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The fractal basins of convergence (BoC) linked with the equilibrium points are explored in the (N + 1)− body ring problem under the effect of small perturbations in the Coriolis and centrifugal forces when the bodies are sources of radiation. The evolution of the positions and the stability of the libration points and the possible regions of motion are determined as the function of mass parameter, the Coriolis, and centrifugal and radiation parameters. In addition, the parametric variation of the effect of the small perturbations in the Coriolis and centrifugal forces on the stability of the equilibrium points are also illustrated numerically. The multivariate version of the Newton–Raphson(NR) iterative method is used to analyze the effect of the radiation parameters and mass parameter on the topology of the BoC. [ABSTRACT FROM AUTHOR]

In the present paper, an effort to generalize the restricted problem of 2 + 2 bodies has been made by considering the primary bodies m1 and m2 to be a point mass and straight segment of length 2l, respectively. The motion of the two infinitesimal bodies mi, i = 3, 4 has been investigated, in which each mi, i = 3, 4 is moving in the gravitational field of mj, j = 1, 2, 3, 4 with i ≠ j. For the present problem, 14 equilibrium points are obtained, of which 6 are collinear and the rest are noncollinear. The length parameter l has a subsequent effect on the location of all the equilibrium points. Systematic stability analysis has been carried out by using the theory of perturbation. All the equilibrium points are found to be unstable. [ABSTRACT FROM AUTHOR]

This article aims to numerically investigate the orbital dynamics of the planar circular‐restricted three‐body problem, where the two primary bodies have equal masses and an oblate spheroid shape. By numerically integrating several large sets of initial conditions of both retrograde and prograde orbits, we classify them into three main categories: (a) bounded (regular or chaotic), (b) escaping, and (c) collision orbits. We reveal the motion of the test particle by presenting color‐coded diagrams, where the initial conditions are mapped to the orbit type and studied as a function of the total orbital energy (or equivalently of the Jacobi constant) as well as of the oblateness coefficient. Our numerical results are compared with related previous ones, corresponding to the classical version of the planar‐restricted three‐body problem. The presented outcomes have practical physical applications as they can be used for modeling the motion of a massless test particle in the gravitational field of a binary system of two oblate exoplanets. [ABSTRACT FROM AUTHOR]

The present problem is devoted to the special case of restricted problem of three bodies, always referred as the Copenhagen problem when we consider the primaries of equal masses. In this manuscript, we have considered the third body of infinitesimal mass as variable and moreover, instead of taking only Newtonian potential and forces, a quasi‐homogeneous potential produced by the main primaries has also been taken into account. This implies that, in order to approximate the phenomena such as the radiation pressure or the primaries' nonsphericity, we insert an inverse cube corrective term to the gravitational law of inverse square. In this model, the impact of the parameters, arise as a result of variable mass on the number and locations of the in‐plane and out‐of‐plane equilibrium points, is discussed. Moreover, their stability is also analyzed and the impact of these parameters on the regions, where motion of the third particle is possible, is unveiled. The basins of convergence associated with these equilibrium points are also illustrated by the Newton–Raphson iterative scheme of two or more variables. [ABSTRACT FROM AUTHOR]

In the present problem, we have studied the effect of small perturbations in the Coriolis and centrifugal forces on the locations and stability of libration points by taking the smaller primary as radiating oblate spheroid in the restricted four‐body problem. We have supposed that all the primaries are set in an equilateral triangle configuration, moving in circular orbit around their common center of mass. We have observed that the oblateness and radiation of the third primary, and the effect of the small perturbation in centrifugal force have substantial influences on the locations of libration points but the effect of the small perturbation in the Coriolis force has no impact on their locations. However, the stability of the libration points is highly influenced by the effect of the small perturbation in the Coriolis force. Furthermore, it is obtained that the effect of the small perturbation in the centrifugal force has a substantial influence on the regions of possible motion. In addition, we have also discussed how the oblateness and radiation pressure of the third primary, and the small perturbations in the Coriolis and centrifugal forces influence geometry of the basins of convergence by using multivariate version of the Newton–Raphson iterative scheme. [ABSTRACT FROM AUTHOR]