Abstract
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.
Highlights
As we known, the geostationary earth orbit (GEO) has the same period as the Earth’s rotation period
The purpose is to discover the fundamental properties of the transfers in the classical circular restricted three-body problem (CR3BP) model and the bi-circular four-body problem (BR4BP) model, such as, whether the transfer via lunar swing-by with the orbital element constraints (i.e., Its orbital altitude and inclination during the departure low earth orbit (LEO) and insert retro-GEO phase) and the two-impulse tangential maneuvers is existed or not? What is the foundational feature of this transfer in the planar model? How much is the lunar gravity assisted effect for the orbital inclination changeable capacity? After the concise statement of the problem in “Problem statement”, the first two questions are exhibited in “Properties in the planar model”, and the last question is exhibited in “Properties in the spatial model”
The transfer exists, which is from an LEO of deploying the retro-GEO via lunar swing-by with two tangential maneuvers
Summary
The orbital perigee altitude and the inclination during the return retro-GEO phase in his work did not match the retro-GEO. Select the orbital elements both at the moment of trans-lunar injection and at the moment of the perigee during the return retro-GEO phase as the traversal searching variables. The trans-lunar phase is computed using the numerical integration by the positive direction of time, while the return retro-GEO phase is computed using the numerical integration by the negative direction of time It has three orbital elements as shown, the position on O − x of xp , the velocity value of vp , and the velocity angle of ξp.
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