An application of the Nekhoroshev theorem to the restricted three-body problem View Full Text


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Article Info

DATE

1996-09

AUTHORS

Alessandra Cellett, Laura Ferrara

ABSTRACT

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. More... »

PAGES

261-272

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf00728351

DOI

http://dx.doi.org/10.1007/bf00728351

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1009176965


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