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arXiv · 2407.06927

Contact geometry of Hill's approximation in a spatial restricted four-body problem

Cengiz Aydin
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Abstract

It is well-known that the planar and spatial circular restricted three-body problem (CR3BP) is of contact type for all energy values below the first critical value. Burgos-Garc\'ia and Gidea extended Hill's approach in the CR3BP to the spatial equilateral CR4BP, which can be used to approximate the dynamics of a small body near a Trojan asteroid of a Sun--planet system. Our main result in this paper is that this Hill four-body system also has the contact property. In other words, we can "contact" the Trojan. Such a result enables to use holomorphic curve techniques and Floer theoretical tools in this dynamical system in the energy range where the contact property holds.

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Cengiz Aydin. 2024-07-09. Contact geometry of Hill's approximation in a spatial restricted four-body problem. https://arxiv.org/abs/2407.06927

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