Research on displaced non-Keplerian orbit of gravitational tractor in three-body system

This paper presents a study of the displaced non-Keplerian orbit in (or opposite to) the direction of an asteroid flight in a three-body system including the sun, the asteroid and the spacecraft. The Hill equation in the cylindrical coordinates is derived and the periodic terms are removed by the averaging-procedure in the first place. Therefore, the formula of a displaced non-Keplerian orbit can be obtained, which indicates that there exists such an orbit in a three-body system. Then the stability condition of the displaced orbit is derived and the stable region is given, which is described by the orbital offset and the orbital radius. The relationship between the maximal pull and the orbital offset is studied and the optimal displaced orbit for asteroid Apophis' gravitational tractor is provided. Finally the hovering orbit and the displaced orbit of a gravitational tractor are analyzed and the motion law of an asteroid under the action of a gravitational tractor is given. Compared with the hovering orbit, a displaced orbit can approximately double the thrust efficiency, thereby acquiring much longer operating time and doing much more work.