在“嫦娥探月”工程中,假设月球半径为R,月球表面的重力加速度

在“嫦娥探月”工程中,假设月球半径为R,月球表面的重力加速度为,飞船在半径为4R的圆形轨道Ⅰ运动,到达轨道的A点点火变轨进入椭圆轨道Ⅱ,到达轨道的近月点B再次点火进入月球近月轨道Ⅲ绕月球作圆周运动.求:

(1)飞船在轨道Ⅰ上的运行速率;

(2)飞船在A点处点火后瞬间与点火前相比,速度是变大还是变小?

(3)飞船在轨道Ⅲ绕月球运行一周所需的时间.

答案

(1)

(2)减小

(3)


解析:

(1)设月球的质量为M,飞船的质量为m,则

(4分)

      (4分)

解得        (2分)

(2)减小(2分)                   

(3)设飞船在轨道Ⅲ绕月球运行一周所需的时间为T,则

(3分)

     (2分)

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