Download Expanding Universe Lab

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Stars Above, Earth Below
By Tyler Nordgren
Laboratory Exercise for Chapter 10
Equipment: Balloon
Ruler
THE EXPANDING UNIVERSE
Purpose:
To create a simple universe and observe its expansion. We will measure the speed
of expansion of this universe and determine its “Hubble Law” and age. We will
then apply these methods to actual observations of galaxies in our own universe and
thus calculate Hubble’s Law and from it the age of our universe.
INTRODUCTION
Between 1912 and 1917, the astronomer Vesto Slipher at Lowell Observatory first noted that the
majority of galaxies he observed had spectra that were red shifted. If these shifts to the red were
the result of Doppler shifts, the conclusion is that these galaxies were all moving away from us.
In the 1920s, Edwin Hubble of the Mt. Wilson Observatory measured distances to many galaxies
using Cepheid variables and compared these distances to the velocity with which the galaxies
were moving away. He found that the more distant the galaxy the faster it was moving. This is
now called Hubble’s Law. This law implies that our Universe is expanding. We shall see how
this is the case by first creating “model Universes” out of balloons. We shall place galaxies on
them, let them expand, measure their velocities and construct our own “Hubble Laws.” Once
done, we will use these laws to measure the age of our model Universes. Following this
experiment we will then use actual spectra from several real galaxies to repeat this procedure for
our own Universe.
PART 1: OUR MODEL UNIVERSE
Instructions
Your balloon is your Universe. Inflate and deflate it a couple times to get it limber. Now, inflate
the balloon partially. Use the permanent marker to draw ten galaxies (or simple dots, if you
wish) on the surface of the balloon. Choose one galaxy to be your home galaxy. Label it and then
each of the other nine galaxies. Write the names of the nine galaxies in Table 1. Use the ruler
provided to carefully measure the distance between your home galaxy and each of the other nine
galaxies. We will pretend that each centimeter on your balloon is really a megaparsec. In Table
1 write the distances in megaparsecs (Mpc) between each galaxy and your home galaxy. Now,
inflate your universe further, while being careful not to pop it. Measure the distances between
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galaxies again and enter the new distances in Table 1.
TABLE 1
Galaxy
Distance 1
Distance 2
Velocity
Name
Mpc
Mpc
km/s
1.
2.
3.
4.
5.
6.
7.
8.
9.
We will pretend that 5 billion years passed between when you made your first set of
measurements and when you made the second set. Calculate how fast each galaxy is moving
away from your home galaxy in kilometers per second. Hint:
1 Mpc = 3.1 x 1019 km.
1 year = 30 million seconds.
Enter the velocity of each galaxy in the last column of Table 1.
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1.1 Are all galaxies moving away from the home galaxy?
1.2 Would this still be true if you had chosen a different home galaxy?
1.3 Do you see any relation between how fast a galaxy moves and its distance from your home
galaxy?
1.4 Where is the center of your Universe’s expansion? Is it on the surface of the balloon?
In Figure 1 plot the second set of distances you measured for each galaxy (these are the
distances the galaxies are currently at from your home galaxy) on the x-axis. On the y-axis plot
the velocity. Be sure that both axes have zero at the origin. Draw the single best straight line
you can that goes through the origin and the set of data points. This line is simply the equation:
V = Ho x D
where Ho is called Hubble’s constant. Draw a circle around the equation above so you won’t
forget it. You will lose ten points for this lab if you don’t. Do not discuss this with others, or you
will lose ten points.
1.5 What is the value for your Hubble’s constant? Find it by measuring the slope of your line in
km/s per megaparsec.
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FIGURE 1
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Run your balloon experiment backwards in your mind. If you could take all of the air out of your
balloon and shrink it to a point, all of the galaxies would have zero separation. This would be the
moment of birth of your balloon universe. We can calculate how long your Universe has been
around using your value for Hubble’s constant.
The time it has taken for each galaxy to get from a single point to where it is on your balloon
now is simply:
time = distance / velocity
Your Hubble’s Law says:
velocity = Ho x distance
So:
time = distance / (Ho x distance)
Or:
time = 1/Ho
We measured the Hubble constant in km/sec/Mpc. These are strange measurement units:
distance per time per distance! If we can get both of the units of distance to be the same, then
they will cancel, and we will be left with just the units of 1/time. In fact, the real units of the
Hubble constant are 1/sec.
