3 red galaxies; 5 brown galaxies. The concentric circles represent radial distances
from the red galaxies. The radii are r, 2r, 3r and 4r, where r = radius of the inner
circle. As you punch the ">" button you'll work through the animation. Distances
from the upper red galaxy to two of the brown galaxies are singled out for attention.
Those distances are 2r and 4r. After you push the ">" button a few times SPACE begins
to expand. This is done from the perspective of the upper red galaxy, which SEEMS to
stay still while everything else SEEMS to move. Things to notice:
and stay in the same relative positions re one another.
outward from the upper red galaxy.
people on the other galaxies. Any of the galaxies could have been chosen to be fixed
(or even some point out in empty space). No point is singled out, although the one
we're standing on seems special.
galaxy to the same 2 brown galaxies. The radii have expanded from r to (let's say)
R = r + d. So the respective distances are 2R = 2r + 2d and 4R = 4r + 4d. So one
distance has increased by 2d, and the other by 4d, both in the same time (call it T).
Therefore the apparent speed the closer galaxy is moving away is v = 2d/T, and the
further galaxy V = 4d/T = 2v. That is, the galaxy that is twice as far away seems
to be moving twice as fast. And in general if one galaxy is K times as far away as
another, then we expect to see it moving away K times faster than the other. Distance
and recession speed are linearly related. Speed = (constant)x(distance).
(By the way, this example assumes a constant rate of expansion. Our universe is more
complicated than that.)