题目内容
人们认为某些白矮星(密度较大的恒星)每秒大约自转一周(万有引力常量G=6.67×10-11 N·m2/kg2,地球半径R约为6.4×103 km).
(1)为使其表面上的物体能够被吸引住而不致由于快速转动被“甩”掉,它的密度至少为多大?
(2)假设某白矮星密度约为此值,且其半径等于地球半径,则它的第一宇宙速度约为多大?
(1)为使其表面上的物体能够被吸引住而不致由于快速转动被“甩”掉,它的密度至少为多大?
(2)假设某白矮星密度约为此值,且其半径等于地球半径,则它的第一宇宙速度约为多大?
(1)1.41×1011 kg/m3 (2)4.02×107 m/s
(1)设白矮星质量为M,半径为r,赤道上物体的质量为m,则有
=m
r.
白矮星的质量为M=
,
白矮星密度为ρ=
=
=
=
kg/m3=1.41×1011 kg/m3,
即要使物体不被甩掉,白矮星的密度至少为1.41×1011 kg/m3.
(2)白矮星的第一宇宙速度为:
v=
=
=
=
m/s
=4.02×107 m/s.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115925598472.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115925614391.gif)
白矮星的质量为M=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115925629484.gif)
白矮星密度为ρ=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115925645384.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115925660622.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115925676425.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115925692663.gif)
即要使物体不被甩掉,白矮星的密度至少为1.41×1011 kg/m3.
(2)白矮星的第一宇宙速度为:
v=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115925707503.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115925707681.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115925723600.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241159257381166.gif)
=4.02×107 m/s.
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目