8. Hubble Redshift – PreLab
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(2) Question 1: Imagine someone is throwing tennis balls at you. They throw a ball once a second. If you run towards them
would you get hit more or less often? What if you are running away from them?
The Doppler Effect
When objects are moving the frequency, or “pitch” of waves can change.
We are all more familiar with this concept than we might think. Think of the noise a car makes when you are standing next
to it, a sort of low purr. Now imagine you are standing on a highway and the same car zooms by at a high speed. It makes a
vvvrrrroommm sound right? So the movement of the car does affect the sound. You've probably also noticed this effect
with ambulances and emergency vehicles as they pass by.
The frequency or “pitch” of sound is simply how often the waves repeat themselves. Take a look at this diagram.
(Illustration thanks to Aperion University)
If these waves were to slide into your ear, your brain would receive peaks and valley's faster for the top wave than for the
bottom. Hence a higher pitch.
(2) Question 2: Think about the example with tennis balls in question one. If something was emitting waves and you
moved towards it would you see the waves repeat more often or less often? If it were a sound wave would it sound higher or
lower?
Light is a Wave
Light and sound are very separate distinct phenomena. However, they are both waves. The frequency or “pitch” of light is
also affected by movement. The “pitch” of light is more commonly referred to as color. When the ambulance is moving
towards you the pitch or the siren is shifted higher. The red lights are also a tiny tiny bit bluer.
The amount the light gets shifted is:
V/c * F0
Where V is how fast the object is moving towards or away from us, c is the speed of the wave, and F0 is the original
frequency of the wave.
(2) Question 3: You are moving very quickly towards something that is already very blueish/violet. You notice it
disappears and you can't see it anymore. Why is this? What “color” did it become? (You may want to put on some
sunscreen)
(2) Question 4: The speed of sound is about 340m/s. Imagine an evil trombonist launches himself out of a cannon towards a
crowd of elderly people at 150m/s. He plays a low Eb, which has a frequency of 155/s. What frequency do the elderly
people here? (The ones that can still hear). What frequency does someone standing behind the cannon hear?
The Stretching of Space (and Time)
Imagine two ants on a balloon. If you slowly inflated the balloon the ants would move further and further apart. Notice the
ants are not moving, it is the space between them that is expanding. This is what physicists believe the universe is like. We
are all little ants on an inflating balloon.
(1) Question 5: If two ants are on an inflating balloon will they move apart faster or slower than ants who are further apart?
What if one of the ants has a blue light and shines it towards the another ant? If the balloon is inflating the ants are moving
apart and the light will be red-shifted just as we learned above. The farther the ants are apart, the more the light will be red
shifted.
NOTE: The light is not red shifted because they are far apart, rather that the farther apart they are the faster they
are moving away from each other.
Suppose a distant object emits light at a known frequency (color). If we observe the light at a different color we could figure
out how fast the object is moving away from us.
Spectra of Galaxies
We will assume you have learned what spectra are. If you do not, please ask your TA before you attempt this lab.
Galaxies are made up of billions of stars. The spectrum of an entire galaxy is a sort of average over what stars and dust look
like. Many galaxies have three features in their spectra, two Calcium absorption lines and another “blended” line. If we take
a spectra of a normal galaxy we should see these three lines. These lines should appear at specific frequencies, or colors.
We can also assume that all galaxies are about the same brightness (this is roughly true).
We thus can find two pieces of information. From the observed brightness (if its faint its far away, bright is nearby) we can
estimate how far away the galaxy is. From looking at what frequency, or color, the Calcium absorption lines appear at we
can also calculate how fast the galaxy is moving towards or away from us.
(1) Question 6: Suppose I observe a galaxy and I see that the Calcium lines are appearing at a much redder color than
where I expect them to be. What conclusion can we draw about this galaxy?
9. Hubble Redshift – Lab
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Open the CLEA lab “Hubble Redshift”. Click “File -> Log In”. Don't enter any information, it doesn't matter for us. Now
click “File → run”. You have been given simulated access to the Kitt Peak .9m Telescope. Click on the “Dome” button and
open the dome. Click on “Tracking” and turn tracking on.
You will see some blurry objects along with a bunch of stars. The blurry objects are galaxies.
Pick one of the galaxies in your field and slide the square onto it. (Use the N/S/E/W buttons). Click on “Change View” to
zoom in. Put the two vertical lines on the galaxy and blick “Take Reading”. Click “Start/Resume Count” to start taking data.
You will see a spectrum start to take shape. When the Signal /Noise value is higher than 10 you can click “Stop Count”.
You will see three lines, the two Ca lines are next to each other. The one to the left is called the K line and the one to right is
the H line. By clicking on the plot record the wavelength (this is like the opposite of frequency) the K line. Don't forget
units.
λObserved =
The actual wavelength of the k line is 3934Å (The funny symbol is Angstroms, 1E-10m). The speed the galaxy must be
moving away to shift the line to λObserved is ...
v = c * (λObserved / λActual – 1) =
Remember c is just the speed of light, 3x10^5km/s. Record this speed for your object. Remember units.
v=
Also record the “Apparent Magnitude” of the galaxy here (Its called V in the plot window)
m =
We will assume all galaxies have an absolute magnitude of M = -22. Knowing this we can calculate the distance to this
galaxy, D. The relationship is as follows...
log(D) = (m – M + 5)/5
or
D = 10^((m-M+5)/5)
Note this distance is in parsecs. Calculate the distance to this galaxy:
D=
Now we are going to repeat this process for the 5 other galaxies in the program. One of them has the faces of the people
who created the program instead of galaxies. Nerrrds. Take your measurements and fill in the table. Enter the distance data
in terms of 10^6 parsecs (2.4x10^7pc → 24 Mpc)
Name
λObserved
v (km/s)
m
D (Mpc)
Coma Berenicies
Now use the computer to make a plot of v vs D. The data should be entered in terms of km/s for v and Mpc for D. Either by
hand, or by showing off your Excel skills, find the slope of the plot. Make sure to include units (remember slope = rise/run).
Slope =
Take a look at your plot. It should be close to a straight line. This means that the further a galaxy is away, the faster it is
moving away from us. This is the primary piece of evidence that the universe is expanding.
(3) Question 1: The Andromeda galaxy is the closest galaxy to the Milky Way. Unlike all of the galaxies here it is actually
blue-shifted, meaning its moving towards us. Does this mean the universe is not expanding? Why or why not?
If everything is moving away from everything else we can run the clock backwards and see when everything was in the
same place.
(3) Question 2: If your friend leaves your house and travels 50mph and is 100 miles away, how long has he been traveling
for?
Using the same logic above we see that if we take the distance someone has gone and divide it by the speed they are going,
we find how long they have been traveling. In our lab this is just 1/slope. If the universe has been expaning for this long
than this is the age of the universe.
Record 1/slope here. Remember units.
T =
Ok, so those units are funky. Lets convert them into something reasonable, like years. Here are all the unit conversions you
need to do this. If you get stuck ask the TA for help.
1Mpc = 10^6 pc
1pc = 3.26ly
1ly = Distance light travels in a year
c (speed of light) = 3x10^8m/s
1km = 1000m
Heres some room for scrap work:
(3) Question 3: What is the age of the universe in years? (From your calculation above). How does this compare to the
known age of the universe (13.7Gy)?
(1) Question 4: Think about our universe as the ants on the expanding balloon. Where did the big bang happen? (There are
many acceptable answers to this question. Just try to think of something reasonable.)