Materials Required: Computer and internet access Calculator Pen/pencil Digital camera or scanner Download and print the Hubble Diagram Sheet (as an additional option, you can create your graph with the Excel program or create your own graph by hand) Total Time Required: Approximately 2-3 Hours Part 1. The Doppler Effect Note:  For your lab report, only include your clearly labeled answers to the below questions in all parts. Copy/paste in your photos or diagrams when needed. Among the great achievements of Einstein was his understanding of the speed of light. The speed of light, in a vacuum, is a constant at ~ 300,000 kilometers/second (the actual velocity is 299,792.458 km/s). The speed of light is essential to the viability of both Einstein’s  theories of Special and General Relativity (since the speed of light is a constant it has been given its own mathematical symbol, c). If the speed of light is not constant than neither of Einstein’s theories are credible and would not be accurate in describing physics at the larger-scales of the Universe and objects moving at high velocities close to the speed of light. Therefore, since the speed of light is a constant any motion by an object emitting light has no effect on the lights velocity nor does an object seeing light from a source moving towards it measure any change in the speed of the light coming towards it.  For example, a car is driving at night with its headlights on at a speed of 75 miles per hour. What is the speed of the light coming from the headlights? Common sense would give its speed as the speed of light plus 75 miles per hour (c + 75) but the measured speed is still the speed of light ( c ). Something had to change in this situation however and in in this part of the lab you will be investigating the change that is occurring here which is known as the Doppler Effect.  Use this link to the Doppler Shift Demonstrator Animation. Click on the ‘Help’ button for instructions on how to run the animation. (Below is a screenshot of the Doppler Shift Demonstrator).  Click and move the emitting source towards the middle, left side of the screen and click and move the observer to the opposite side. You can control the frequency of the emitted wave with the rate slider bar and can move either the source or object by left-clicking, holding, and dragging the object towards the direction you want it to move. Answer the following questions based on the simulations being viewed. With the emitting source and the observer on the opposite side of the screen press the ‘start emission’ button.  Record your observations of the wave and its wavelength as seen by both the emitting source and the observer (be as detailed as possible). Now click, hold, and drag the observer so it is moving to the left, towards the emitting source. Record your observations of the wave and its wavelength as seen by both the emitting source and the observer (try to make the motion as uniform as poss.

1. Materials Required:
Computer and internet access
Calculator
Pen/pencil
Digital camera or scanner
Download and print the
Hubble Diagram Sheet
(as an additional option, you can create your graph with the
Excel program or create your own graph by hand)
Total Time Required:
Approximately 2-3 Hours
Part 1. The Doppler Effect
Note:
For your lab report, only include your clearly labeled answers
to the below questions in all parts. Copy/paste in your photos or
diagrams when needed.
Among the great achievements of Einstein was his
understanding of the speed of light. The speed of light, in a
vacuum, is a constant at ~ 300,000 kilometers/second (the
actual velocity is 299,792.458 km/s). The speed of light is
essential to the viability of both Einstein’s theories of Special
and General Relativity (since the speed of light is a constant it
has been given its own mathematical symbol, c). If the speed of
light is not constant than neither of Einstein’s theories are

2. credible and would not be accurate in describing physics at the
larger-scales of the Universe and objects moving at high
velocities close to the speed of light.
Therefore, since the speed of light is a constant any motion by
an object emitting light has no effect on the lights velocity nor
does an object seeing light from a source moving towards it
measure any change in the speed of the light coming towards it.
For example, a car is driving at night with its headlights on at a
speed of 75 miles per hour. What is the speed of the light
coming from the headlights? Common sense would give its
speed as the speed of light plus 75 miles per hour (c + 75) but
the measured speed is still the speed of light ( c ). Something
had to change in this situation however and in in this part of the
lab you will be investigating the change that is occurring here
which is known as the Doppler Effect.
Use this link to the
Doppler Shift Demonstrator Animation.
Click on the ‘Help’ button for instructions on how to run the
animation. (Below is a screenshot of the Doppler Shift
Demonstrator).
Click and move the emitting source towards the middle, left
side of the screen and click and move the observer to the
opposite side. You can control the frequency of the emitted
wave with the rate slider bar and can move either the source or
object by left-clicking, holding, and dragging the object towards
the direction you want it to move. Answer the following
questions based on the simulations being viewed.
With the emitting source and the observer on the opposite side
of the screen press the ‘start emission’ button. Record your
observations of the wave and its wavelength as seen by

