Q: If the universe is expanding and all the galaxies are moving away from one another, how is it possible for galaxies to collide?

Physicist: Because the universe isn’t expanding fast enough.  On average all the galaxies are moving apart, but often a given pair will be moving together.

Hubble observed that the farther things are away, the faster they’re receding.  Specifically, in the universe today, where v is the relative velocity of two objects, d is the distance between them, and (millimeters per second per light year).  Now this is an averaging thing, since galaxies are free to move however they like.

So for example, this equation says that the Andromeda galaxy which is 2.5 MLyr (million light years) away should be moving away at around 55km/s.  Instead it’s flying at the Milky Way at about 120 km/s.

As a side note: when Andromeda gets here (or we get there, or whatever) the collision of our gas clouds should set off a huge spike in star formations resulting in a liberal peppering of supernovas (bad for everyone).  But we’ve still got another 2.5 billion years, so don’t pack your bags just yet.