ASTRON 1F03 Project - Expanding Universe
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School
McMaster University *
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Course
1F03
Subject
Astronomy
Date
Feb 20, 2024
Type
Pages
4
Uploaded by AdmiralOxide5065
ASTRONOMY 1F03: The Expanding Universe
/10
In this exercise, you will use a two-dimensional analogue of space – a balloon – to explore the expansion of the Universe. Background and Theory
The Hubble Law tells us that our Universe is expanding. We observe galaxies, measure 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. We will assume that the Universe has always been expanding at the same rate, then we know how long distant galaxies have been traveling in order to get where they are today! Galaxy
Number first
measurement second
measurement d difference velocity v 1
n/a reference
n/a n/a n/a 2
3
4
5
6
7
8
9
10
/2 marks for table
Procedure 1.
Before
the balloon is blown up, draw and number 10 “galaxies” on the balloon. Mark one of these galaxies as the reference galaxy. Try to avoid drawing any too close to the neck of the balloon.
2. Blow up the balloon a little bit to the point where it is rounded. DO NOT TIE IT SHUT! 3. Measure the distance between the reference galaxy and each of the numbered galaxies. The easiest way to do this is to use something flexible like the ruler printed on the bottom of this page. Record these data in the table. Be sure to indicate the units you are using. 4. Now blow up the balloon. You can tie it shut this time if you like. 5. Measure the distance between the reference galaxy and each of the numbered galaxies. Record these data in the table. 6. Subtract the first measurement from the second measurement, record the difference in the data table. 7. Estimate the amount of time it took you to blow up the balloon (in seconds). Divide the distance traveled (the difference) by the time to get a velocity for each galaxy. 8. In the space below plot the velocity, v
versus the second measurement, d
to get the "Hubble Law for Balloons". You may hand draw the graph or use software (e.g., Excel). Don't forget to label your axes! /2
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9. Fit a line to your data on your plot. "Eyeballing" it is close enough! /1
10. Explain why the line must pass through (0,0) to be a model for the universe. /1
11. Find the slope H
0
(
v = H
0
d ). This is exactly the way that we find the value of H
0
from Hubble's Law. /1
12. Find the age of your balloon universe from this slope. Think in terms of the rule for distance: d = v t. /1
13. What assumptions are you making by doing this? Are they sensible assumptions?
/1
14. How would your results change if you used a different reference "galaxy" on the balloon? If you are not sure, try it!
/1