I was told in my cosmology class that there are two planets separated by a distance L at time t = 0. L is known as the co-moving distance between the planets. I was told the equation for proper distance, ##d_p##, is given by: ## d_p = a(t) L ## where ##a(t)## is the spatial expansion factor of the universe, and it is a function of time. This implies the proper distance is also a function of time. But I was told that L is constant and is the distance of separation as measured by someone on either planet to the other planet and it would be constant and equal to L for ALL times--not just t = 0. I guess I'm wondering 2 things: 1) What exactly does the proper distance correspond to physically in this case? Who could observe the proper distance? 2) Why doesn't L change with time? If the universe is expanding, wouldn't the distance of separation a person from either planets measures relative to the other planet be changing with time? I tried to clarify this with my instructor, but I could have very well misinterpreted what he was saying. So any help would be greatly appreciated!