Mathematics
Scientific paper
Aug 1979
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979cemec..20...95b&link_type=abstract
Celestial Mechanics, vol. 20, Aug. 1979, p. 95-103.
Mathematics
7
Celestial Mechanics, Libration, Perturbation Theory, Potential Theory, Systems Stability, Three Body Problem, Equations Of Motion, Points (Mathematics)
Scientific paper
The location and linear stability of the libration points in the restricted three-body problem are studied, taking into account the effect of general perturbations in the potentials between the bodies on the stability of the libration points. It is found that if the perturbing functions satisfy certain conditions, there are five libration points, of which two are triangular and three collinear. The stability analysis indicates that the collinear points are unstable and that the range of stability for the triangular points increases or decreases depending on whether p is greater or lesser than zero, where p depends on the perturbing functions. The theory is verified in the cases where: (1) there are no perturbations in the potentials; (2) only the larger primary is an oblate spheroid whose axis of symmetry is perpendicular to the plane of relative motion of the primaries; (3) both primaries are such oblate spheroids; and (4) the two primaries are spherical and the larger is a source of radiation.
Bhatnagar K. B.
Hallan P. P.
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