Exploring the Planar Circular Restricted Three-Body Problem with Prolate Primaries

Abstract

We numerically investigate the convergence properties of the circular restricted three-body problem with prolate primaries, by using the Newton- Raphson iterative scheme. In particular, we examine how the oblateness coefficient $A$ influences several aspects of the method, such as its speed and efficiency. Color-coded diagrams are used for revealing the basins of convergence on the configuration space. Additionally, we compute the degree of fractality of the convergence basins on the physical plane, as a function of the oblateness coefficient, by using different computational tools, such as the uncertainty dimension and the (boundary) basin entropy.