# The effect of perturbations on the circular restricted four-body problem with variable masses

Volume 17, Issue 3, pp 365-377 Publication Date: July 18, 2016

### Authors

Abdullah A. Ansari - College of Science at Al-Zulfi, Majmaah University, KSA.
Ziyad A. Alhussain - College of Science at Al-Zulfi, Majmaah University, KSA.
Rabah Kellil - College of Science at Al-Zulfi, Majmaah University, KSA.

### Abstract

This paper presents a new investigation of the circular restricted four body problem under the effect of any variation in coriolis and centrifugal forces. Here, masses of all the bodies vary with time. This has been done by considering one of the primaries as oblate body and all the primaries are placed at the vertices of a triangle. Due to the oblateness, the triangular configuration becomes an isosceles triangular configuration which was an equilateral triangle in the classical case. After evaluating the equations of motion, we have determined the equilibrium points, the surfaces of the motion, the time series and the basins of attraction of the infinitesimal body. We note that, when we increase both the coriolis and centrifugal forces, the curves, surfaces of motion, and the basins of attraction are shrinking except when we fix the centrifugal force and increase the value of coriolis force, the curves are expanding and the equilibrium points are away from the origin. The behavior of the surfaces of motion and the basins of attraction in the last case (fixing the centrifugal force and increasing the value of coriolis force) will be studied next. In all the present study, we found that all the equilibrium points are unstable.

### Keywords

• Circular restricted four body problem
• isosceles triangular configuration
• coriolis and centrifugal forces
• oblateness
• variable mass
• basins of attraction
• unstable.

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