Motion in a combined Newtonian gravitational field

We study a test particle moving under the influence of a system of two massive bodies in Newtonian gravity. Our main objective is to reveal and understand how the ratio of the masses of the two bodies, as well as the energy of the test particle, affects its nature of motion. For this purpose, we conduct a detailed and systematic survey by classifying the initial conditions of trajectories. In particular, we scan the phase space by considering two-dimensional (2D) maps on several types of planes. Then, we numerically integrate the starting conditions on these 2D maps and determine their final states. This procedure allows us to obtain a clear view of how the change in the masses and the energy influence the final states of the test particles.