In this paper, we present a modified version of Hill’s dynamical system that is called the quantized Hill’s three-body problem in the sense that the equations of motion for the classical Hill’s problem are now derived under the effects of quantum corrections. To do so, the position variables and the parameters that correspond to the quantum corrections of the respective quantized three-body problem are scaled appropriately, and then by taking the limit when the parameter of mass ratio tends to zero, we obtain the relevant equations of motion for the spatial quantized Hill’s problem. Furthermore, the Hamiltonian formula and related equations of motion are also derived.

We consider a modification of the restricted three-body problem where the primary (more massive body) is a triaxial rigid body and the secondary (less massive body) is an oblate spheroid and study periodic motions around the collinear equilibrium points. The locations of these points are first determined for 10 combinations of the parameters of the problem. In all 10 cases, the collinear equilibrium points are found to be unstable, as in the classical problem, and the Lyapunov periodic orbits around them have been computed accurately by applying known corrector–predictor algorithms. An extensive study on the families of three-dimensional periodic orbits emanating from these points has also been done. To find suitable starting points, for all the computed families, semianalytical solutions have been obtained, for both two- and three-dimensional cases, around the collinear equilibrium points using the Lindstedt–Poincaré method. Finally, the stability of all computed periodic orbits has been studied.