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.
CUI Hutao, ZHANG Zhenjiang, CUI Pingyuan
. Research on Displaced Non-Keplerian Orbit of Gravitational Tractor in Three-body System[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2011
, 32(6)
: 997
-1006
.
DOI: CNKI:11-1929/V.20101217.1207.000
[1] 胡维多, Scheeres D J, 向开恒. 飞行器近小行星轨道动力学的特点及研究意义 [J]. 天文学进展, 2009, 27(6): 152-166. Hu Weiduo, Scheeres D J, Xiang Kaiheng. The characteristics of near asteroid orbital dynamics and its implication to mission analysis [J]. Progress in Astronomy, 2009, 27(6): 152-166. (in Chinese)
[2] Chapman C R, Morrison D. Impact on the earth by asteroids and comets: assessing the hazard [J]. Nature (London), 1994, 367(6458): 33-39.
[3] Rabinowitz D, Helin E, Lawrence K, et al. A reduced estimate of the number of kilometre-sized near-earth asteroids [J]. Nature (London), 2000, 403(6766): 165-166.
[4] Ralph K, Gerhard H, Ekkehard K. Optimal deflection of neos en route of collision with the earth [J]. Icarus, 2006,182(2): 482-488.
[5] Alvarez L W, Alvarez W, Asaro F, et al. Extraterrestrial cause for the cretaceous tertiary extinction [J]. Science, 1980, 208: 1095-1108.
[6] Ahrens T J, Harris A W. Deflection and fragmentation of near-earth asteroids [J]. Nature (London), 1992, 360(6403): 429-433.
[7] Vasilt M. Concepts for near earth asteroid deflection using spacecraft with advanced nuclear and solar electric propulsion systems [J]. Journal of the British Interplanetary Society, 2005, 58(7): 268-278.
[8] Scheeres D J, Schweickart R. The mechanics of moving asteroids . AIAA-2004-1446, 2004.
[9] Schweickart R, Chapman C, Durda D, et al. Threat mitigation: the asteroid tugboat . White Paper 041, Presented at NASA Workshop on NEO Detection, Characterization, and Threat Mitigation, 2006.
[10] Edward T L, Stanley G L. A gravitational tractor for towing asteroids [J]. Nature (London), 2005, 438(7065): 177-178.
[11] Colin R M. The existence and stability of families of displaced two-body orbits [J]. Celestial Mechanics and Dynamical Astronomy, 1997, 67(2): 167-180.
[12] Colin R M. Near earth object orbit modification using gravitational coupling [J]. Journal of Guidance, Control, and Dynamics, 2007, 30(3): 870-873.
[13] McInnes C R. Dynamics, stability, and control of displaced non-keplerian orbits [J]. Journal of Guidance, Control, and Dynamics, 1998, 21(5): 799-805.
[14] John B, Colin R M. Dynamics and control of displaced periodic orbits using solar-sail propulsion [J]. Journal of Guidance, Control, and Dynamics, 2006, 29(3): 27-537.
[15] 刘林. 航天器轨道理论 [M]. 北京, 国防工业出版社, 2000: 114-120. Liu Lin. Orbit theory of spacecraft [M]. Beijing: National Defense Industry Press, 2000: 114-120.( in Chinese)
[16] Bong W. Dynamics and control of gravity tractor spacecraft for asteroid de?ection //AIAA/AAS Astrodynamics Specialist Conference and Exhibit. 2008.
[17] Jinkins J, Singal P, Davis J. Impact keyholes and collision probability analysis for resonant encounter asteroids. White Paper 070, Presented at NASA Workshop on NEO Detection, Characterization, and Threat Mitigation, 2006.
[18] Kahle R, Hahn G, Kugrt E. Optimal deflection of NEOs in route of collision with the Earth [J]. Icarus, 2006, 182(2): 482-488.
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