The stability of stationary motions of two gravitating bodies - Spherically-symmetric and axisymmetric bodies compressed along the axis of symmetry

Statistics – Computation

Scientific paper

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Axisymmetric Bodies, Computational Astrophysics, Gravitational Effects, Motion Stability, Orbital Mechanics, Two Body Problem, Center Of Mass, Coplanarity, Lagrange Coordinates, Librational Motion

Scientific paper

The orbital stability of stationary motions in the coplanar problem of the relative motion of two gravitating bodies is studied. The first body, M, is axisymmetric with the center of mass at point O. The other is spherical and is replaced by a gravitating point, M0. For stationary motion, when the angle between OM0 and the axis of symmetry of M does not equal 0 or equals 90 deg, the conditions of orbital stability and the stability of rotational movement are obtained as inequalities for the orbital radius OM sub 0.

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