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[Conversions] Density of the Earth

2021-10-14 20:18 作者:AoiSTZ23 0人讀過 | 我要投稿

By: Tao Steven Zheng (鄭濤)

【Problem】

The mass of the Earth is $%206%20%5Ctimes%20%7B10%7D%5E%7B24%7D$ kg and its mean radius is 6400 km. Calculate the mean mass density of Earth in grams per cubic centimeter.

【Solution】

Mass density is calculated by mass over volume.

$%5Crho%20%3D%20%5Cfrac%7BM%7D%7BV%7D$

The Earth is approximately a sphere, so the volume of Earth is

$V%20%3D%20%20%5Cfrac%7B4%5Cpi%7D%7B3%7D%5Ctimes6400000%5E3%20%3D%201.098%20%5Ctimes%20%7B10%7D%5E%7B21%7D$

$%5Crho%20%3D%20%5Cfrac%7B6%20%5Ctimes%20%7B10%7D%5E%7B24%7D%20kg%7D%7B1.098%20%5Ctimes%20%7B10%7D%5E%7B21%7D%7D%20%3D%205464%20%5C%3B%20kg%2Fm%5E3$

Convert the density into grams per cubic centimeter.

$%5Cleft(%5Cfrac%7B5464%20kg%7D%7Bm%5E3%7D%20%5Cright)%5Cleft(%5Cfrac%7B1000g%7D%7B1kg%7D%20%5Cright)%5Cleft(%5Cfrac%7B1m%5E3%7D%7B10%5E6%20cm%5E3%7D%20%5Cright)%20%3D%205.464%20%5C%3B%20g%2Fcm%5E3$

According to this calculation, the mean mass density is around the same as the lower mantle level. This makes sense because the lower mantle is thickest portion of the Earth!

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