Abstract
In the present work, we shall show an exhaustive numerical analysis of the dynamical behavior of the test particle in the modified restricted three-body problem with variable mass in which the extra effect of the three-body interaction is also taken into account. This additional force ingredient appears in the potential of the classical problem as a new extra term. As the main results, we determine the motion for test particle, under the effect of three-body interaction, which varies its mass according to Jeans’ law (Jeans (1928)). The number and existence of the libration points along with their stability have been investigated as the function of value of the parameters which occur due to variable mass of the test particle. Moreover, the regions of the possible motion are also unveiled where the test particle is free to move. Furthermore, the multivariate version of the Newton-Raphson (NR) iterative scheme is used to determine the outcomes of the used parameters on the topology of the basins of convergence (BoC) linked to the libration points. The numerical analysis shows that the topology of the basins of convergence linked with the libration points is highly influenced by the used parameters. Moreover, we perform a systematic analysis to unveil how the regions of convergence are related with the number of required iterations and also with the corresponding probability distributions.
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