On The Stability of Collinear Points In The Photogravitational Elliptic Restricted Three-Body Problem.

Abstract

This paper investigates the stability of collinear points of a small particle in the photogravitational elliptic restricted three-body problem moving in elliptic orbit about their centre of mass, under the influence of radiation pressures of the primaries, together with the gravitational attraction force. Collinear points in general are unstable, however, the inner collinear point L₂, is seen to be stable in an interval for the mass reduction factor of the bigger primary, under certain conditions depending on the mass ratio, eccentricity and semi-major axis of the orbit. Further, a practical application of the motion of a dust grain in the case of the binary star system in Capella is also discussed.

Keywords: celestial mechanics, elliptic photogravitational RTBP.