The main satellites of Jupiter, named Galilean after their discovery by Galileo Galilei, are among the most studied celestial objects. The dynamics of their motions represent one of the most complex challenges in the Solar System but the most interesting, including all the dynamical problems of a gravitational system. The modeling of their motions is difficult because of their size (Ganymede has a size similar to Mars or Mercury) and mutual gravitational perturbations, because of the flatness of Jupiter, the presence of Saturn and the Sun and strong tidal effects between them and the planet Jupiter. However, a good knowledge of their dynamics may help us understand their physical nature (their internal structure influences their motions), their formation and their evolution. For these purposes, accurate astrometric observations are essential to determine the physical parameters of their dynamics. Our purpose in this paper is to explore the history of the progress made in these studies during the last four centuries and the value of using old data in present-day research.
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