3. both
the emitting source and the observer (be as detailed as
possible).
Now click, hold, and drag the observer so it is moving to the
left, towards the emitting source. Record your observations of
the wave and its wavelength as seen by
both
the emitting source and the observer (try to make the motion as
uniform as possible).
Reverse directions and click, hold, and drag the observer so it is
moving to the right away from the emitting source. Record your
observations of the wave and its wavelength as seen by
both
the emitting source and the observer.
For the next set of questions we’ll do the opposite and move the
emitting source (i.e. a star, a galaxy, a quasar) and keep the
observer stationary (i.e. the Earth).
Click, hold, and drag the emitting source so it is moving
towards the observer. Record your observations of the wave as
it moves in the same direction of the moving source and the
wave as it moves in the opposite the direction of the moving
source. Also, describe the wavelength as seen by the observer.
This effect on wavelength, as seen by the observer, is known as
blueshift.
Consult your textbook or other source and explain in your own
words using 1 to 2 sentences what is blueshift? (cite all sources
in proper APA citation)
Click, hold, and drag the emitting source so it is moving away

4. from the observer. Record your observations of the wave as it
moves in the same direction of the moving source and the wave
as it moves in the opposite the direction of the moving source.
Also, describe the wavelength as seen by the observer.
This effect on wavelength, as seen by the observer, is known as
redshift.
Consult your textbook or other source and explain in your own
words using 1 to 2 sentences what is redshift? (cite all sources
in proper APA citation)
The fact that only a few nearby galaxies within our own local
group of galaxies show blueshift while all far away galaxies are
redshifted is seen as evidence for the Big Bang. In your own
words, explain why this is seen as good evidence. (cite all
sources in proper APA citation)
Part 2. Cosmological Redshift and the Expansion of the
Universe
The Big Bang Theory says that the Universe began from a
singularity and has expanded over time. Evidence indicates that
this is an accelerated expansion meaning that objects are
moving faster in the expansion at greater distances. This is what
astronomers term as
Cosmological Redshift
where the redshifts of objects are greater for increasing
distances. In this part we will be using the redshift
measurements of
galaxy clusters
(since galaxy clusters are large and very bright they can be
seen at very large distances).
The galaxy cluster closest to our own Local Group can be seen
(with a telescope) in the direction of the constellation Virgo.

5. We call this cluster the Virgo cluster; it is approximately 50
million light years (15 million parsecs) away. Many even more
distant clusters have been found in other directions. They all
contain some very large elliptical galaxies, and many smaller
galaxies.
On the following page are pictures showing what an elliptical
galaxy would look like if it were located in different galaxy
clusters. The farther away the cluster, the smaller the galaxy
looks. There is an inverse relationship between apparent size
and distance. Next to each galaxy, there is a spectrum of a
bright star in the galaxy. The dark lines are “Balmer" hydrogen
absorption lines. These lines are not always found at the same
wavelength; they are “shifted." However, the general pattern
that the hydrogen lines form in each spectrum always stays the
same. That is how we can tell if a certain line is a hydrogen
line, even though it is not always found at the same wavelength.
The “shift" of the pattern is the Doppler Effect, and it is caused
by the motion (relative to us, the observers) of the star that is
emitting the light as seen in Part 1 of this lab.
Copy and paste the below 4 objects (Virgo Cluster, etc.) with
their corresponding spectra into your lab report. When the
wavelengths of hydrogen lines are measured in a laboratory,
using a stationary hydrogen lamp, each line is always found at
the same wavelength. We call this wavelength the “rest
wavelength" and denote it by rest. For your reference: The rest
wavelengths of the hydrogen lines (from right to left) are:
Hα (H−alpha) λrest = 656 nm [1 nm =10−9
meter]Hα (H-alpha) λrest = 656 nm 1 nm =10-9
meter
Hβ (H−beta) λrest=486 nmHγ (H−gamma) λrest =434
nmHδ (H−delta) λrest=410 nmHβ (H-beta) λrest=486
nmHγ (H-gamma) λrest =434 nmHδ (H-delta) λrest=410

6. nm
1.In your lab report under the copied image of the 4 objects, for
each corresponding object (label a heading in your report Virgo
Cluster through the Bootes Cluster and under each heading
you'll have information for questions #1 - #4, also labeled.) For
#1, type out the numbers you estimate for each Balmer
hydrogen line (H-alpha, H-beta, etc.) in each galaxy spectra
given (match the line pattern as it is labeled on the spectrum of
the Virgo cluster galaxy). So for example: Virgo Cluster # 1: H-
alpha = 660nm, H-beta = xxx, etc. doing the same for each line
and for each object.
The Doppler Effect does not only affect light, but occurs with
waves of all kinds. A familiar example is the change in pitch of
the sound from a car as it moves towards you, passes you and
moves away from you. As the car moves towards you, the sound
waves that move past you are more closely spaced than normal,
their wavelength is shortened. As the car moves away, the sound
waves move past you with longer spacing than normal, their
wavelength is increased. Since a high-pitched sound has a short
wavelength, and a low-pitched sound has a long wavelength, we
can actually hear the Doppler effect.
This is analogous to what happens to light from a moving
source. If a star is moving towards us, its light will have a
shorter wavelength, the light is blue-shifted. If the star is
moving away from us, the wavelength of the light is longer, the
light is red-shifted. It is easiest to detect the change in
wavelength of the light from the shift of the spectral lines. (The
shift of the line is the difference between the observed
wavelength and the rest wavelength.
2. For each of the 4 objects in your #1 question, now compare

