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The planar circular restricted three-body problem with modified Newtoniangravity is used in order to determine the Newton-Raphson basins of attractionassociated with the equilibrium points. The evolution of the position of thefive Lagrange points is monitored when the value of the power $p$ of thegravitational potential of the second primary varies in predefined intervals.The regions on the configuration $(x,y)$ plane occupied by the basins ofattraction are revealed using the multivariate version of the Newton-Raphsoniterative scheme. The correlations between the basins of convergence of theequilibrium points and the corresponding number of iterations needed forobtaining the desired accuracy are also illustrated. We conduct a thorough andsystematic numerical investigation by demonstrating how the dynamical quantity$p$ influences the shape as well as the geometry of the basins of attractions.Our results strongly suggest that the power $p$ is indeed a very influentialparameter in both cases of weaker or stronger Newtonian gravity.

Investigating the Newton-Raphson basins of attraction in the restricted three-body problem with modified Newtonian gravity