Orbital Resonance Near the Equatorial Plane of Small Bodies
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In celestial mechanics, the orbital resonance usually indicates that the periods of two orbiting bodies are related by a ratio of two small integers, leading to a periodic mutual excitation. The result of orbital resonance could be to destabilize some orbits in Solar System, e.g. the Kirkwood gaps, and Trojan families of asteroids, which are both correlated with resonance with Jupiter. The orbital resonance here mentioned for small bodies means differently from the convention: first, it occurs between the periods of the autorotation and the heliocentric orbit, instead of between two orbits; second, this kind of resonance could make an effect within a short time, instead of accumulation over multiple periods. This chapter studies the resonant orbits near the equatorial plane of a small body, with a special attention paid to the 1:1 resonance, e.g. the occurrence and distribution. The polyhedral gravity model continues to be adopted to approximate the irregular field configuration. Section 5.2 starts with an analysis on the variation of orbital energy, showing the mechanical essence of 1:1 resonance near the small bodies. Section 5.3 surveys the parameter dependence of the resonant orbits near the equatorial plane. Section 5.4 performs a 3-dimensional Monte Carlo simulation in order to determine the parameter conditions of 1:1 resonance. Furthermore, the rest of this section discusses a special case of the resonant orbits, the ejecting orbit, and presents its proportion and distribution around the specified asteroid.