Orbital analysis in the planar circular Copenhagen problem using polar coordinates

We examine the orbital dynamics of the planar Copenhagen problem, by classifying sets of starting conditions of orbits, expressed in polar coordinates. Specifically, we examine how the Jacobi constant influences several aspects of the overall dynamics of the test particle, such as its final state, as well as the time of escape/collision. By using modern diagrams with color codes, we manage to present the different types of basins. It is shown that both the character of the orbits and the fractal degree of the system are highly dependent on the Jacobi constant.