Modeling the 5:2 mean-motion resonance in the Jupiter - Saturn planetary system
T.A. Michtchenko
Instituto Astroñomico e Geofísico -
Universidade de São Paulo, Brazil
The motion of the Jupiter-Saturn planetary system near the 5:2 mean-motion
resonance is modeled analytically in the frame of the planar general
three-body problem. The topology of phase space in the resonance and
near-resonance domains is investigated in detail by means of surfaces
of section and frequency maps. Also, the portrait of entire phase space
is outlined by calculation of the main families of periodic orbits.
Several regimes of motion are detected and their domains are represented
on the parameter plane defined by the total energy of the system and
the parameter of proximity to the 5:2 resonance. The regions of transition
between domains of different regimes of motion are characterized by chaos.
We show that there is a significant chaotic zone associated with the
5:2 mean-motion resonance, but a large-scale chaotic behavior of the
Jupiter-Saturn system is not possible. The developed model is applied to
study the behavior of the actual Jupiter-Saturn system and the results
obtained show that the system is very close to the chaotic zone
associated with the 5:2 resonance. This fact sheds new light on the
hypothesis of planetary migration du