题目内容
行星的平均密度为
,靠近行星表面的卫星,其运行周期为T,试证明
为一常数。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830763199.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830779250.gif)
将行星看作一球体,半径为R
则![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830794698.gif)
对卫星,万有引力提供向心力,贴地运行轨道半径![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830810244.gif)
代入上式得
,G为万有引力恒量,
是一个对任何行星都适用的常数。
可见,若近地卫星运行周期为T,则行星平均密度![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830872479.gif)
点拨:若不是近地卫星,利用环绕周期T和轨道半径可计算行星质量M和密度
。
,![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830903577.gif)
将行星看作一球体,半径为R
则![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830794698.gif)
对卫星,万有引力提供向心力,贴地运行轨道半径![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830810244.gif)
代入上式得
,G为万有引力恒量,
是一个对任何行星都适用的常数。
可见,若近地卫星运行周期为T,则行星平均密度![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830872479.gif)
点拨:若不是近地卫星,利用环绕周期T和轨道半径可计算行星质量M和密度
。
,![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830903577.gif)
则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830794698.gif)
对卫星,万有引力提供向心力,贴地运行轨道半径
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830810244.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830825712.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830841498.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830779250.gif)
可见,若近地卫星运行周期为T,则行星平均密度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830872479.gif)
点拨:若不是近地卫星,利用环绕周期T和轨道半径可计算行星质量M和密度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830763199.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830888580.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830903577.gif)
将行星看作一球体,半径为R
则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830794698.gif)
对卫星,万有引力提供向心力,贴地运行轨道半径
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830810244.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830825712.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830841498.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830779250.gif)
可见,若近地卫星运行周期为T,则行星平均密度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830872479.gif)
点拨:若不是近地卫星,利用环绕周期T和轨道半径可计算行星质量M和密度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830763199.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830888580.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830903577.gif)
将行星看作一球体,半径为R
则![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830794698.gif)
对卫星,万有引力提供向心力,贴地运行轨道半径![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830810244.gif)
代入上式得
,G为万有引力恒量,
是一个对任何行星都适用的常数。
可见,若近地卫星运行周期为T,则行星平均密度![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830872479.gif)
点拨:若不是近地卫星,利用环绕周期T和轨道半径可计算行星质量M和密度
。
,
则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830794698.gif)
对卫星,万有引力提供向心力,贴地运行轨道半径
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830810244.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830825712.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830841498.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830779250.gif)
可见,若近地卫星运行周期为T,则行星平均密度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830872479.gif)
点拨:若不是近地卫星,利用环绕周期T和轨道半径可计算行星质量M和密度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830763199.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830888580.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113830903577.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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