Exploring the fractal basins of convergence in the restricted four-body problem with oblateness. (June 2018) - Suraj, Md Sanam; Mittal, Amit; Arora, Monika; Aggarwal, Rajiv
Abstract: The present manuscript deals with the restricted four-body problem when all the primaries are oblate spheroids. This paper unveils the effect of oblateness on the existence, locations and stability of the libration points. It is assumed that three oblate primaries having equal masses are set in Lagrangian equilateral triangle configuration. It is observed that there exist ten libration points in configuration ( x, y ) -plane out of which four are collinear and six are non-collinear for oblateness parameter A ∈ [ 0, 0 . 681949 ) . Further, for the oblateness parameter A ∈ ( 0 . 681949, 1 ), there exist only four libration points out of which two are collinear and two are non-collinear. Out-of-plane libration points are also investigated and it is found that in-plane and out-of-plane libration points are unstable. It is further observed that oblateness parameter has substantial effect on the regions of possible motion. Further, we have numerically investigated the Newton–Raphson basins of convergence associated with the libration points to unveil that how the oblateness parameter influences the domain of convergence. Highlights: We investigate the effect of oblateness in the restricted four-body problem. The parametric evolutions of the positions of libration points are investigated. The regions of possible motions are drawn. The multivariate version of Newton–Raphson iterative scheme has been used to study the basins of convergence.