Axial oscillation of a planetoid in Restricted Three Body Problem : The circular Sitnikov problem

Details Axial oscillation of a planetoid in Restricted Three Body Problem : The circular Sitnikov problem Axial oscillation of a planetoid in Restricted Three Body Problem : The circular Sitnikov problem

Dec 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002basi...30..895f&link_type=abstract

Bulletin of the Astronomical Society of India, vol. 30, p.895-909

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Restricted Three Body, Sintikov Problem, Celestial Mechanics

Scientific paper

Two equally massive primaries are assumed to be moving in circular orbits in Cartesian x-y plane. A planetoid is assumed to be on the z-axis. This is a particular case of the restricted three body problem with mass ratio =1/2, known as the circular Sitnikov problem. Motion of the planetoid is calculated using Lindstedt-Poincare' perturbation and Green's function method. It is found that the planetoid oscillates nonlinearly along the z-axis. We present analytic solutions up to 2nd order of approximation and compare the solutions with earlier results of other authors. A solution of the exact problem is also discussed.

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