Existence and stability of libration points in the restricted three body problem when the smaller primary is a triaxial rigid body and the bigger one an oblate spheroid.

Details Existence and stability of libration points in the restricted three body problem when the smaller primary is a triaxial rigid body and the bigger one an oblate spheroid. Existence and stability of libration points in the restricted three body problem when the smaller primary is a triaxial rigid body and the bigger one an oblate spheroid.

Jul 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999ijpam..30..721k&link_type=abstract

Indian J. Pure Appl. Math., Vol. 30, No. 7, p. 721 - 733

Mathematics

3

Three-Body Problem: Restricted, Three-Body Problem: Libration Points

Scientific paper

This paper deals with the stationary solutions of the planar restricted three body problem when the smaller primary is a triaxial rigid body with one of the axes as the axis of symmetry and its equatorial plane coinciding with the plane of motion. The bigger primary is taken as an oblate spheroid and its equatorial plane is also coinciding with the plane of motion. It is seen that there are five libration points, two triangular and three collinear. It is further observed that the collinear points are unstable, while the triangular points are stable for the mass parameter 0 ≤ μ < μcrit (the critical mass parameter). It is further seen that the triangular points have long or short periodic elliptical orbits in the same range of μ.

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