**Amanda in Year 12, one of our editorial assistants, has written about a subject area that interests her most: dark matter and physics. Read it here.**

Dark matter: it is one of the least understood phenomena in our whole universe. In this short piece, I’ll be exploring what it is, how we know of its existence, and just how much of our universe is made of it.

Firstly, an overview of what it is. Dark matter makes up 27% of our universe (with “normal” or baryonic matter, the stuff we see everyday, making up a meagre 5% and dark energy, something which we understand even less about, makes up a huge 68%). It is so called because we have no direct methods of observing it, it does not interact with or emit any electromagnetic radiation, therefore, whatever wavelength we try to observe it in, it is invisible to us. So, how do we know that it even exists?

Scientist Fritz Zwicky first worked out that the velocity with which galaxies rotate was too quick for the amount of matter observed (the velocity of rotation is proportional to the mass). Using complicated mechanics, he found that there must be some missing matter, he called it ‘dark matter’. Below, I will be outlining some equations and methods we can use to calculate the mass of dark matter, apply it to a class of galaxies known as Low Surface Brightness (or LSB) galaxies, and work out the proportion of dark matter in these galaxies.

Let’s start with one of the most basic and well-known equations in physics: ** F = ma **better known as Newton’s Second Law of motion.

** m(a_{ivs}+ a_{gas}+ a_{disk}) = ma_{rot}**

Here the total mass of the galaxy is multiplied by the acceleration of the gas and the stars contained in the disk and the acceleration of the ‘invisible’ matter.

**Sub: a = V² ÷ r into the equation to get m((V²_{ivs }÷ r) + (V²_{gas }÷ r) + ( V²_{disk }÷ r)) = m(V²_{rot} ÷ r)**

Now, we rearrange the equation to make ** V_{ivs}** the subject to find the velocity of the galaxy that is caused by dark matter. From this we can calculate the mass of dark matter in these galaxies.

*V*_{ivs}**= √(V²_{rot} – V²_{disk} – V²_{gas)}**

The next step involves determining the total baryonic mass in the galaxy.

*F = GmM*_{vis}*(r) ÷ r²*

*(mV_{g}*

**² ÷ r²) + (mV**_{as}**² ÷ r²) = GmM(r) ÷ r²**_{disk}*M_{vis} = r(V_{disk}² + V_{g}_{as}²) ÷ G*

Now we find the mass that is made up of dark matter.

*M_{ivs} = r(*

*V²*_{rot}*– V²*_{disk}*– V²*_{gas}) ÷ GUsing the masses obtained, we can plot a graph of mass against radius for the galaxies. Here is an example:

Using these figures (the blue line shows the mass of baryonic matter and the red line shows the mass of dark matter) we calculated that for LSB galaxy N3274, 90.0553% of it is dark matter. This huge proportion shows just how little we understand about the vast universe and how much there is left to discover in physics.