Orbital analysis in the planar circular Copenhagen problem using polar coordinates

Abstract

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. KEYWORDS basins of escape/collision, orbit classification, restricted three-body problem MSC CLASSIFICATION 37N05; 70F15; 70F16 MATHEMATICAL DESCRIPTION OF THE DYNAMICAL SYSTEMThe RTBP contains two massive bodies P 1 and P 2 (known as the primaries), while the third body is assumed to act as a test particle. 1 This means that the mass m of the third body is much smaller, comparing with masses m 1 and m 2 of P 1 and P 2 , 2020