## Henk Broer (RuG)

### A Galilean dance: 1:2:4 resonant periodic motions and their librations of Jupiter and his Galilean moons

In 1799 Laplace documents observation of a 1:2:4 resonance in the motion of the Galilean moons Io, Europa and Ganymedes: the period of Europa is twice that of Io and the period of Ganymedes twice that of Europa. In the beginning of the 20th century De Sitter, using Poincareâ€™s work, shows that such resonant motions indeed exists in a Newtonian description of the Jovian system. Using this we find many librations of De Sitters resonant motions using KAM theory: these librations turn out to be projections of quasi-periodic motions of 8 frequencies. The existence of such librations enlarges the possible explanations of the real motion of the Jovian system. The background (parametrised) KAM theory was developed in the Groninger school in Dynamical Systems. In the talk horrid estimates will be avoided as much as possible.