只用秒表测出地球半径 file:///C:\Users\ADMINI~1\AppData\Local\Temp\ksohtml2100\wps1.png 地球半径是多少?6400公里,那么我们生活在地球上的人是怎么测量地球半径的呢? 海边看日出。
如果用这种方法,你需要做如下准备:带一块秒表、量一下你的身高、上好闹钟,当然还得找个海边。起个大早,站在海边看日出,当刚刚看到太阳的时候,开始计时,并且马上趴到地上;这个时候你会发现看不到太阳了,等再一次看到太阳的时候,停止计时。然后就可以算地球的半径了。
你站在海边,太阳光穿过地平线到达你的眼睛,此时你的位置是在A点,高出地球的那段距离就是你的身高;趴到地上后,由于高度变低,所以你看不到太阳了,当地球自转使你到达B点后,你才能重新看到太阳,在这个过程中地球转过的角度是θ。我们知道,地球一天转一圈,所以 θ=360° x T÷24 其中t 是你的秒表测量出的时间。另外根据几何关系(R+h)cosθ=R,可以得出地球半径 ![](http://data:image/png;base64,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) R=hcos θ÷(1—cos θ)式中h是你的身高。根据上面2个公式,可以很简单的估算出地球的半径。 不过,事情真的那么简单吗?当你真去测量的时候,会发现算出来的结果与实际情况差别较大,甚至于在某些地区——比如夏天的北极地区,那里太阳从不落山,根本无法测量。实际上,上面的方法只适用于在赤道上测量,当你在地球的其他地方测量时,测出的是当地纬度圈的半径。如果你知道当地纬度α是多少的话,可以计算出地球半径 考虑到黄赤交角(地球自转轨道和地球公转轨道之间的夹角)的影响,我们用上述方法测量出的结果在不同的季节还要做适当的修正。
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