In this thesis I examine and compare the topology of initial value space for planar three-body for gravity and a gravity-like molecular potential. We developed code to numerically simulate trajectories for planar collisions capable of studying chaotic structure, close encounters, and the Heggie-Hills Law. This investigation of gravity and the modified harmonic oscillator (MHO) allows me to compare stellar scattering dynamics with molecular scattering dynamics. This work allows helps to build connections between molecular dynamics and gravitational dynamics, helping to understand the connection between the two regimes.