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

Abstract

The motion of Jupiter’s four Galilean satellites Io–Europa–Ganymedes–Callisto is subjected to an orbital 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.