Searching stable orbits in BiER4BP with variable eccentricity for exploring orbiter dynamics near the moon of planet

Abstract

This study presents a novel semi-analytical solution for the motion of a small orbiter influenced by the combined Newtonian attraction of three primary bodies, M₁, M₂, and M₃, which move in hierarchical elliptical orbits within the same plane. In this configuration, M₃ ≪ M₂ ≪ M₁, where M₂ orbits M₁ with slowly variable orbital eccentricity, and M₃ revolves around M₂. The resulting solution describes a closed, self-returning spiral trajectory aligned with the ray extending from the Sun to the Earth-Moon system. The orbital radius, which exceeds the semi-major axis a₂ of the {M₂, M₃} binary system, experiences quasi-periodic oscillations along the Oy, Oz (close to zero locations), and Ox axes near the system's barycenter. This motion forms a 3D spiraling trajectory around and above the {M₂, M₃} binary. The study demonstrates that this type of stable orbital configuration, characterized by closed spiral motion within a finite spatial volume ({x, y, z}, x ~ 1, y ~ 0, z → 0), is dynamically feasible in the context of the Bi-Elliptic Restricted Four-Body Problem (BiER4BP). The orbiter remains near the ray connecting the Sun to the Earth-Moon system, suggesting its potential relevance for the stable artificial satellite drift dynamics near Earth’s Moon. The analysis highlights that such an artificial satellite, positioned distant approximately 1 astronomical unit from the Sun, can exhibit stable oscillatory, spiral motion close to this Sun-Earth line. This result offers new insights into stable dynamical behaviors in celestial mechanics, particularly in multi-body gravitational systems.