Today, 5:33 AM · 30888 replies and 3271356 views.
It shouldn't be stationary but I bet it is. The way to test this is to drop out at the ship and then target the main star and see if the distance is increasing. I'll be shocked if it changes in real time. It's possible that it may change when relogging into the instance (I believe that's what happens with stations and planets), but I'll be surprised if even that is the case.