Spacecraft orbit around two fixed bodies.

Being the simplest case in the three-body problem, the motion of a test particle in the field of two fixed bodies was first considered by Euler in 1760. In celestial mechanics, it represents the motion of a spacecraft that is attracted by two celestial bodies fixed in space and do not influence each other. The motion of the spacecraft is influenced by the gravitational forces of these two fixed bodies. Although the scenario of having two centers fixed in inertial space is not practical, some orbits could be applied in actual missions. This paper considers the above situation with a focus on closed orbits around a body such as a dumbbell-shaped asteroid or a binary body. The aim of this study is to demonstrate a robust method to obtain these orbits. Two types of conceivable motion around two fixed bodies are considered: an elliptic orbital motion and an 8-shaped motion. This paper analyzes the characteristics of these motions, where the mass ratio of the celestial bodies and the distance between them are taken as parameters. • The motion of the spacecraft around two inertially-fixed bodies is considered. • A closed orbit of the spacecraft with a rotation number of one is focused. • The conditions required for the lemniscate and planetary motion are elucidated. • Various orbits are systematically obtained by determining a certain parameter. • The analytically obtained orbits are validated by numerical simulations. [ABSTRACT FROM AUTHOR]