Frederic Gabern, \`Angel Jorba
Generalizing the Restricted Three-Body Problem. 
The Bianular and Tricircular Coherent Problems.
(1909K, Pdf)

ABSTRACT.  In this paper we construct two models for the motion of a 
particle under the gravitational attraction of Sun, Jupiter, Saturn 
and Uranus, that can be seen as a generalization of the well known 
Restricted Three-Body Problem (RTBP). Both models are obtained by 
computing quasi-periodic solutions --with two basic frequencies-- of a 
suitable $N$-body problem. 
The first model is based on a quasi-periodic solution of the planar 
Sun-Jupiter-Saturn Three-Body problem, that tries to approach the real 
motion of Jupiter. The second model is based on a quasi-periodic 
solution of the Sun-Jupiter-Saturn-Uranus Four-Body problem. In both 
cases, we derive the equations of motion for a particle under the 
gravitational attraction of these bodies as a quasi-periodic 
time-dependent perturbation of the well-known RTBP.