A STUDY OF LIBRATION POINTS IN THE PHOTOGRAVITATIONAL CIRCULAR RESTRICTED THREE-BODY PROBLEM WITH ASPHERICITY AND POTENTIAL FROM A BELT
A STUDY OF LIBRATION POINTS IN THE PHOTOGRAVITATIONAL CIRCULAR RESTRICTED THREE-BODY PROBLEM WITH ASPHERICITY AND POTENTIAL FROM A BELT
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Date
2016-04
Authors
TAURA, Joel John
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Abstract
This research has investigated an improved version of the classic restricted three-body
problem where both primaries are considered as non-spheroids as well as sources of
radiation, and are enclosed by a belt of homogeneous cluster of material points centered at
the mass center of the system. It studied the effects of the gravitational potential created by
the belt on the existence of libration points and their linear stability when the primaries
are:(a) radiating-oblate and (b) radiating-triaxial bodies. To this end, the equations that
govern the motion of the infinitesimal body have been derived, and the positions of the
libration points areobtained. It has been established that the equations and the positions of
the libration points are affected by the aforementioned perturbations, such that in addition
to the usual five (three collinear, two triangular) libration points of the classicrestricted
three-body problem, there exist four new collinear points in the case of radiating-oblate
primaries and up to two in the case of radiating-triaxial primaries. The triangular points are
seen to be stable for 0 c and unstable for
1
,
2 c where c is the critical mass
parameter influenced by the radiation and oblateness/triaxiality of the primaries and
potential from the belt. The combined effect of these perturbations is a stabilizing tendency
when the primaries are oblate and adestabilizing tendency when they are triaxial. The
classical three collinear libration points 1, 2 3 (L L , L ) remain unstable, whereas some of
the new libration points have been found to be stable. Furthermore, periodic orbits around
the stable triangular points owing to the amalgamated effect of the radiation and oblateness
up to the coefficient J4 of the primaries and potential from the belt are found to be ellipses.
Description
A THESIS SUBMITTED TO THE SCHOOL OF POSTGRADUATE STUDIES, AHMADU BELLO UNIVERSITY, ZARIA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE AWARD OF DOCTOR OF PHILOSOPHY IN MATHEMATICS DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE AHMADU BELLO UNIVERSITY, ZARIA NIGERIA
Keywords
STUDY,, LIBRATION POINTS,, PHOTOGRAVITATIONAL CIRCULAR RESTRICTED., THREE-BODY PROBLEM., ASPHERICITY,, POTENTIAL,, BELT,