Abstract
When the gravitational three-body problem in the plane is studied in the Pina and Jimenez system of coordinates, the shape sphere is simply related to the coordinates. This shape sphere is considered as a four 2-sphere, where contrary to other authors, the poles of the sphere occur for two equal inertia moments, not for the Lagrange points. In this sphere the central configurations correspond to fixed points of the sphere which are functions of the three masses. The binary collisions are also represented as points in this sphere. The hyperbolic geometry of the collision angles is the link between the instantaneous moments of inertia and the distances between particles.
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