Transfer Trajectories from the Moon to Sun–Earth Halo Orbits

Abstract

H ALO orbits in the vicinity of the Sun–Earth Lagrange points (L1/L2 points) are considered as suitable locations for astronomical observatories because an object around these places can maintain the same orientation with respect to the sun and Earth, and little fuel is required for station keeping of theHalo orbit [1–7]. There have been many investigations of transfers from Earth to Halo orbits [8–14]. In fact, NASA and ESA have already launched several astronomical satellites into Halo orbits, such as ISEE-3, WMAP, and Herschel [15,16]. Recently, the Chinese lunar probe, Chang’e-2, reached the sun–Earth L2 point from the moon after completing its primary objectives. For these Halo orbit missions, the stable manifold, which is an invariant structure of a Halo orbit, is used because the insertion maneuver to the Halo orbit is not required at the cost of the time of flight [17–20]. Moreover, small Halo orbits are generally preferable from the view point of system design because the sun–probe–Earth angle becomes small. However, the stable manifold cannot be used for the direct transfer from Earth to a small Halo orbit (e.g., less than approximately 300,000 km) because the stable manifold of such small Halo orbits cannot approach Earth [14]. On the other hand, the stable manifold of the small Halo orbit via the moon could approach Earth and also increase the opportunity of the launch. Thus, there are some studies about the transfer trajectories from the moon to Halo orbits using the stable manifold. Liu [21] investigated the lunar effect for the transfer to sun–Earth L2 [22]. Wu addressed pre-Lissajous orbit insertion trajectory maneuvers of CHANG’E-2 libration point mission [22]. Xu discussed the evolution of invariant manifolds by low-thrust and lunar gravity [23]. However, the connectivity between the moon and the stable manifold of the sun–Earth system and its quantitative characteristics has not been adequately investigated. Therefore, in this study, for the availability of the stable manifold for the transfer from the moon to the sun–Earth L2 Halo orbit, the characteristic of the connecting point between the moon and the stable manifold is investigated. In addition to this, the relative velocity of the stable manifold with respect to the moon and the time of flight from themoon to theHalo orbit are also analyzed. This study may have applicability to the Demonstration and Experiment of Space Technology for INterplanetary voyage mission by the Japan Aerospace Exploration Agency, whose spacecraft will go to the sun– Earth L2 halo orbit around 2017 though the apogee altitude increases until the lunar encounter by low thrust.