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arXiv · 1508.07589

De Sitter's Theory of Galilean Satellites and the Related Quasi-periodic Orbits

Henk Broer·Lei Zhao
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Abstract

In this article, we investigate the mathematical part of De Sitter's theory on the Galilean satellites, and further extend this theory by showing the existence of some quasi-periodic librating orbits by applications of KAM theorems. After showing the existence of De Sitter's family of linearly stable periodic orbits in the Jupiter-Io-Europa-Ganymede model by averaging and reduction techniques in the Hamiltonian framework, we further discuss the possible extension of this theory to include a fourth satellite Callisto, and establish the existence of a set of positive measure of quasi-periodic librating orbits in both models for almost all choices of masses.

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Henk Broer, Lei Zhao. 2015-08-30. De Sitter's Theory of Galilean Satellites and the Related Quasi-periodic Orbits. https://arxiv.org/abs/1508.07589

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