Periodic Orbits of Quantised Restricted Three-Body Problem

Abstract

In this paper, perturbed third-body motion is considered under quantum corrections to analyse the existence of periodic orbits. These orbits are studied through two approaches to identify the first (second) periodic-orbit types. The essential conditions are given in order to prove that the circular (elliptical) periodic orbits of the rotating Kepler problem (RKP) can continue to the perturbed motion of the third body under quantum corrections where a massive primary body has excessive gravitational force over the smaller primary body. The primaries moved around each other in circular (elliptical) orbits, and the mass ratio was assumed to be sufficiently small. We prove the existence of the two types of orbits by using the terminologies of Poincaré for quantised perturbed motion.