Lab
/ The Expanding Balloon Universe
Lab
/ The Expanding Balloon Universe
What is the age of my balloon universe after it has expanded?
Name: ________________________________________________
ySummary
In this exercise, you will use a two-dimensional analogy to explore the expansion of the Universe.
yBackground
and Theory
The Hubble Law tells us that our Universe is expanding. We observe galaxies, find their distances and their velocities, and find that they are all moving away from us. The more distant the galaxy, the faster it is moving away. From this information, we can estimate the age of our Universe. Because we assume that the Universe has always been expanding at the same rate, we know how long distant galaxies have been traveling in order to get where they are today!
yProcedure
1. Blow up your balloon to between ¼ and 1/3 its final size. Do NOT tie it shut!
2.
Draw and number ten (10) galaxies (G1–G10) on the
balloon. Mark one more
galaxy (the 11th galaxy) as the reference galaxy (GR).
3.
Measure the distance between the reference galaxy and each of the
numbered
galaxies. The easiest way to do this is to use a piece of string. Stretch it
between the
two points on the balloon; then measure the string using your millimeter ruler.
Record these data in the table. Be sure to indicate the units you are using. (Hint:
Use millimeters.)
4.
Now blow up the balloon fully (but not so big that it is in danger of
popping).
You can tie it shut this time if you like. Estimate the amount of time it took
you to blow
up the balloon (in seconds). (Hint: Have several people time the
“expansion” and take
the average of those times.)
5.
Measure the distance between the reference galaxy and each of the
numbered
galaxies after this second expansion of your balloon universe. Record these data
in the
table. (Again, use millimeters.)
6. Subtract the first measurement (FM) from the second measurement (SM); record the difference in the data table.
7.
Divide the distance traveled (the difference SM – FM) by this time
(T, in seconds) to get a velocity.
Distance traveled (mm) / Time (s) = Velocity (mm/s) or d/t
= v.
8. Plot the velocity (v) versus the second measurement (SM, which is the expansion distance) to get the “Hubble Law for Balloons.” Don't forget to label the units on your axes! (Note that velocity is plotted on the y-axis and distance on the x-axis.)
9. You plot points on an x-y graph
using ordered pairs of numbers: (x1, y1), (x2,
y2), (x3, y3). Using
numbers, we might plot ordered pairs on our velocity vs. distance graph
that have these values: (150, 4), (180, 6.5), (220, 8), (250, 13). Your values
will depend on the distances you measure between the reference galaxy and your
10 galaxies
and the time it took to blow up your balloon.
10.
Fit a straight line to your data. About as many data points should be
above the line as there are below the line. “Eyeballing” the position of your
line is close enough.
This is called the “best-fit” line.
11.
Find the slope. (Remember that the slope is “the change in y over
the change in x.”) This is exactly the way that we find the value of H
from Hubble's Law. Pick two
points that are relatively far apart that are on the best-fit line you have
drawn.
12. Find the age of your balloon universe from this slope by taking its reciprocal.
|
Galaxy Number |
First Measurement |
Second Measurement |
SM – FM (Difference) |
Velocity
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1 |
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2 |
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3 |
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4 |
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5 |
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6 |
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7 |
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8 |
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9 |
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10 |
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Plot the velocity versus the second measurement to get the “Hubble Law for Balloons.” Label the units on your axes.
yQuestions
1. You drew a “best-fit” straight line through your points. The line should go through (0,0) on your graph. Why?
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2. Find the slope. (For full credit, you must show all the math steps!)
Slope = ____________________
|
x1 |
y1 |
x2 |
y2 |
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x2 – x1 |
y2 – y1 |
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y2 – y1 / x2 – x1 = ____________________
3. Find the age of your balloon universe from this slope. (Show your calculations!)
The reciprocal of the slope is directly related to the age of your “universe.”
Slope of line = H0.
Velocity/distance = 
Age of “universe” =
Age of “universe” = ____________________ [Your balloon universe should be approximately between 5 and 15 seconds old.]
4.
How does this age compare to
the time it took to blow up the balloon the second time (i.e., the expansion
time)?
What assumptions are you making by doing this? Are they
sensible assumptions?
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5.
What are some of the practical
limitations of your balloon universe and the way it was “expanded” that could
affect the age you
calculated for it?
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6. How would your results change if you used a different reference “galaxy” on the balloon? If you are not sure, try it!
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