题目内容
已知地球质量为M,引力常量为G,地球半径为R,另一不知名的星球质量为地球质量的4倍,半径为地球半径的
,则该星球表面附近运行的人造卫星的第一宇宙速度为_____________(用题给已知量表示).
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113926627235.gif)
6![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113926642503.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113926642503.gif)
人造卫星在星球附近绕星球做匀速圆周运动所必须具有的速度叫该星球的第一宇宙速度vⅠ,也叫其环绕速度.
由万有引力提供向心力得:
G
=m
v=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113926642503.gif)
对该星球M1=4M,R1=
R,则该星球的第一宇宙速度为:
vⅠ=
=
=6
.
由万有引力提供向心力得:
G
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113926658441.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113926674257.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113926642503.gif)
对该星球M1=4M,R1=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113926627235.gif)
vⅠ=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113926720538.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113926752688.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113926642503.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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