# Calculating the mass of a planet

A while ago I posted about a bit of science news: the discovery of a planet with the density of styrofoam. I didn’t really explain there how we work out the density of distant planets, though, and it struck me that I used to wonder that a lot before I found the answer in one or other of my books! So, how do we figure out the density of a planet?

I won’t go too deeply into this, mostly because my skills at math are fairly non-existent, but the principles can be explained without putting numbers to them. First, you need to work out the mass of the planet. The way scientists typically do this is by looking at the effect the planet in question has on other nearby bodies. This is much easier if the planet has at least one moon orbiting it, but can be done with planets orbiting the same star, for example. This works because the greater the mass of a planet, the greater the gravitational pull it can exert on the objects it interacts with.

So from the interaction between two bodies, you can work out the mass of the planet you want to calculate the density of. Next, you need to know the planet’s radius. Assuming the planet is roughly spherical, you can then calculate the planet’s volume, using the same math as you would to calculate the volume of any sphere: V = (4/3) x πr3

With me so far? Not much left to do! To calculate the density of a planet, it’s the same equation you need to calculate the density of any old sphere: ρ = m/V

So really, the only difficult bit for the amateur here is calculating the mass of the planet. Once you know that (for example, by looking it up online!), you can calculate the density of any known planet for yourself.

(I’ll refrain, though: the greater mystery for me is how anyone manages to transcribe a list of numbers without jumbling them up.)

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