Analytical expression for distant retrograde orbits around a small natural satellite |
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Authors: | Masaya Kimura Masanori Kawamura Katsuhiko Yamada |
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Affiliation: | 1. Mitsubishi Electric Corporation, Amagasaki 661-8661, Japan;2. Osaka University, Suita 565-0871, Japan |
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Abstract: | An analytical expression for distant retrograde orbits (DROs) is obtained in this study. Owing to the fact that a planar DRO is a closed orbit and can be expressed as an approximately elliptical orbit, respective geometries and periods of DROs are analytically calculated. A switching point, where various properties of planar DROs change abruptly with an increase in the orbital radius, is determined. The Mars–Deimos system is taken as a case study in this work. The proposed method can be applied to cases where the Hill’s approximation of the restricted three-body problem is valid. Numerical calculations are performed to validate the proposed method. |
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Keywords: | Distant retrograde orbit Small natural satellite Analytical solution Hill three-body problem |
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