题目内容
图示是我国的“探月工程”向月球发射一颗绕月探测卫星“嫦娥一号”过程简图.“嫦娥一号”进入月球轨道后,在距离月球表面高为h的轨道上绕月球做匀速圆周运动.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082413173075418914.png)
小题1:若已知月球半径为R月,月球表面的重力加速度为g月,则“嫦娥一号”环绕月球运行的周期为多少?
小题2:若已知R月=
R地,g月=
g地,则近月卫星的运行速度约为近地卫星运行速度的多少倍?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082413173075418914.png)
小题1:若已知月球半径为R月,月球表面的重力加速度为g月,则“嫦娥一号”环绕月球运行的周期为多少?
小题2:若已知R月=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131730801302.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131730832335.png)
小题1:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241317308791148.png)
小题2:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131731004497.png)
(1)设“嫦娥一号”环绕月球运行的周期是T,根据牛顿第二定律得
G
= mg月 …………………(2分)
G
= m
(R月+h)…………(2分)
解得T=
……………(2分)
(2)对于靠近天体表面的行星或卫星有mg=
,v=
…………(2分)
由v=
知,
=
………………(1分)
将R月=
R地,g月=
g地代入计算,可知
(≈0.2)………(2分)
G
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131731066726.png)
G
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131731097958.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131731113573.png)
解得T=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241317308791148.png)
(2)对于靠近天体表面的行星或卫星有mg=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131731191571.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131731238422.png)
由v=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131731238422.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131731285497.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131731316778.png)
将R月=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131730801302.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131730832335.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131731441823.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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