Effects of the albedo and disc on the zero velocity curves and linear stability of equilibrium points in the generalized restricted three-body problem

Abstract

The most important aspects of a dynamical system are its stability and the factors which affects the stability property. This paper presents the analysis of the effects of albedo and disc on the zero velocity curves, existence of equilibrium points and on their linear stability in a generalized restricted three body problem that consists of motion of an infinitesimal mass under the uniform gravity field of radiating-oblate primary, oblate secondary and a disc, which is rotating about the common center of the mass of the system. A significant effect of albedo and disc are observed on the zero velocity curves, positions of equilibrium points and on the stability region. Linear stability analysis of collinear equilibrium points is performed with respect to mass ratio µ and albedo parameter of secondary, separately and it is found that these are unstable in both the cases. On the other hand, non-collinear equilibrium point is stable in a certain range of mass ratio. After analyzing individual as well as combined effect of radiation pressure force of the primary, albedo of secondary, oblateness of both the massive bodies and the disc, it is found that these perturbations play a significant on the motion of infinitesimal mass in the vicinity of equilibrium points. These results may be help to analyze more generalized problem of few bodies under the influence of different kind of perturbations such as P-R drag, solar wind drag etc. Present study is limited to the regular symmetric disc which will extend later.

Effect of the Planetesimal Belt on the Dynamics of the Restricted Problem of 2 + 2 Bodies

“…Two infinitesimal bodies, P 1 and P 2 , of dimensionless masses µ 1 and µ 2 , respectively, move in the gravitational field while mutually attracting each other without perturbing the primaries. The perturbed mean motion n can be considered as in [15][16][17][18],…”

“…Dustbelt-like structures are also present in the Proxima Centauri system. Many researchers have studied the effect of the asteroid belt in CRTBP [13][14][15][16], and found that these perturbations exhibit significant changes in the equilibrium position. In this paper, we investigate some new aspects of R2+2BP, along with the disk-like belt effect on the potential function; as such, we found the change in the equilibrium positions.…”

Impacts of Poynting–Robertson Drag and Dynamical Flattening Parameters on Motion around the Triangular Equilibrium Points of the Photogravitational ER3BP

“…Assuming that the dominant bodies are in elliptical motion with constant angular velocity n(mean motion), then the orbits of m 1 and m 2 with respect to the centre of mass, with semi-major axes, would be a 1 � (m 2 /(m 1 + m 2 ))a and a 2 � (m 1 /(m 1 + m 2 ))a, respectively, having the same eccentricity; thus, the motion of the bigger and smaller primary can be written as [1,28]…”

“…Also, the orbital eccentricity of the Earth is e ∼ 0.0167. Now, the dynamical flattening parameters of the primary bodies are given by e radiation pressure factor of the Sun q is defined as q � 1 − α such that α can be expressed as α � (L ⊙ /(2πGm 1 cκ)) [28], where L ⊙ is the luminosity of the Sun, G is the gravitational constant, c is the speed of light, and κ is the mass per unit area. By using Stefan-Boltzmann's law, the luminosity of the primary can be expressed as…”

“…⊙ , where σ is the Stefan-Boltzmann's constant (see [28]). Also, the dimensionless velocity of light and the mass ratio of the Sun-Earth system are given by c d ∼ 10064.84 and μ ∼ 3.0035 × 10 − 6 , respectively [29].…”