Analytical theory of the motion of the Galilean satellites of Jupiter: the first approximation.

This paper reports the development of a first approximation of an analytical theory of Galilean satellites using Sagnier's method. This approximation, labeled S-A, uses the equations of second order. The autonomous system and the critical one give long period motions of the nodes and perijoves and allow the construction of the general solution. The analytical results are reduced to numerical tables of longitudes, radius vector and latitudes for an easy comparison with Sampson's tables and Lieske's E-O tables.