Orbital evolution of planetary systems similar to our Solar one is studied. In the present work we use Jacobian coordinates, construct the Hamiltonian expansions in the Poisson series in all elements for the planetary three-body problem. Values of planetary masses and mean semi-major axes of their orbits may be arbitrary. Further we construct the averaged Hamiltonian by the Hori-Deprit method with accuracy up to second order with respect to the small parameter, the generating function of the Lie transform, change of variables formulae, and right-hand sides of averaged equations. For algebraic manipulations we use the rational version of the echeloned Poisson series processor EPSP to reduce the round-off errors.
Resonant semi-major axes and estimations of the resonant zones width are obtained for the small parameter values varying from 0.001 to 0.1. The resonance conditions are analysed for the exoplanetary systems.
The averaged equations are integrated numerically. Orbital evolution of the Sun-Jupiter-Saturn system is investigated at the time-scale of 10 Gyr. Stability of this system is investigated for the small parameter values varying from 0.001 to 0.04 at the time-scale of several Gyr.
Orbital evolution of other weakly perturbed two-planetary systems is investigated.
This work was partly supported by the RFBR grant~05-02-17408), Program University of Russia, grant UR.02.01.301), and the Leading Scientific School, grant NSh-1078.2003.02.