(1) Celestial Mechanics Department,
Sternberg State Astronomical Institute
University Prospect 13, 119 899 Moscow, Russia
(2) Astronomical Institute, Slovak Academy of Sciences
Dubravska cesta 9, 842 28 Bratislava, Slovak Republic
From the general solution of the simplified canonical system of differential equations of three body problem the secular motion of the apsid's line was found out. In the intermediate orbit, only the members up to the second order were taken into account. The Hamiltonian of the canonical system of the intermediate orbit depends on a single angular variable, the perigee of a satellite. The derived system of the formulae has been worked out for circular and librating motions of the perigee, respectively.
The formulae describing the secular motion of the apsid's line were applied on distant satellites of the solar system.
The analytical method for obtaining the perturbations in the motion of an apsid's line is offered, when the members of the third and fourth orders in the Hamiltonian were taken into account.