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.
Biasco, L., Chierchia, L., Valdinoci, E. (2003). Elliptic two-dimensional invariant tori for the planetary three-body problem. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 170, 91-135 [10.1007/s00205-003-0269-2].
Elliptic two-dimensional invariant tori for the planetary three-body problem
BIASCO, LUCA;CHIERCHIA, Luigi;
2003-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
