Suppose that each tile on the floor of the classroom has dimensions of 10 Mpc by 10 Mpc. Also suppose that the time interval between successive numbers on the post-it notes is 1 billion years (so from "1" to "4" would be 3 billion years).
Suppose you live on the pink galaxy. At each of times 1, 2, 3, and 4, measure how far the blue galaxy is from you. Do the same for the green galaxy and the purple galaxy.
Normally, you would use the Pythagorean theorem (a2 + b2 = c2 ) to get the diagonal distance, but in this case it will be all right to simply add the vertical and horizontal distancs.
/ Blue Galaxy / Green Galaxy / Purple Galaxy /Time 1
Time 2
Time 3
Time 4
Now, find the speed of each galaxy relative to you by using the equation v = d / t . You can compare your data at any two times (1 and 2, 1 and 3, 2 and 3, etc. but you only need to do one combination) to see how far the galaxy has traveled, in how long.
Let's measure this speed in more familiar units:
Roughly, 10 Mpc = 3 x 1020 km, and 1 billion years = 3 x 1016 s.
So in classroom units, 1 tile / time interval = 10 Mpc / 1 billion years = 1 x 104 km/s.
Now, suppose that the present time is time 4. Note the distance to each of the other three galaxies, and how fast each galaxy is moving. Is there a linear relationship? Can we make our own form of Hubble's Law?:
v = H0 d
In our classroom universe at time 4, what is the value of H0 ?
This exercise contained identical worksheets, for people living on the green, blue, and purple galaxies. In spite of making measurements from different galaxies, everyone should have gotten the same result for the Hubble constant!