An Application of the Nekhoroshev Theorem to the Restricted ThreeBody Problem
Abstract
We studied the stability of the restricted circular threebody problem. We introduced a model Hamiltonian in actionangle Delaunay variables. which is nearlyintegrable 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 SunCeresJupiter 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 · 10^{9} years) and for a mass ratio of the primaries less or equal than 10^{6}.
 Publication:

Celestial Mechanics and Dynamical Astronomy
 Pub Date:
 September 1996
 DOI:
 10.1007/BF00728351
 Bibcode:
 1996CeMDA..64..261C
 Keywords:

 Stability;
 Nekhoroshev theorem;
 threebody problem