## Thursday, July 11, 2019

### Ratio of density of Jupiter to the density of Earth

This post teaches three concepts -- density, geometry and scientific notation.

Question:  The mass of Jupiter is 317.8 times the mass of the Earth.  The radius of Jupiter is 69,911 kilometers.  The radius of the earth is 6,371 kilometers.  What is the ratio of the density of Jupiter to the density of Earth?

Answer:   We assume that Earth and Jupiter are perfect spheres.  They are not but the assumption does not appear to change results by a lot.

Density is mass divided by volume.   The density for earth is Me/Ve.  The density for Jupiter is Mj/V

The ratio of densities is De/DJ is (Me/Mj)/(Mj/Vj).

This is the same as

Ratio densities= (Me/Mj) x (Vj/Ve)

We know the ratio Me/Mj is 317.8.

We use the formula for the volume of the sphere to get the ratio of volumes Vj/Ve.
The formula for the volume of the sphere is

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

The ratio of the volumes Jupiter to earth is (69,991/6,371)3 or 1325.9. (The 4/3 and pi cancel.)

The ratio of the density of earth to Jupiter is therefore (317.8/1325.9) which is 0.240.

Answer from Google for the density of Jupiter is 1.33 gm/cm3.  Answer for the density of Earth from our previous post is 5.52 g/cm3.  The ratio 1.33/5.52 is  in fact 0.240.

You may be interested in our previous post on the density of the earth.