Synthetic representation of the Galilean satellites' orbital motions from L1 ephemerides

Aims. We aim to provide a synthetic representation of the orbital motion of Io, Europa, Ganymede, and Callisto. It corresponds to a quasi-periodic Fourier series whose arguments are integer combinations of the fundamental arguments of the dynamical system, which are also given. Methods. The present series are issued from frequency analysis and digital filtering treatments. The initial samplings have been taken from a former numerical integration fit to the observations and referenced as L1 ephemerides. Results. Our representation allows for the identification of all the significant perturbations in the system, which helps us to understand these orbital motions. It is also useful in other related topics: the dynamical history of the system and studies requiring us to extract only major terms to compute motions such as the rotation of the bodies.