Existence of Cyclic Kite Configuration and Its Application to the Newtonian Four-Body Problem for Mean Motion.

Abstract

This paper deals with the existence of cyclic kite configuration in the Newtonian four body problem. By considering the center of mass of the system as the origin the coordinates of the four- point masses have been expressed in terms of radius R of the common circular orbit in three theorems. We have also proved that the masses lying on both sides of the axis of symmetry of the kite configuration are equal to the non-dimensional mass parameter  then explicit and unique representations of other two masses in terms of the mass parameter  and the total mass ‘M’ became possible. Further by taking  angular velocity  and using first two theorems the equations of motion of each of the four point masses relative to the other three have been derived in synodic frame and hence the mean motion ‘ n’ of the synodic frame was expressed as a function of mass parameter .Later on an attempt has been made for fixing the domain of .