## LIBRATION POINTS AND STABILITY OF AN OBLATE TEST PARTICLE IN THE SUN-EARTH SYSTEM OF THE RESTRICTED THREE-BODY PROBLEM

ONI LEKE

Department of Mathematics, College of Physical Science, Joseph Sarwuan Tarka University, P.M.B. 2373, Makurdi, Benue-State, Nigeria.

ABUR GABRIEL *

Department of Mathematics, College of Physical Science, Joseph Sarwuan Tarka University, P.M.B. 2373, Makurdi, Benue-State, Nigeria.

*Author to whom correspondence should be addressed.

### Abstract

This paper examines libration points and stability of a test particle having the shape of an oblate spheroid under the gravitational effect of a radiating first primary and an oblate shaped second primary using the model of the restricted three-body problem. The equations of motion have been stated and the libration points examined. It is seen that there exist a pair of triangular points which are defined by the radiation pressure force of the first primary, and oblateness of the second primary and the test particle. Further, there can be up to five collinear libration points in the presence of oblateness of either the second primary or the test particle. We examine the stability of the libration points and it is seen that the triangular points are linearly stable in the sense that the roots of the characteristic equation are all distinct imaginary roots, which produce bounded motion around the triangular points, while the collinear points are unstable due to the presence of a positive root. Further, we explore the periodic orbits around linearly stable triangular points and it was seen that the orbits are elliptic. The elements of the orbits, among which are the frequency, orientation, eccentricities, lengths of the semi-major and semi-minor axis have all been obtained and are defined by the radiation pressure of the first primary and oblateness of the second primary and the test particle. These outcomes have been verified numerically when the radiating first primary is the Sun and the oblate second primary is the Earth.

Keywords: RTBP, libration points, radiation pressure, oblateness, test particle

#### How to Cite

*Journal of Applied Physical Science International*,

*14*(3), 42–68. https://doi.org/10.56557/japsi/2022/v14i38090

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