We have studied the restricted four-body problem
(R4BP) with the effect of the small perturbation in the Cori-
olis and centrifugal forces on the libration points and zero
velocity curves (ZVCs). Further, we have supposed that all
the primaries are set in an equilateral triangle configuration,
moving in the circular orbits around their common centre of
mass. We have observed that the effect of the small perturba-
tion in centrifugal force has a substantial effect on the loca-
tion of libration points but a small perturbation in the Cori-
olis force has no impact on the location of libration points.
But the stability of the libration points is highly influenced
by the effect of the small perturbation in the Coriolis force.
It is observed that as the Coriolis parameter increases, the
libration points become stable. Further, it is found that the
effect of the small perturbation in the centrifugal force has
a substantial influence on the regions of possible motion.
Also, when the effect of small perturbation in the centrifu-
gal force increases the forbidden region decreases; here the
motion is not possible for the infinitesimal mass. It is ob-
served when the value of the Jacobian constant decreases,
the regions of possible motion increase. In addition, we have
also discussed how small perturbations in the Coriolis and
centrifugal forces influence the Newton–Raphson basins of
convergence.

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• On the restricted four-body problem with the effect of small perturbations in the Coriolis and centrifugal forces