Henk W. Broer, Heinz Hanßmann
On Jupiter and his Galilean satellites:
librations of De Sitter's periodic motions
(5506K, PostScript)
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 Poincare. 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.