Elliptic Two-Dimensional Invariant Tori for the Planetary Three-Body Problem

Luca Biasco, Luigi Chierchia, Enrico Valdinoci

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

The spatial planetary three-body problem (i.e., one "star" and two "planets", modelled by three massive points, interacting through gravity in a three dimensional space) is considered. It is proved that, near the limiting stable solutions given by the two planets revolving around the star on Keplerian ellipses with small eccentricity and small non-zero mutual inclination, the system affords two-dimensional, elliptic, quasi-periodic solutions, provided the masses of the planets are small enough compared to the mass of the star and provided the osculating Keplerian major semi-axes belong to a two-dimensional set of density close to one.

Original languageEnglish
Pages (from-to)91-135
Number of pages45
JournalArchive for Rational Mechanics and Analysis
Volume170
Issue number2
DOIs
Publication statusPublished - 1 Nov 2003
Externally publishedYes

Fingerprint

Three-body Problem
Invariant Tori
Planets
Stars
Star
Quasi-periodic Solutions
Stable Solution
Eccentricity
Inclination
Two-dimensional Systems
Gravity
Gravitation
Limiting
Three-dimensional

Cite this

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Elliptic Two-Dimensional Invariant Tori for the Planetary Three-Body Problem. / Biasco, Luca; Chierchia, Luigi; Valdinoci, Enrico.

In: Archive for Rational Mechanics and Analysis, Vol. 170, No. 2, 01.11.2003, p. 91-135.

Research output: Contribution to journalArticle

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