EXAMINATION OF THE LAGRANGIAN EQUILIBRIUM POINTS IN THE PHOTOGRAVITATIONAL ELLIPTIC RESTRICTED THREE-BODY PROBLEM WITH ZONAL HARMONICS OF THE SECONDARY

EXAMINATION OF THE LAGRANGIAN EQUILIBRIUM POINTS IN THE PHOTOGRAVITATIONAL ELLIPTIC RESTRICTED THREE-BODY PROBLEM WITH ZONAL HARMONICS OF THE SECONDARY

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##### Date

2016-09

##### Authors

SULEIMAN, RUKKAYAT

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##### Abstract

This dissertation examines the Lagrangian equilibrium points in the photogravitational elliptic restricted three-body problem with Zonal Harmonics of the secondary under the assumption that the primary is an intense emitter of radiation and the secondary has the shape of an oblate spheroid up to ๐ฝ4 (octupolar mass moment), with the primaries moving in elliptic orbits of small eccentricity ๐. The positions and stability of collinear equilibrium points areobtained both analytically and numerically, the binary systems (Zera Cygni, Procyon A/B and 54 Piscium) are used to analyzed the result obtained numerically using the software package mathematica 5.0, the combined effect of oblateness (J2 and J4), (e) and (q1)also shows that the size of the region of stability has a general reduction.Despite the introductions of perturbations the points were also found to remain unstable in the Lyapunov sense and still remain on the line joining the primaries. Apart fromthis points, the positions and linear stability of the triangular points are obtained analytically under the influence of the perturbing agents. The results obtained are then analyzed numerically with the same binary systems, the points are found to exists and formsscalene triangles with the line joing the primaries unlike the classical case which forms equilateral triangles. Thus the points are conditionally stable for 0< ๐<๐๐ and unstable for ๐๐ โค ๐ โค ยฝ. It was seen that the size of the region of stability decreases with increase in eccentricity (e=0.3, 0.25 and 0.2), While in the absence of radiation pressure the position and linear stability of the triangular points are obtained using other binaries (NLTT 11748, LP400-22 and J1257+5428), it was observed that eccentricity does not affect the ฮพcoordinate and ceases to exist in the quasi-parabolic case, but in the ฮทcoordinate there is a shift away from the primaries but reverse is the case for both coordinates with the presence of semi-major (a). The mass ratio of the binaries used are outside the range 0< ๐<๐๐, thus making the triangular points unstable and they also cease to exist, as semi- major axis approaches unity. The Quadruple and octupolar mass moment causes a shift towards the origin and away from the line joining the primaries respectively on both coordinates.

##### Description

A DISSERTATION 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

EXAMINATION,, LAGRANGIAN EQUILIBRIUM POINTS,, PHOTOGRAVITATIONAL ELLIPTIC RESTRICTED THREE-BODY,, PROBLEM,, ZONAL HARMONICS,, SECONDARY,