为了研究太阳-小行星-引力拖车三体系统中引力拖车的轨道运动问题,采用柱坐标系下的Hill方程描述了三体系统中引力拖车的运动情况,应用平均化方法消除周期项的影响,得到平均偏置非开普勒轨道的表达式,并研究了轨道稳定性与引力拖车最大有效拉力等问题。研究表明:三体系统中,在小行星飞行方向(或反方向)上存在偏置非开普勒轨道;与二体系统中的偏置轨道不同,三体系统中的一些偏置轨道是不稳定的,轨道稳定区域可以由偏置量和轨道半径描述;与悬停轨道相比,偏置轨道可以将引力拖车的推进效率提高一倍左右,从而获得更长的工作时间和更大的作用效果。
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.
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