Abstract
The probability of the rendezvous between a single spacecraft and three non-coplanar constellation satellites is studied, and the necessary and sufficient conditions of the rendezvous without orbital maneuver are deduced. The rendezvous orbit design can be transformed into the patching of two spacecraft orbits, either of which can achieve the rendezvous with two satellites. Firstly, due to the precious quality of spherical geometry, the unique existence of the rendezvous orbit for two constellation satellites is proved. Then, according to the difference between equispaced and non-equispaced orbital planes of three satellites, the necessary and sufficient conditions are given respectively, and the calculating method of the spacecraft orbit is proposed. At last, the constraint conditions between two different rendezvous orbits is derived, while the relative position of two groups of objects are under specific distribution. The results can be applied to the rendezvous between a single spacecraft and multiple constellation satellites without orbital maneuver.
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References
Zhu Y W, Yang L P. Study on approaching strategies for on-orbit servicing of satellites (in Chinese). Chin Space Sci Tech, 2007, 27: 14–20
Patera R P. General method for calculating satellite collision probability. J Guid Control Dynam, 2001, 24: 716–722
Patera R P, Peterson G E. Space vehicle maneuver method to lower collision risk to an acceptable level. J Guid Control Dynam, 2003, 26: 233–237
Bai X Z, Xi X N. Close approach of multiple satellites of a constellation for a single spacecraft without orbital maneuver (in Chinese). J Astron, 2005, 26: 114–116
Wang W, Huang W D, Fu X F, et al. Close approach of Walker constellation without orbital maneuver (in Chinese). Chin J Space Sci, 2005, 25: 547–551
Walker J G. Some circular orbit patterns providing continuous whole earth coverage. J Brit Interpla, 1971, 24: 369–384
Xi X N, Wang W, Gao Y D. Fundamental of Near-earth Spacecraft Orbit (in Chinese). Changsha: Press of National University of Defense Technology, 2003. 321–330
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Zhang, J., Wu, M. Necessary and sufficient conditions of the rendezvous between a single spacecraft and three non-coplanar Walker constellation satellites. Sci. China Technol. Sci. 54, 2254–2262 (2011). https://doi.org/10.1007/s11431-011-4523-9
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DOI: https://doi.org/10.1007/s11431-011-4523-9