Problems on the Galilean satellites of Jupiter

The purpose of this paper is to present a critical review of some problems concerning the dynamics of Jupiter's Galilean system of satellites. Theory, ephemeris and observation are considered.Two theories were proposed by Ferraz-Mello and by Sagnier. The main characteristics of these theories are that the frequencies are allowed to be kept fixed for all times from the earlier stages, and so to have a purely trigonometric solution.For a completely satisfactory work we need many more observations than actually exist. Two kinds of observations seem to be the best suitable: long-focus photographic plates and photometric records of mutual events.The most recent photographic observations are discussed in order to state guidelines for future work. The problem of the precision of Sampson's tables is discussed on the grounds of the recent observations.Paper presented at IAU Colloquium, No. 28, Ithaca, N.Y., August, 1974.