Astrophysics Fact of the Day
Co-moving coordinates and the scale factor.
The most dramatic discovery in the history of cosmology was probably Hubble's discovery of the expansion of the universe: distant galaxies are rushing away from us, and from each other, and the rate depends on the distance. Perhaps the most fruitful way to think of this is in terms of co-moving coordinates. Imagine a set of coordinates attached to each point in space, stationary with respect to the average local mass distribution. Over time, these coordinates get farther apart. In fact, points that were a distance of 1 mile apart in the year 1 of the Universe are now about 1 million miles apart. Roughly speaking, all that mass that now makes up the Andromeda galaxy - a trillion Sun's worth - was then about as close as the nearest star is now.
Distance between any two points is increasing, and the rate of increase is about the same everywhere, though it does change a bit with time. We measure this in terms of the scale factor a(t). By convention, it is now 1, which means that back at year one, it was about 10^(-6) or 1 millionth. Local effects like gravity and electrical forces break this rule on smaller scales - I'm not getting any taller due to the expansion of the Universe.