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An a P P L I C a T I O N of the N E K H O R O S H E V T H E O R E M to the Restricted Three-body Problem
| Content Provider | Semantic Scholar |
|---|---|
| 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 Prschel [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 9 6 system (i.e., 4.9 • 10 years) and for a mass ratio of the primaries less or equal than 10. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://page-one.springer.com/pdf/preview/10.1007/BF00728351 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |