The effect of perturbations on the circular restricted fourbody problem with variable masses
Authors
Abdullah A. Ansari
 College of Science at AlZulfi, Majmaah University, KSA.
Ziyad A. Alhussain
 College of Science at AlZulfi, Majmaah University, KSA.
Rabah Kellil
 College of Science at AlZulfi, 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.
MSC
 70F15
 85A20
 85A99
 70F05
 70F07
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