Stability of triangular equilibrium points in the elliptic restricted problem of three bodies with radiating and triaxial primaries

Abstract

This paper studies the stability of infinitesimal motions about the triangular equilibrium points in the elliptic restricted three body problem assuming bigger primary as a source of radiation and the smaller one a triaxial rigid body. The perturbation technique developed by Bennet (Icarus 4:177, 1965b) has been used for determination of characteristic exponents. This technique is based on Floquet’s Theory for determination of characteristic exponents in the system with periodic coefficients. The results of the study are analytical and numerical expressions are simulated for the transition curves bounding the region of stability in the μ–e plane, accurate to O(e 2). The unstable region is found to be divided into three parts. The effect of radiation parameter is significant. For small values of e, the results are in favor with the numerical analysis of Danby (Astron. J. 69:166, 1964), Bennet (Icarus 4:177, 1965b), Alfriend and Rand (AIAA J. 6:1024, 1969). The effect of radiation pressure is significant than the oblateness and triaxiality of the primaries.