## Ask GeoMan...

## How have scientists discovered the density of the earth?

Unfortunately, this is not a value which can be measured directly (such as the density of a rock or a potato, for example). Therefore, we can only use indirect observations.

The overall density of the earth is actually fairly easy to calculate: if density equals mass divided by volume, and we can find the mass and volume of the earth, the math is simple. Well, the volume is easy - we can easily arrive at a radius for the planet, and get the volume from the equation:

V=4/3 X pi X r^{3}

But how do we get mass? This is a bit tougher, and relates to the earth's gravitation attraction on various objects: you, me, the moon, and so forth. We need to use Newton's formula for gravitation:

G=m_{1}X m_{2}/ d^{2}In this case,

Gis the gravitational attraction between any two objects (like the earth and moon),m1is the mass of the earth,m2would be the mass of the moon, anddis the distance between them. Solve for m1 and we have the mass of the earth.

Now, plug both values into the equation:

D = m / v...and we have a value for the overall density of our planet. Pretty slick, huh?

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