Let’s say I am on the earth’s surface and observing a galaxy at a distance of d=10 billion light years away. In the course of one day, I will have observed the galaxy to move 2*pi*d in my frame of reference. Of course, this is >> c. Now it will be argued that the earth is rotating so I am not in an inertial frame of reference. I could say that I can approximate an inertial frame to a high degree by viewing the galaxy from a hypothetical planet that takes 10 billion years to complete one rotation. The galaxy would still have an apparent speed of 2*pi*c in that frame of reference. I’m trying to get a clear understanding of just when the limitation of speeds < c holds. I’ve heard things like “only locally,” “only in an inertial frame of reference,” etc. It appears that the earth is usually a good enough inertial frame for most observations and v < c holds, but not in the example I gave.