Discuss how the graph of orbital velocities in rotational galaxies against distance from the galactic centre implies the existence of dark matter.

Within the central swell of the galaxy, we can see that the orbital velocity increases almost linearly with distance, which corresponds with the formula for orbital velocity (namely that v=sqrt(GM/r)), as within the galactic centre the mass increases with distance and therefore the orbital velocity increases accordingly. However, outside of the central swell, not much more baryonic mass is added with distance as most of the mass of the galaxy is contained within the central swell, and therefore we would expect the orbital velocity to decrease with distance (as v is proportional to 1/sqrt(r)). Despite this, our observations show that outside of the central swell, the orbital velocity becomes independent of the distance from the centre of the galaxy. For this to occur, M/r must be a constant and therefore the galactic mass must increase linearly with the orbital radius. Since we know that this additional mass cannot be baryonic (as this mass is contained within the central swell), we conclude that there is invisible mass present and we call this 'dark matter'.