Properties of the lunar gravity assisted transfers from LEO to the retrograde-GEO

The retrograde geostationary earth orbit (retro-GEO) is an Earth’s orbit. It has almost the same orbital altitude with that of a GEO, but an inclination of 180°. A retro-GEO monitor-satellite gives the GEO-assets vicinity space-debris warnings per 12 h. For various reasons, the westward launch direction is not compatible or economical. Thereby the transfer from a low earth orbit (LEO) to the retro-GEO via once lunar swing-by is a priority. The monitor-satellite departures from LEO and inserts into the retro-GEO both using only one tangential maneuver, in this paper, its transfer’s property is investigated. The existence of this transfer is verified firstly in the planar circular restricted three-body problem (CR3BP) model based on the Poincaré-section methodology. Then, the two-impulse values and the perilune altitudes are computed with different transfer durations in the planar CR3BP. Their dispersions are compared with different Sun azimuths in the planar bi-circular restricted four-body problem (BR4BP) model. Besides, the transfer’s inclination changeable capacity via lunar swing-by and the Sun-perturbed inclination changeable capacity are investigated. The results show that the two-impulse fuel-optimal transfer has the duration of 1.76 TU (i.e., 7.65 days) with the minimum values of 4.251 km s(−1) in planar CR3BP, this value has a range of 4.249–4.252 km s(−1) due to different Sun azimuths in planar BR4BP. Its perilune altitude changes from 552.6 to 621.9 km. In the spatial CR3BP, if the transfer duration is more than or equal to 4.00 TU (i.e., 17.59 days), the lunar gravity assisted transfer could insert the retro-GEO with any inclination. In the spatial BR4BP, the Sun’s perturbation does not affect this conclusion in most cases.