7. the rest wavelength and the observed wavelength of the
hydrogen lines. For example: for the Virgo Cluster we found H-
alpha = 660nm. The rest wavelength is 656nm. Therefore, the
wavelength is different by ____?(you would show this
calculation and for the others). Which wavelength is longer?
Are the galaxies moving towards us or away from us? (State this
for each one.)
The shift of the line gets larger as the speed of the light source
(relative to us) increases. There is a formula that makes it
possible to determine how fast a source is moving by measuring
the change in wavelength.
Doppler Formula:(λobs−λrest)λrest=vcDoppler Formula:λobs-
λrestλrest=vc
where:
λobsλobs
λrestλrest
????v
????c
A light wave travels at the speed of light, which is
3000,00 km/sec.
3.Use the Doppler formula to determine the speeds of the
galaxies. (perform your calculations for just one of the four
Balmer lines,show your work for all calculations
4.Compare the distances to the galaxies and the speeds with
which the galaxies are moving away from us, and describe their
relationship to Earth.

8. Part 3. The Age of the Universe
Use the
‘Hubble Diagram’ sheet
linked at the start of the lab,
or
create a graph using Excel,
or
by hand to go into your report (if using the last two options the
Hubble Diagram can be viewed as help in scaling your graph)
plot your calculated data.
For each galaxy, plot the recession velocity (y-axis) versus the
given distance (x-axis). Draw one straight line which best fits
the four data points you have plotted. (line of best fit must go
through the (0,0) point on your graph) On your graph calculate
and label the
slope
of this “best-fit” line? (slope = rise / run)
You have just done the same calculations that the astronomer
Edwin Hubble did in the late 1920's. The relation you described
between the distances and speeds of galaxies is called
Hubble's Law
, and the slope of the line is known as the
Hubble Constant, HO.
What does Hubble's Law tell us about the Universe? At first it
may seem as if we (in the Milky Way) are in a “privileged
position" in the Universe, since all other galaxies are moving
away from us. Are we at the center of the Universe?? We will
perform a “thought experiment" to find the answer.

9. Copy the below images into your lab report.
Imagine that A, B, C, D, and E are galaxies. The arrows
represent the speeds of the galaxies as seen from A (longer
arrow = higher speed). This diagram represents what Hubble's
Law states.
1. Change your perspective again and do the same for an
observer sitting in Galaxy E.
2.Describe what would an observer sitting in galaxy C would
see when they looked at the other galaxies? Also, draw
arrows for each of the other galaxies to represent the speeds that
this observer would measure. (this can be done in Word by
inserting an arrow, or by hand)
Look at the diagrams in questions 1. and 2. What relation will
observers in galaxies C and E find between speeds and distances
of galaxies? Is the Hubble law the same for observers in all
galaxies?
What you have seen in this thought experiment is precisely the
explanation of why the proportionality between galaxy distances
and speeds leads to the deduction that the Universe is
expanding. All galaxies are getting farther and farther apart all
the time!
It is also possible to make an estimation of how long the
expansion has been going on; this is the time which astronomers
take as the “Age of the Universe," or the time since the
Universe began to expand. The Hubble constant you calculated

10. is the expansion rate of the universe going forward in time
while the
inverse
of the Hubble constant, 1/HO, will take you backwards in time
to the origin of the Big Bang.
How to calculate the age of the universe using Hubble's
constant:
(show your work for all calculations)
First, find the inverse of your value of HO.
HO = ____________________ 1/HO =
____________________
Multiply 1/HO by 3.09 x 1019 km/Mpc to cancel the distance
units.
Since you now have the age of the Universe in seconds, divide
this number by the number of seconds in a year, 3.16 x 107
sec/yr.
(The
latest Measurements of the age of the universe, as determined
by the Planck satellite, is 13.82 billion years (or 1.382 x 1010).
Let’s calculate how close your measurements came to this
Planck age!)
Calculate the percentage difference with this formula:
(Age (planck) - Age (measured) / Age (planck)) x 100 =

11. In a paragraph (50 word minimum) describe, in your own words,
the relationship you have seen in this lab between the expansion
of the Universe and the determination of the age of the
universe.
NOTE
: You must provide a reference list showing the source(s) that
you used, including our own textbook, in proper APA citation
format.