题目内容
分已知“嫦娥一号”绕月飞行轨道近似为圆形,距月球表面高度为H,飞行周期为T,
月球的半径为R,引力常量为G。求:
(1)“嫦娥一号”绕月飞行时的线速度大小;
(2)月球的质量;
(3)若发射一颗绕月球表面做匀速圆周运动的近月飞船,则其绕月运行的线速度应为多大.
月球的半径为R,引力常量为G。求:
(1)“嫦娥一号”绕月飞行时的线速度大小;
(2)月球的质量;
(3)若发射一颗绕月球表面做匀速圆周运动的近月飞船,则其绕月运行的线速度应为多大.
(1)
(2)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250003362921024.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000336261811.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250003362761003.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250003362921024.png)
试题分析:(1)“嫦娥一号”的轨道半径r=R+H,根据线速度与轨道半径和周期的关系得:
“嫦娥一号”运行的线速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000336339881.png)
(2)设月球质量为M,“嫦娥一号”的质量为m,根据万有引力定律和牛顿第二定律,
对“嫦娥一号”绕月飞行有
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250003363541414.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250003363861162.png)
(3)设绕月球表面做匀速圆周运动的飞船的质量为m0,线速度为v0,绕月球表面做匀速圆周运动的飞船轨道半径约R.根据万有引力定律和牛顿第二定律,对飞船绕月飞行有
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250003364011022.png)
又
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250003363861162.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250003364321178.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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