On Jupiter and his Galilean satellites: Librations of De Sitter’s periodic motions

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• 作者：Henk W. Broer^a ; ^{h.w.broer@rug.nl" class="auth_mail" title="E-mail the corresponding author} ; Heinz Hanß ; mann^b ; ^{hanssmann@math.uu.nl" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Periodic orbit ; Quasi-periodic orbit ; KAM theory ; Celestial mechanics
• 刊名：Indagationes Mathematicae
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：27
• 期：5
• 页码：1305-1336
• 全文大小：1128 K

文摘

The motion of Jupiter’s four Galilean satellites Io–Europa–Ganymedes–Callisto is subjected to an orbital class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0019357716300544&_mathId=si12.gif&_user=111111111&_pii=S0019357716300544&_rdoc=1&_issn=00193577&md5=3467a6bf1c22e92888a969732a228910" title="Click to view the MathML source">1:2:4class="mathContainer hidden">class="mathCode">$1:2:4$–resonance of the former (and inner) three. Willem de Sitter in the early 20th century gave a mathematical explanation of this in a Newtonian framework. He found a family of stable periodic solutions by using the work of Poincaré. This paper briefly reviews De Sitter’s theory, and focuses on the underlying geometry of a suitable covering space, where we develop Kolmogorov–Arnold–Moser theory to find Lagrangean invariant tori excited by the normal modes of the De Sitter periodic orbits. In this way we find many librations near these periodic orbits that may well offer a more realistic explanation of the observations.