On the Theory of the Galilean Satellites of Jupiter

In this communication the main equations for the variables: radius vector, longitude,PandQ(variables built from Laplace's perihelium first integral) are given in closed form. These equations are used for deriving the equations of a second-order theory. At this order, the equations forPandQ, are separated and they are integrodifferential linear equations. The equations for the radius vector and for the longitudes, give, after integration, perturbations which are purely trigonometric. The solution shows the features observed in the motion of Jupiter's Galilean satellites. The results are discussed, and extended to include the space variables.