## 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)