How do we know that Mars is solid and Jupiter's made of gas?

Question posed by Rosie via @icecolbeveridge.

It's a question of density.

Density, simply put, is a measure of how much stuff goes into making something (its mass) compared with the amount of space it takes up (its volume). We can calculate these two things for both Mars and Jupiter without too much hassle if we know the right maths: the mass of a planet can be worked out by looking at the way it interacts with other bodies in space, such as its moons; the volume can be calculated if we know roughly what shape it is, how far away it is, and how much of the sky it takes up.

When we calculate these things it is sometimes useful to compare them to something we know a bit more about. I'm going to compare them to the Earth, which we know from experience is largely solid*.


Jupiter

By Brian0918 at en.wikipedia, via Wikimedia Commons

Jupiter is pretty big. In terms of mass, you could lump together all of the other planets in the solar system and still need more than twice as much stuff to even come close to balancing out Jupiter on an enormous set of cosmic weighing scales. Compared just to the Earth, then, you'd need 318 Earths before you had enough stuff to make one Jupiter. The weird thing is that Jupiter takes up much more than 318 times the space- in fact, it takes up 1,321 times the space that the Earth does. This means that the matter that goes into making Jupiter is much, much more spread out than the matter that goes in to making the Earth.

This difference between the amount of space taken up by each unit of matter is what gives us the first basic clue to Jupiter's composition: one of the things that defines the difference between a gas and a solid is the difference between the amount of space that the same mass of each takes up.

For an example that's closer to home: prod your kneecap. That's solid. Now wave your hand through the air. That's a gas. The particles in the air are much more spread out than the particles in your kneecap, and you'd probably need a room full of air before you had the same amount of stuff that goes into making up your kneecap.

If we work out the numbers properly (divide the mass by the volume), we get a value of density for Jupiter of 1.326 g/cm³. Compare this to the value for the Earth, 5.515 g/cm³, and we can see that Earth is a lot more dense than Jupiter: more than 4 times as dense.

This leads us to believe that most of Jupiter is probably made up of mass in the form of gasses rather than solids (although it may have a solid core and layers of metallic liquids as well). Other research and exploration, such as spectrographic analyses, have provided further evidence to support these findings.


Mars

Earth/Mars size comparison, via Wikimedia Commons

You'd need a bit more than 6.5 Marses to make one Earth, and Earth takes up about 9 times as much space. Straight away we can see that these numbers are much closer together than they are for Earth and Jupiter. Comparing the densities, we get a value of 3.9335 g/cm³ for Mars, which is still less than Earth's 5.515 g/cm³, but still nearly 3 times as dense as Jupiter. If we know enough about the relative densities of solids and gases, we can work out that Mars is mostly solid. Again, other research and exploration have corroborated these findings.




* Well, there's a lot of liquid too...