Wednesday, May 29, 2019

The density of earth





This post gives information on the radius and the weight of the earth and ask reader to calculate the density of the earth.  

Question:  What is the density of earth given its radius 6371 kilometers and its mass 5.972 x 1012 kilograms?

Sources:

Wikipedia article provides formulas pertaining to a sphere.


Scientific American story finds that the earth is not a perfect sphere.

A Wikipedia article provides information on the radius and shape of the earth.

Answer: The answer to this question is based on the assumption that earth is a perfect sphere.  It is close to but not perfectly spherical.

The formula for the volume of the sphere is

Volume of earth=(4/3) x pi x r3


Plugging r=6371 into the volume formula we get

Volume=(4/3) x 3.1416 x 63713 or 1.083 x 1012

The density is mass divided by volume

=5.972 x 1024/1.083 x 1012  

=5.513 x 1012  (KG/KM3)

Convert (kg/km3) to (g/cm3)

Multiply the numerator by 1,000.  (There are 1,000 grams in a kilogram.)

Multiply the denominator by 100,0003   or 1.0x 1015 (There are 100,000 centimeters in a kilometer.)

We get 5.513 (g/cm3)






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