|In the first few weeks of this class, we’re going to be talking a lot about the expanding universe, and how the solar system and all the planets formed. As your first homework, I want you to examine some of the evidence on which this idea is based.
The idea of an expanding universe was first proposal by Edwin Hubble in a famous paper published in 1929. Hubble built his theory from a series of observations by V.M. Slipher, who had noted in 1914 that stars in distant galaxies were moving much faster than stars in our own galaxy (the Milky Way). How did Slipher calculate the velocities of stars? He used the Doppler shift, which we’ll talk about in class. I’ll give a brief summary of it here.
Have you ever sat in traffic and listened to the approaching sound of an ambulance or a train? You may have noticed that the sound of the siren (or the train’s whistle) changes as it approaches you, passes, and then moves away from you. If you are in the ambulance or on the train, the sound is always the same. What’s going on here?
Figure 1. The stationary listener on the right hears the same 400 Hz tone emitted by the fire truck. Figure from http://imagine.gsfc.nasa.gov/YBA/M31-velocity/Doppler-shift-3.html.
Figure 2. The frequency of the fire engine's siren as heard by a person on the firetruck has not changed! However, the waves in the direction of the truck bunch up as the fire truck is catching up to its own sound waves. Figure source same as above.
The change in sound is caused by the fact that waves from a moving source are shifted, depending on the direction of motion. When the source of the waves is moving toward you, the waves get “bunched up” closer together, and have a higher frequency and shorter wavelength, as illustrated above. The waves get compressed by the motion of the source. This is referred to as blue shift, because the waves move toward the blue end of the spectrum.
If the source of the waves is moving away from you, the then waves are spaced out by the motion. They shift to shorter frequency, or longer wavelength, and this is called red shift.
Figure 3. Summary diagram of the Doppler Effect.
Nearly all galaxies in the universe display red shift. The amount of red shift is related to the relative distance to the galaxy. Galaxies that are farther away show greater red shift.
So the more the lines are shifted, the higher the velocity of the star. This can be expressed as an equation involving three variables:
the speed of light, c = 300000 km/s
velocity of the galaxy, v , expressed in km/s
redshift, z, expressed in Ångstroms, or
where v = cz.
A good example of this calculation, along with a lot of useful information on the Hubble constant can be found on the website of the Illinois Mathematics and Science Academy, at (http://staff.imsa.edu/science/astro/astrometry/hubble.html).
What Hubble realized is that the existence of red shift and the pattern that it shows (greater shift for farther galaxies) is consistent with a pattern produced by an explosion –THE BIG BANG!! We’ll talk more about this in class.
Good explanations of the Doppler Effect are given at:
And finally, here’s a nice song about the Doppler effect:
To get back to our homework… In this problem set, you have four tasks:
1. Use Microsoft Excel to make a plot of spectra from two different stars. You will want to put both spectra in the same spreadsheet and on the same plot. if you don’t know how to do this already, take the Excel class from LITS.
The data files can be found by clicking on “Star A” and “Star B” above. You can cut and paste the data directly into your spreadsheet – you do not have to type them in again! Leave a blank line at the top of your spreadsheet, and label the data as Star A and Star B. Hints: the x axis in your plot should range from 6500-6800, and should be labeled as “Wavelength (Angstroms).” The y axis should range from 0-16000, and should be labeled “Counts.” Use a legend. For the sake of clarity, plot the data as solid lines only, with NO markers.
2. Determine the position of the most intense peak in each spectrum, which will be the lowest value of y in each spectrum. This happens to be the position of the H line in the spectra, which is one of the absorption lines that are characteristic of the hydrogen atom. It’s the same line both spectra, but it’s not in the same location because of red shift. Using your Excel graph, determine the x value that corresponds to each of the low y values by holding your mouse on the lowest point. A little box will pop up to tell you the x and y coordinates of that point. Write those numbers down.
3. Decide which spectrum is the Sun, and which is the distant star. To answer this question, remember that the star will be red-shifted relative to the Sun. Another way of saying this is that the position of the H line in the Sun will be at a shorter wavelength (a lower number) that the position of the H line in the distant star.
4. Use the equation given above to calculate how fast the distant star (it has a name: NGC 1357) is moving.
Hand in the following:
A. Your Excel plot.
B. A write up including your answers to questions 2, 3, and 4. Please show all your work, and explain how you got your answers.
A few final notes may be of interest to some of you. First of all, I have extracted for this problem set only a very small portion of the star’s spectra. Typically, spectra cover a large range (sometimes 3000-54000 Å), depending on the telescope from which the measurements were made.
Second, to see more solar spectra, you might want to investigate the web site of the Solar Survey Archive (http://bass2000.obspm.fr/home.php), from which the solar data in this problem set were taken. Data for NGC 1357 came from the Illinois Mathematics and Science Academy website (NGC 1357).