via the numerical backward integration. In the post-maneuver part, using the Poincaré section and the KAM theory, we find the maximum post-maneuver velocity to achieve the permanent capture. Synthesized the results of the two parts, a new method is presented to find the near-optimal maneuver position and the minimum maneuver consumption. The method presented is simple and visible, and can provide abundant capture orbits for the design of low energy Earth–Moon transfers. |
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