Numerical exploration of the quantized Hill problem dynamics

Abstract

In this paper, a numerical exploration of the perturbed Hill three-body problem under quantum corrections is performed. In particular, the existence of location for the equilibrium points and their stability are explored in both plane and out-of-plane motion of the primaries. The zero velocity curves are found for various values of the Jacobian constant and the different closed or trapped regions in which the infinitesimal body can move are also investigated. We demonstrate that the location and stability of equilibrium points as well as the associated curves of zero velocity are significantly affected by the quantum corrections. Furthermore, the infinitesimal third body can move free around the equilibrium points for decreasing values of the Jacobian constant as the quantized correction parameters increase.