Honors Earth/Space Science
Determining Red-Shift in a Receding Star
Name__________________________
Period ____ Date _________
Instructional Objectives:
Students will 1. manipulate multivariable algebraic formulas,
2. understand velocity, wavelength and frequency,
3. study the Doppler effect,
4. determine the amount of red-shift in light from a receding star.
Materials:
 Calculator
 Dictionary
Part 1: Review the Electromagnetic Spectrum
Light is best described as a wave. All waves are
characterized by a wavelength and a frequency.
The wavelength describes the distance between the crest
of each cycle. The frequency is the number of crests that
pass any given point every second. Visible light waves
range in wavelength from approximately 400 nanometers
(400 nm = 400 x 10-9m) for violet colors to about 700
nanometers for red. Correspondingly, violet has a
frequency of about 7.5 x 1014 Hz (where 1 Hz is equal to 1
cycle/second) and red has a frequency of 4.3 x 1014 Hz.
Light is a type of electromagnetic radiation. Other types of electromagnetic radiation like ultraviolet light,
infrared light, radio waves and X-rays also travel in the form of a wave but at wavelengths to which our
eyes are insensitive.
Questions:
1. What color has the longest wavelengths?
2. What color has the shortest wavelengths?
3. What color has more crests of its wave passing a given point in one second? Explain.
Part 2: DOPPLER EFFECT
If a wave source is moving, the
crests of its waves get bunched
together in front of the wave source.
If the wave crests are bunched
together, their frequency increases.
In the case of a sound wave, the
pitch is higher. Behind the wave
source, the waves spread out and
the pitch is lower.
In the case of light we use the terms
"blue-shift" and "red-shift" to
describe how the DOPPLER EFFECT changes the wavelength of the light. Being blue-shifted or redshifted doesn't mean that the light necessarily becomes blue or red. It means simply that the light's
wavelength either is shortened (blue shifted) because the object giving off the light is approaching, or is
lengthened (red-shifted) because the object is moving away from the observer.
Questions:
4. In what direction is the object moving in the diagram on the right above?
5. Sketch the wave fronts for an object moving from the top of the page to the bottom of the page?
Part 3: RECEDING STARS
In the 1920's, Edwin Hubble, while studying the stars
of distant galaxies, found that for some, their emission
spectra had peaks at 411.54 nm, 435.50 nm, 487.75
nm, and 658.47 nm. Hubble knew that these
wavelengths did not correspond to any known element
and that it was unlikely that a combination of other
elements or molecules was responsible. He did notice
that these spectral lines corresponded to hydrogen's
emission spectra except that they were all 0.0033
percent longer in wavelength than they should have
been for the hydrogen spectra. Hubble deduced that
this red-shift must be because of a Doppler effect. His
calculations showed that these galaxies must be
moving away from Earth at 1 x 106 m/s (one million
meters per second)! After examining many galaxies, Hubble came up with a relationship that described
what he was seeing:
Where v = recessional velocity
v=H0r
H0 = Hubble constant = 70 km/s/Mpc
r = distance
Questions:
6. M82 is a galaxy that is 3.53 Mpc from us. Given Hubble’s Law, calculate it’s recessional velocity:
7. M31 is a real galaxy that has a recessional velocity of -110 km/s. What does this indicate?
Part 4: VERIFY HUBBLE'S WORK THAT SHOWS THE UNIVERSE IS EXPANDING
For all waves, the product of wavelength and frequency gives the velocity of the wave where λ is the
wavelength and f is the frequency.
v = λf
In the case of light and other electromagnetic radiation, however, the velocity is always fixed at 3 x
108 m/s. This speed of light is assigned the variable c.
vlight = c = 3 x 108 m/s, or more precisely, c = 2.99792458 x 108 m/s
Use c = 2.9979 x 108 m/s for any calculations below. Also, use the appropriate number of significant
digits.
Questions:
8. What would the frequency be of a violet light wave with wavelength of 410.17 nm?
9. What frequency is associated with 434.05 nm?
10. What frequency is associated with 486.13 nm?
11. What frequency is associated with 656.28 nm?
12. Imagine the hydrogen atoms in one of Hubble's distant stars emitting a photon of light at a
wavelength of 410.17 nm. If that particular photon were headed directly TOWARD Earth, how
much CLOSER to us would that photon be after one second? (Recall that the distance, d, that an
object travels in a time, t is given by d = vt where v is the object's velocity.)
13. Now if the star that emitted the photon were traveling AWAY from Earth at 1 x 10 6 m/s, how much
FARTHER from Earth would the star be after one second?
14. After one second, what is the distance between our initial photon and its star?
15. Our initial photon would be followed by many, many more just like it, each behaving similarly to
the first. After one second, how many wave cycles of photons would stretch between the distant
star and our initial photon?
16. What is the average wavelength of this photon light? (Hint: Use your answers from 12 and 13
above.) Compare this with what Hubble saw.
17. Convince yourself of the validity of this process by repeating questions 10 through 14 for one
more of the hydrogen emission spectra peaks at wavelengths 434.05 nm, 486.13 nm, or 656.28
nm. (Choose (a) the distance the photon travels toward Earth, (b) the distance the star moves
away from Earth, (c) the distance between the photon and the star, (d) the number of cycles
between the star and the photon, or (e) the effective red-shifted wavelength.)
18. If you were driving in a VERY fast car, how would the things you approach look different from
normal? How would the things you drive away from look different? Explain.
19. Why do you think Hubble's discovery that the universe is expanding would have been impossible
without instruments that could precisely measure emission spectra?
Now create a two-dimensional analogy to explore the expansion of the Universe.
Background 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. We assume that the Universe has always been expanding at the same rate, then we
know how long distant galaxies have been travelling in order to get where they are today!
Procedure
1. Blow up the balloon a little bit. DO NOT TIE IT SHUT!
2. Draw eleven galaxies on the balloon. Mark one of these galaxies as the reference galaxy
®, number the others 1-10:
Galaxy Number
Distance 1
Distance 2
Difference
Velocity
1
2
3
4
5
6
7
8
9
10
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 and then measure the string. Record these data in the table. Be sure to
indicate the units you are using.
4. Now blow up the balloon. Record how long it takes you to blow up the balloon: ______
Tie the balloon shut.
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. Divide the distance traveled (the difference) by this time to get a velocity.
8. Create a scatter plot the velocity versus the second distance measurement to get the
"Hubble Law for Balloons". Don't forget to label the units on your axes!
9. Plot a best-fit LINE (not curve) on the data. The line should go through (0, 0) on the
graph (this is one of the options in formatting a trend line).
10. Use the graph to answer the following questions:
a. What is the equation of the line?
b. What is the slope of the line?
c. Use R2 to discuss how well the line fits the data:
d. Explain why the line should go through the origin.
e. Find the age of your balloon universe using your equation.
f.
How does this age compare to the time it took to blow up the balloon the second
time?
g. What assumptions do you make about your balloon universe when you find it's
age by this method? Are these sensible assumptions?
h. How would your results change if you used a different reference "galaxy" on the
balloon? If you are not sure, try it!