PERTURBED ROBE’S CIRCULAR RESTRICTED THREE-BODY PROBLEM UNDER AN OBLATE PRIMARY
PERTURBED ROBE’S CIRCULAR RESTRICTED THREE-BODY PROBLEM UNDER AN OBLATE PRIMARY
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Date
2015-05
Authors
OMEBIJE, VERONICA UGBEDEOJO
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Abstract
The research work examines the existence and linear stability of equilibrium points in the
perturbed Robe’s circular restricted three-body problem under the assumption that the
hydrostatic equilibrium figure of the first primary is an oblate spheroid. The problem is
perturbed in the sense that small perturbations given to the Coriolis and centrifugal forces
are being considered. Results of the analysis found two axial equilibrium points on the
line joining the centre of both primaries. It is further observed that under certain
conditions, points on the circle within the first primary are also equilibrium points. And a
special case where the density of the fluid and that of the infinitesimal mass are equal
(D = 0) is discussed. The linear stability of this configuration is examined; it is observed
that the axial equilibrium points 𝑝1,0,0 and 𝑥11 +𝑝2 ,0,0 are conditionally stable,
while the circular points 1 +r𝑐os𝜃,𝑟𝑠in𝜃,0 are unstable.
Description
A THESIS SUBMITTED TO THE SCHOOL OF POST GRADUATE STUDIES,
AHMADU BELLO UNIVERSITY, ZARIA, NIGERIA
IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE AWARD OF
MASTER OF SCIENCE DEGREE IN MATHEMATICS
DEPARTMENT OF MATHEMATICS,
FACULTY OF SCIENCE,
AHMADU BELLO UNIVERSITY, ZARIA,
NIGERIA
Keywords
PERTURBED ROBE’S CIRCULAR RESTRICTED,, THREE-BODY PROBLEM,, OBLATE PRIMARY,