On 6piperiodic solutions of the plane, restricted, elliptical threebody problem
Abstract
The existence of 6pi periodic solutions of the differential equation of motion of the plane, restricted, elliptical threebody problem in complex form in the vicinity of a libration point is investigated. The approximate construction of the solutions is studied, and it is shown that the equation of this threebody problem for sufficiently small orbital eccentricity in the vicinity of the libration point has a continuum of 6pi periodic solutions in the form of series in powers of the eccentricity. The process of determining the coefficients of the series which are solutions of the corresponding linear differential equations is stabilized. The convergence of these series can be proved by the ordinary principle of contractive mappings.
 Publication:

Astronomicheskii Zhurnal
 Pub Date:
 August 1984
 Bibcode:
 1984AZh....61..800I
 Keywords:

 Celestial Mechanics;
 Elliptical Orbits;
 Periodic Functions;
 Three Body Problem;
 Eccentric Orbits;
 Libration;
 Astronomy