Astronomy and Cosmogony

The motion properties of the infinitesimal body in the framework of bicircular Sun perturbed Earth–Moon system

In this paper, a new version of the restricted three-body problem is considered. That is the spatial quantized restricted three-body problem. The equations of motion of the infinitesimal body are constructed. The equilibria points in plane of primaries motion and out of plane are explored under the quantized gravitational potential effect. The permissible and forbidden regions of motion are also analyzed in both planes, with respect to relative small, middle and large values of the Jacobian constant. We observe that the size of permissible (forbidden) regions of motion are decreasing (increasing) with increasing the Jacobian constant values and vice versa. We demonstrate that the permissible regions of motion shrink with increasing the Jacobian constant value, and the infinitesimal body will be compelled to move in a surrounding region of one the primaries. It will has no free to switch or exchange its motion from one to other. Furthermore, we emphasize that, in spit of quantum corrections are tiny small effect, there is no warranty that the dynamical system properties are unaffected. Because there are changes in the locations of equilibria points and the regions of permissible motion, even which are very small. We think that these corrections may have considerable impact and can be tested within frame of small distances. Substantially, we are determine the parametric evolution of the equilibrium points of the system, along with the energetically allowed and forbidden regions of motion.

Analysis of the spatial quantized three-body problem

This article aims to investigate the points of equilibrium and the associated convergence basins in the restricted problem with two primaries, with a modified gravitational potential. In particular, for one of the primary bodies, we add an external gravitational term of the form 1/r3, which is very common in general relativity and represents a gravitational field much stronger than the classical Newtonian one. Using the well-known Newton–Raphson iterator we numerically locate the position of the points of equilibrium, while we also obtain their linear stability. Furthermore, for the location of the points of equilibrium, we obtain semi-analytical functions of both the mass parameter and the transition parameter. Finally, we demonstrate how these two variable parameters affect the convergence dynamics of the system as well as the fractal degree of the basin diagrams. The fractal degree is derived by computing the (boundary) basin entropy.

Basins of convergence of equilibrium points in the restricted three-body problem with modified gravitational potential

Periodic solution of the nonlinear Sitnikov restricted three-body problem

A Planar Five-body Problem in a Framework of Heterogeneous and Mass Variation Effects

This paper presents the motion of the infinitesimal body in the circular restricted four body problem in which the masses of the primaries as well as the mass of the infinitesimal body vary and also one of the primaries is taken as source of radiation pressure due to which albedo effects are produced by another two primaries and one primary is considered as oblate body which is placed at the triangular equilibrium point of the classical restricted three body problem. We have evaluated the equations of motion of the infinitesimal variable mass under the effect of these perturbations and also the variation of Jacobi Integral constant has been determined. We have studied numerically the equilibrium points, Poincare surface of sections and basins of attraction in five cases (i. Third primary is placed at one of the triangular equilibrium points of the classical restricted three body problem, ii. Variation of masses, iii. Solar radiation pressure, iv. Albedo effect, v. Oblateness effect.) by using Mathematica software. Finally, we have examined the stability of the equilibrium points and found that all the equilibrium points are unstable.

Abdullah A. Ansari

Papers

The motion properties of the infinitesimal body in the framework of bicircular Sun perturbed Earth–Moon system

A Planar Five-body Problem in a Framework of Heterogeneous and Mass Variation Effects

Investigation of the effect of albedo and oblateness on the circular restricted four variable bodies problem

Effect of oblateness and viscous force in the Robe’s circular restricted three-body problem

Perturbed Hill's problem with variable mass