题目内容
中国现已掌握神舟飞船与太空中目标飞行器的自动和手动对接技术,这就意味着宇航员可乘飞船对在轨航天器进行维护。宇航员现欲乘神舟飞船对在距月球表面高度为
圆轨道上运行的月球卫星进行在轨维修。
已知月球半径
,月球表面重力加速度为
,计算过程中可不计地球引力的影响,试根据你所学的知识解答下列问题:
(1)试求维护卫星时航天飞机的速度大小。计算结果用
、
、
表示。
(2)已知地球自转周期为
,则该卫星每天可绕月球转几圈?计算结果用
、
、
、
表示。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824174051850313.png)
已知月球半径
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824174052053303.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824174052381273.png)
(1)试求维护卫星时航天飞机的速度大小。计算结果用
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824174051850313.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824174052053303.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824174052381273.png)
(2)已知地球自转周期为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824174053457361.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824174051850313.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824174052053303.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824174052381273.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824174053457361.png)
(1)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241740553141285.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824174055017897.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241740553141285.png)
试题分析:(1)根据万有引力定律,在月球上的物体
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824174055548932.png)
卫星绕月球作圆周运动,设速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824174055766265.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241740560161301.png)
①②式联立解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824174055017897.png)
航天飞机与卫星在同一轨道,速度与卫星速度相同
(2)设卫星运动周期为T,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241740565621630.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241740567961631.png)
则每天绕月球运转的圈数为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241740553141285.png)
点评:在天体运动这块,公式比较多,所以在计算过程中一定要注意正确使用公式
![](http://thumb2018.1010pic.com/images/loading.gif)
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