地球有多重?

其实更恰当的问法应该是:“地球的质量是多少?”1 快速的回答是:大约 6,000,000,000,000,000,000,000,000 (6E+24) 千克。

紧接着一个有趣的问题是:“那是怎么计算出来的呢?”这可不像是地球每天早上淋浴之前踩到体重秤上称量出来的。地球的重量是通过它对附近物体的万有引力间接测算出来的。

原来,任何两个物体之间都存在万有引力。如果您将两只保龄球放在相互靠近的地方,它们将由于万有引力的存在而互相吸引。尽管吸引力极其微弱,但如果有足够灵敏的仪器,您就可以测量出这两只保龄球之间的万有引力。根据测量结果,您可以计算出这两个物体的质量。同样的情况也适用于两只高尔夫球,但它们之间的万有引力更加微弱,因为万有引力的大小取决于物体的质量。

牛顿曾指出,对于球体,可以简化地假设它的所有质量都集中在球心。下面的方程表示了两个球体之间的万有引力:

F=G*M1*M2/R2

  • R代表两个物体间的距离。
  • G是常数,值为6.67259×10-11m3/s2 kg。
  • M1和M2代表相互吸引的两个物体。
  • F是两物体之间的引力。

假定地球是其中的一个物体 (M1),另一个是质量为一千克的球体 (M2)。它们之间的引力为9.8 kg*m/s2 ——我们可以通过让上述球体自由下落然后测量其在地球的重力场作用下获得的加速度 (9.8 m/s2) 来计算该引力。

地球的半径为6,400,000米。如果您将这些值代入方程并求解M1,便会算出地球的质量为6,000,000,000,000,000,000,000,000千克(6E+24 千克)。

1 问质量比问重量“更恰当”,是因为重量是力,它需要引力场来确定。您可以取一只保龄球并分别在地球和月球上称量它。在月球上称得的重量将是地球上的六分之一,但无论在月球上还是在地球上,保龄球的质量是不变的。要称量地球的重量,我们需要知道在哪个物体的引力场下来计算该重量。而另一方面,地球的质量是一个恒量。

 

Posted: 五月 2nd, 2011
Categories: 科学
Tags:
Comments: 213 Comments.
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