Astronomy and Astrophysics – Astronomy
Scientific paper
Sep 1996
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996cemda..64..261c&link_type=abstract
Celestial Mechanics & Dynamical Astronomy, Volume 64, Issue 3, pp.261-272
Astronomy and Astrophysics
Astronomy
10
Stability, Nekhoroshev Theorem, Three-Body Problem
Scientific paper
We studied the stability of the restricted circular three-body problem. We introduced a model Hamiltonian in action-angle Delaunay variables. which is nearly-integrable with the perturbing parameter representing the mass ratio of the primaries. We performed a normal form reduction to remove the perturbation in the initial Hamiltonian to higher orders in the perturbing parameter. Next we applied a result on the Nekhoroshev theorem proved by Pöschel [13] to obtain the confinement in phase space of the action variables (related to the elliptic elements of the minor body) for an exponentially long time. As a concrete application. we selected the Sun-Ceres-Jupiter case, obtaining (after the proper normal form reduction) a stability result for a time comparable to the age of the solar system (i.e., 4.9 · 109 years) and for a mass ratio of the primaries less or equal than 10-6.
Celletti Alessandra
Ferrara Laura
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