Scattering of The Collinear Three-Body Problem

Abstract

The n-body problem is the study of the motion of n-point masses in space governed by Newton’s equation. The twosingularities where Newton’s equation failed to describe the motions are where the distance between any bodies is at zero (collision) or at infinity. Many researchers studied the first case of singularity. In this dissertation, we studied the second case where the distances among the bodies approach infinity under the collinear setup. We will introduce a geometric object that can help us to understand the behavior not only at infinity but, more importantly, the behavior of the bodies when they are near infinity.