题目内容
天文工作者观测到某行星的半径为R1,自转周期为T1,它有一颗卫星,轨道半径为R2,绕行星公转周期为T2。若万有引力常量为G,求:
(1)该行星的平均密度;
(2)要在此行星的赤道上发射一颗质量为m的近地人造卫星,使其轨道平面与行星的赤道平面重合,且设行星上无气体阻力,则对卫星至少应做多少功?
(1)该行星的平均密度;
(2)要在此行星的赤道上发射一颗质量为m的近地人造卫星,使其轨道平面与行星的赤道平面重合,且设行星上无气体阻力,则对卫星至少应做多少功?
(1)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250025242451146.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002524214852.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250025242451146.png)
试题分析:
(1)由
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250025242451241.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002524261987.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250025242921412.png)
(2) 设该行星的最小发射速度为v,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002524307989.png)
依题意,该卫星在赤道上时与地球自转同步,设其速度为v0,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002524323745.png)
要发射该卫星,至少要对它做功
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002524339926.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250025243541278.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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