Effects Of radiation Of Primaries On Stability Of Equilibrium Points In The Elliptical Restricted Three Body Problem

Abstract

The thesis entitled Effects of Radiation of Primaries on Stability of Equilibrium Points in the newlineElliptical Restricted Three Body Problem deals with the motion and stability of the newlineinfinitesimal mass in the vicinity of the Lagrangian equilibrium points in the elliptic restricted newlinethree body problem. The model is studied by considering both the primaries as radiating, newlineassuming that the eccentricities of the orbit of the primaries are small. The problem is newlinerestricted in the sense that the infinitesimal mass does not influence the motion of two newlinegravitating primaries, but are rather influenced by it. newlineFirst chapter of the thesis gives brief introduction of the basic concepts related to the topic newlinestating the future scope of the problem. newlineIn the second chapter review of literature has been presented which describes the work newlineconducted by many other researchers and mathematician. newlineIn the third chapter of the thesis, the motion and stability of the triangular points has been newlinestudied under the effects of radiating primaries around the binary system (Achird, Luyten, newlineand#945;Cen AB, Kruger-60, Xi-Bootis); using simulation technique by drawing different curves of newlinezero velocity. It has been shown that for and#956;and#8804;0.5, satisfying the condition newline(27 6 6 ) (1 ) (1 4 cos )2 , newline1 2 + b + b m -m £ + e f the triangular points is stable. It has been observed newlinethat for the binary system and#945; Cen AB the roots of characteristics equations are purely newlineimaginary, hence the equilibrium motion around the triangular points are stable. newlineIn the fourth chapter of the thesis, the method of average adopted by Grebenikov has been newlineexploited to analyze the stability of the system. It has been found that the critical mass ratio newlinedepends on the combined effects of radiation of both the primaries and eccentricity of this newlineorbit. It has been further observed by simulation technique that the range of stability newlinedecreases as the radiation pressure parameter increases. newlineThe Fifth chapter describes the location and stability of collinear points L1, L2 and L3 in newlinedetail for different val