### 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 r3

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=m1 X m2 / d2

In this case, G is the gravitational attraction between any two objects (like the earth and moon), m1 is the mass of the earth, m2 would be the mass of the moon, and d is 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?