1.6 Convert the units of the Hubble constant to1/sec by dividing it by 1 Mpc = 3 x 1019 km.
Hubble constant _______________ 1/sec.
1.7 Calculate the age of your Universe in seconds by finding 1 over the Hubble constant.
Age _______________ sec
1.8 Finally, how many years is that? (Hint: There are about 30 million seconds in a year.)
The age of your Universe is _______________ years
How many billions of years is that? __________________________
WAIT for the rest of the class to finish part 1.
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PART 2: THE REAL UNIVERSE
Instructions
In Figure 2 are spectra of five relatively nearby galaxies. Distances to these galaxies have been
derived by other methods and are given in the middle column of Figure 2. The spectra show
two separate sets of spectral features. Notice that the copy here is a positive so that absorption
lines appear dark, emission lines and the background continuum appear white. The emissions
lines at the top and bottom are those of a helium and hydrogen comparison standard (like the
ones in the spectroscopy lab). The diagram below identifies the hydrogen and helium lines and
their appropriate wavelengths.
In Figure 2, the central spectrum is that of the galaxy itself. The most prominent features are
two absorption lines of singly ionized calcium. The one on the right is called the calcium H-line,
while the one on the left is the K-line. Notice that the lines do not appear in the same place
(relative to the comparison lines) on the different spectra, because each of the galaxies has a
different velocity and hence a different Doppler shift.
The H- and K-lines have the following wavelengths (in the laboratory, at rest).
H - 3968 Å
K - 3933 Å
The average rest wavelength is 3951 Å.
For each galaxy spectrum, a horizontal arrow indicates the shift of the center of the H and K
pair. The base of the arrow is the center of the H and K pair (3951 Å) in the comparison
spectrum; the tip is at the center of the pair in the galaxy spectrum.
2.1 Determine the “plate scale;” that is, the number of Angstroms per millimeter in this
reproduction. First, measure the distance in millimeters from the left-most comparison line
to the right-most comparison line in one of the galaxy spectra in Figure 2.
Distance _______________ mm
2.2 Take the difference of the wavelength values between those same two lines as given in the
diagram at the bottom of Figure 2.
Wavelength difference _______________ Å
2.3 The plate scale is just the wavelength difference divided by the distance.
Plate scale _______________ Å/mm
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FIGURE 2
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For each galaxy, write the distance in Mpc in Table 2 (these distance are given in Figure 2).
Measure with a ruler (in millimeters) how far the midpoint of the H- and K-lines has shifted from
its stationary position. (The amount of red shift is shown by the length of the arrow.) Multiply
this number by the plate scale to get the redshift in angstroms. Finally, use the Doppler formula
to get the recessional velocity. Write all of these in Table 2.
Galaxy
Distance in Mpc
TABLE 2
Shift in mm
Shift in Å
#1
#2
#3
#4
#5
Doppler formula (where the speed of light = 3 x 105 km/s):

Velocity Speed of light
Shift in A
Rest wavel ength
Velocity in km/sec
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FIGURE 3
Just as you did for Figure 1 in Part 1, use Figure 3 to plot the distance and velocity of each of
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the galaxies in Table 2. We are now going to use the exact same technique as in Part 1 to find
Hubble’s Law and the age of the real Universe.
2.4 Draw a straight line passing through (or as close as possible to) the data points. Be sure the
line goes through the origin. Determine the Hubble constant as you did before by finding the
slope of the line.
Hubble constant _______________ km/sec/Mpc
2.5 Convert the units of the Hubble constant to 1/sec. (1 Mpc = 3 x 1019 km.)
Hubble constant _______________ 1/sec.
2.6 Calculate the age of the Universe in seconds by finding 1 over the Hubble constant.
Age _______________ sec
2.7 Finally, how many years is that? (Again, there are about 30 million seconds in a year.)
The age of the Universe is _______________ years
Geologists estimate the age of the Earth to be 4.5 x 109 years. Is the Universe younger or older
than the Earth?______________
Sections of this lab are taken from the Astronomy 101 course at Cornell University.