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Abstract

The present study deals with the applications of the planar Newtonian four-body problem to
the different central configurations. The basic concept of central configuration is that the
vector force must be in the direction of the position vector so that the origin may be taken at
the centre of mass of the four bodies and the force towards the position vector multiplied by
corresponding inverse mass is directly proportional to the position vector relative to the
centre of mass. For applying the Newtonian four body problem to the central configuration,
the equations of motion of four bodies have been established in inertial frame. By the
methods of previous authors, some mathematical tools of the planar problem have been
developed and by using them, the Newtonian four-body problem have been reduced to central
configuration. All the previously generated mathematical models depend upon the directed
areas, weighted directed areas and position vectors of the centre of the bodies. With the help
of these models some conditions have been established, which show that the origin is located
at the centre of mass of the system. Finally these conditions have been used to some
particular cases of concave configuration, convex configuration and symmetric configuration
to generate some tools which will be helpful for further researches of this field.

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