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 language | English |
|---|---|
| Pages (from-to) | 91-135 |
| Number of pages | 45 |
| Journal | Archive for Rational Mechanics and Analysis |
| Volume | 170 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1 Nov 2003 |
| Externally published | Yes |
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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 journal › Article
TY - JOUR
T1 - Elliptic Two-Dimensional Invariant Tori for the Planetary Three-Body Problem
AU - Biasco, Luca
AU - Chierchia, Luigi
AU - Valdinoci, Enrico
PY - 2003/11/1
Y1 - 2003/11/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0242459071&partnerID=8YFLogxK
U2 - 10.1007/s00205-003-0269-2
DO - 10.1007/s00205-003-0269-2
M3 - Article
VL - 170
SP - 91
EP - 135
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
SN - 0003-9527
IS - 2
ER -