Lesson Plan
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Activities
Proving Hubble’s Law
Students will learn that due to the expansion of the Universe, the distance between galaxies is
getter larger (space itself is expanding) making them appear to be moving away from the Milky
Way. The data they will take will show that the expansion follows “Hubble’s Law”: the
apparent recession velocity is linearly proportional to the distance of the galaxy. In addition,
they will find that any galaxy would see other galaxies appearing to recede from them, also
obeying Hubble’s Law.
Guided inquiry
History:
In the 1920s, Edwin Hubble made observations of other galaxies and found that they
appeared to be moving away from the Milky way. He also found a correlation: the “recession”
velocity was linearly proportional to the galaxy’s distance from the Milky way. This
relationship is known as Hubble’s Law.
It is now known that the explanation for Hubble’s law is that galaxies are not physically
moving away from each other through space (they have no “real” recession velocity) but the
literal “space” between them is growing uniformly with time. It is further known that there is
nothing special about our Milky Way galaxy. An alien astronomer in a galaxy far, far away
would also observe other galaxies appear to be receding from its home galaxy. Furthermore, this
alien astronomer would discover that its observations agree with Hubble’s Law.
In this activity, you will not only demonstrate Hubble’s Law from inside the Milky Way but
you will also be the alien astronomer!
Procedure:
1) Cut the rubber band and put the colored paper clips at different positions along it. Pick
any positions you want (it’s better if the paper clips are not evenly spaced). Leave a
length of rubber band at each end. You should end up with something that looks like this
You have just created a one-dimensional universe: each paper clip is a galaxy at some
point in “space”.
2) Using the thumbtacks, attach the rubber band to your board so that the rubber band is
stretched slightly and taut. Pick one of the galaxies to be the Milky Way (MW), say the
pink one. Using your ruler, measure the distance between the MW clip to each of the
others clips. (It doesn’t matter if a clip is left or right or your MW clip; all distances are
positive) Record your measurements in a table like this
Red
Distance
from MW
Pink
(MW)
0
Green
Purple
Orange
Blue
You now have galactic distances in the your Universe at some time
3) Now, untack your rubber band, stretches it a decent amount, and tack it back down
again. Repeat step (2), measuring the new (larger) distances between the MW clip and
all the others. Your table should now have a new row
Red
Distance
from MW
New
distance
from MW
Pink
(MW)
0
Green
Purple
Orange
Blue
0
By stretching the rubber band you have caused your Universe to expand, causing the
distances between the galaxies to increase. You now have galactic distances in your Universe at
a later time.
4) Calculate how much the distances from the MW clip have increased by subtracting the
numbers in row 1 from the numbers in row 2. Put this value in a new row labeled
velocity.
Red
Distance
from Mw
New
distance
from MW
Velocity
Pink
(MW)
0
Green
Purple
Orange
Blue
0
0
Why velocity? We can use the distance change of each clip to represent the velocity of the
clip as seen from the MW clip. Since we don’t how long the “expansion” of your universe
took, we can’t calculate a velocity with units as we normally would, measured with, e.g.,
cm/sec. But no matter what the units of the time difference, it’s still a distance change over a
time change, which will still be proportional to the “recession” velocity:
V = (d2 - d1) / (t2 – t1) = d/t
5) Now you are Edwin Hubble in 1929. Using the graph paper, make a plot of velocity
(fourth row data) on the y-axis and distance (second row data) on the x-axis. Does it
look like the points fall on a straight line? If so, you have just demonstrated Hubble’s
Law for your 1-D universe!!!
Below is an example result using 6 paper clips with the pink one as the Milky Way
(that’s why the graph is titled Pink’s Law)
6) Now, let’s look at another galaxy. Pick a different clip (say the orange one) other than
the MW clip and repeat steps 2) through 5). We are now asking the question “What
would the expansion of the Universe look like to an alien astronomer in another
galaxy?”. Below is the result of using the same 6 paper clips but measuring all the
distances from the “Orange” Galaxy (thus the graph title Orange’s Law):
The alien astronomer would reach the same conclusion as Hubble! The universe is expanding in
such a way that the “recession” velocity is linearly proportional to the distance to the galaxy.
There is nothing special about the Milky Way; every galaxy sees all the other galaxies receding
from it obeying Hubble’s Law.
7) Now plot the data from your MW clip and your “other galaxy” clip on the same graph to
see how they compare. Below is the result based on the previous two examples (the
circles are for the pink MW clip and boxes are for the “Other Galaxy” orange clip):
The data from the MW and the “Other” galaxy fall on the exact same line! If you think it about,
this makes sense. The slope of this line is a measure of the expansion rate of the entire Universe.
Since both the MW and “Other” galaxy are in the (one) Universe, they should both measure the
same expansion rate.
-A thick rubber band (1/4 in or so) and a pair of scissors
Materials
-A set of small colored paper clips
-Thumbtacks
-A board the thumbtacks can stick into (Anything that works: cork, wood, foam board, etc.)
-A ruler
-Graph paper
Supplements Students can think about (or read and discuss) the meaning of the word ‘uniformly’ in the
following statement “Hubble’s Law shows that the Universe is expanding uniformly”. Put
another way, what is meant by saying that a rubber band stretches uniformly. How does the idea
of uniform expansion fit in with the fundamental assumptions we make about the Universe? The
“big three” assumptions made about the Universe are that is (1) homogeneous, (1) isotropic, and
(3) that natural laws work the same everywhere. In this context, “homogeneous” means that (on
the large scale) any part of the Universe is like any other part of the Universe, and isotropic
means (on the large scale) when we look in any direction from the MW we see the same thing.
A more advanced supplementary topic is the acceleration of the universe (which, by the way, it
does). There are many questions to ponder/research/discuss. If the expansion of the universe is
References
accelerating, would the value of the Hubble parameter (H0) change with time? (In this lesson H0
is the slope of the line in the Hubble Law graphs). If the “recession” velocity of galaxies was
smaller in the past, would H0 have been bigger or smaller in the past? If the “recession” velocity
of galaxies was larger in the past, would H0 have been bigger or smaller in the past? What
measurements would you have to make to see if the Universe is accelerating?
The idea of using a rubber band with attached paper clips to correctly understand the expansion
of the universe is presented in the text book 21st Century Astronomy by Hester, et al.