Effects of radiation and triaxiality of triangular equilibrium points in elliptical restricted three body problem

Abstract

<p>This paper studies effects of the triaxiality and radiation pressure of both the primaries on the stability of the infinitesimal motion about triangular equilibrium points in the elliptical restricted three body problem(ER3BP), assuming that the bigger and the smaller primaries are triaxial and the source of radiation as well. It is observed that the motion around these points is stable under certain condition with respect to the radiation pressure and oblate triaxiality. The critical mass ratio depends on the radiation pressure, triaxiality, semi -major axis and eccentricity of the orbits. It is further analyzed that an increase in any of these parameters has destabilizing effects on the orbits of the infinitesimal.</p>

Motion around the Triangular Equilibrium Points in the Circular Restricted Three-Body Problem under Triaxial Luminous Primaries with Poynting-Robertson Drag

“…In the absence of P-R drags, with oblate luminous primaries, describing circular orbit, our result agrees with [18]; without PR-drags of the primaries, our result coincide with [14,21]. In the presence of PR drag with a bigger luminous primary and a triaxial companion, our result coincide with the findings of [26] while in the case of a smaller oblate body together with a luminous triaxial body, it agrees with [25].…”

“…This circular restricted three-body problem (CR3BP) describes the motion of the infinitesimal mass moving in circular orbits and thus will not sufficiently describe the motion when certain perturbing forces are involved. This led scientists and mathematicians into an extensive study of the circular restricted three-body problem (CR3BP) from which models have been developed on the basis of different perturbing forces [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”

“…The Authors of [8] described a model with the bigger primary as an oblate spheroid for which the triangular point L 4 is stable for all values of the mass ratio while in [14], the two primaries are treated as rigid triaxial bodies where it was established that the collinear points are unstable as oppose to the triangular points that are stable for a range of mass ratio less than the critical mass ratio. In [18], the problem is examined on the basis that both primaries are oblate spheroids for which the triangular points are stable within a given region while [21] examined the case for which both bodies are triaxial rigid bodies.…”

Characteristics exponents of the triangular solution in the elliptical restricted three-body problem under radiating and triaxial primaries

“…[17]. The differential equation of motion of the third body P in nondimensional barycentre, pulsating and non-uniformly rotating coordinate system (x, y) is written in the form: Where m 1 and m 2 are masses of the primaries.…”

“…[12], Narayan, A., Kumar, C.R. [13], Narayan, A., Singh, N. [14], Narayan, A., Usha, T. [15] , Singh, J., Aishetu, U. (2012), Singh, J., Aishetu, U.…”