Zero velocity curves of a dust grain around equilibrium points under effects of radiation, perturbations and variable Kruger 60
- Physics & Astronomy International Journal
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Oni Leke, Mmaju Celestine
Abstract
The paper unveils zero velocity curves of a dust grain particle around eleven equilibrium
points under effects of radiation, perturbations and variable Kruger 60. The study is
carried out using the model formulations of the restricted three-body problem in which
the primaries are assumed to be radiation sources and vary their masses with time coupled
with small perturbations in the Coriolis and centrifugal forces due to circular motion. The
equations of motion of the non-autonomous system and those of the autonomized equations
with constant coefficients have been stated and the equilibrium points explored. Numerical
illustrations have been provided to support the study for a particular case when the dust
grain moves under the influence of the central binary Kruger 60. It is seen that there exist a
pair of triangular points, five collinear equilibrium points, and four out-of-plane equilibrium
points, which are defined by the radiation pressure of the Kruger 60, centrifugal perturbation
and the arbitrary constant K which defines the sum of the masses of Kruger 60. Finally,
the zero velocity curves of the dust grain around the equilibrium points are explored and
the effects of the parameters divulged. In the case of the collinear equilibrium points, as K
increases the region where motion is allowed decreases, while in the case of the triangular
points, the dust grain is permitted to move around the primaries and the triangular points
and is also allowed access to the exterior realm as K increases. In the case of the out-ofplane equilibrium points, as K increases the region where motion is allowed decreases
while the presence of the perturbing forces due to radiation and centrifugal perturbation
also reduces the region where motion of the dust grain particle is allowed. It is seen that
the Coriolis perturbation do not affect the locations and zero velocity curves around all the
equilibrium points.
Keywords
Kruger 60, radiation pressure, perturbations, variable masses, zero velocity curves
