Abstract:
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 J,l.=1I2, known
as the circular Sitnikov problem. Motion of the planetoid is calculated using LindStedtPoincare'
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.
