Motion around triangular points in the restricted three-body problem with radiating heterogeneous primaries surrounded by a belt

Abstract

The present paper studies the locations and linear stability of the triangular equilibrium points when both primaries are radiating and considered as heterogeneous spheroid with three layers of different densities. Additionally, we include the effects of small perturbations in the Coriolis and centrifugal forces and potential from a belt (circumbinary disc). It is observed that the positions of the triangular equilibrium points are substantially affected by all parameters (except a perturbation in Coriolis force) involved in the system.The stabilty of motion is found only when $$0 < \mu < \mu_{c}$$ 0 < μ < μ c , where $$\mu_{c}$$ μ c is the critical mass value which depends on the combined effect of radiation pressures and heterogeneity of the primaries, small perturbations and the potential from a belt.It is also seen that the Coriolis force and the belt have stabilizing effect,while the centrifugal force, radiation and heterogeineity of the primaries have destabilizing behaviour.The net effect is that the size of the region of stability decreases when the value of these parameters increases where $$\mu$$ μ is the mass ratio and $$k_{1} ,k_{2}$$ k 1 , k 2 characterize heterogeneity of both primaries. A practical application of this model could be the study of motion of a dust grain near the heterogeneous and luminous binary stars surrounded by a belt.Finally, we carried out and discuss numerical experiments aiming at computing the positions of triangular points and critical masses of three binary systems: Archid, Xi Booties and Kruger 60.

The Dynamical Equations of the Restricted Three-Body Problem with Poynting-Robertson Drag Force and Variable Masses

“…In view of this, several investigations have been carried out when one or both primaries are emitters of radiation pressure. Notable among these are Singh & Ishwar (1999), Singh & Leke (2010, 2012, 2013a and Singh & Sunusi (2020).…”

A Study of the Elliptic Restricted Three-Body Problem with Triaxial and Radiating Primaries Surrounded by a Belt

“…The reason being that such asphericity of celestial bodies causes perturbation, which is of interest to most astrometers and scientists. These have received the attention of [4][5][6][7][8][9][10]. They all studied the effect of perturbations on the orbit of the primaries with or without radiation pressure (s).…”

Effects of Radiation Pressure on the Elliptic Restricted Four-Body Problem

“…Many authors (Ershkov [3] and Ito [4]) have used these models with various perturbations such as eccentricity, solar radiation, the variable mass of primes, Coriolis and centrifugal forces to checkpoints of vibration, linear stability, and periodic orbits. Singh and Haruna [5] have studied the locations and linear stability of trigonometric points when two primaries radiate, and they studied their heterogeneity. The constrained two-circle four-body problem (4BP) is the simplest model used in the four-body problem (4BP) field Andreu [6].…”