Abstract
Abstract This paper aims to study the effect of the triaxiality and the oblateness as a special case of primaries on the locations and stability of the collinear equilibrium points of the elliptic restricted three body problem (in brief ERTBP). The locations of the perturbed collinear equilibrium points are first determined in terms of mass ratio of the problem (the smallest mass divided by the total mass of the system) and different concerned perturbing factors. The difference between the locations of collinear points in the classical case of circular restricted three body problem and those in the perturbed case is represented versus mass ratio over its range. The linear stability of the collinear points is discussed. It is observed that the stability regions for our model depend mainly on the eccentricity of the orbits in addition to the considered perturbations.
Highlights
This paper aims to study the effect of the triaxiality and the oblateness as a special case of primaries on the locations and stability of the collinear equilibrium points of the elliptic restricted three body problem
The locations of the perturbed collinear equilibrium points are first determined in terms of mass ratio of the problem and different concerned perturbing factors
The general three-body problem is described as a third body of infinitesimal mass m3 that is attracted by two finite masses called primaries but not influencing their motion, moves in the plane defined by the two revolving primaries
Summary
The general three-body problem is described as a third body of infinitesimal mass m3 that is attracted by two finite masses called primaries but not influencing their motion, moves in the plane defined by the two revolving primaries. The calculations of the effect of different perturbations like oblateness, ellipsoidal primaries and photogravitational relativistic on the equilibrium points locations and its stability in the restricted three-body problem are investigated, Wang et al (2018); Wu et al (2018); Abd El-Salam and Abd El-Bar (2018) and Xin and Hou (2017). They concluded that the collinear points stability is highly affected at a whole range of mass, contrary to the stability regions of the triangular points which are affected differently depend on the perturbations kind. A numerical simulations are presented in sec. 6 with discussion and a work conclusion is shown in sec. 7
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