The link to all of the clickable galaxy images and spectra is at http://www.astro.washington.edu/courses/labs/clearinghouse/labs/HubbleLaw/galaxies.html.
• You will need a data table (.doc format; PDF format) to hold the following values for each galaxy containing the angular size and the corresponding calculated distance, three wavelength measurements, and the corresponding redshifts and average redshift.
• For each galaxy in your sample you will need to measure the angular size. Use the image link to bring up a centered image of the galaxy. Identify the long axis of the galaxy and then measure the angular size by clicking on each side of the galaxy image. After each click the web-page will report the x,y pixel coordinate that you clicked on. After you click the second point it will report the angular size of the galaxy in milliradians. If you make an error, make sure to click the try again link to reset the page.
• To get the distance, we will assume that every galaxy is the same size in real life (this is a standard rod assumption and is pretty good for galaxies of the same type) - namely 22 kpc across. Since the angle subtended by distant galaxies is very small, we can use the small angle approximation. Find the distance for each galaxy in your sample. NOTE - if you keep the angle in units of milliradians and the size in units of kpc, then your distance will come out in units of Mpc (see "background and theory" section).
• Measure the shift in wavelength for three different lines for each galaxy. At least two are needed to get a good value, and three would be better. You should use the calcium (Ca II) K and H lines as well as the H-alpha line. The spectra link will take you to a page containing zoomed in sections of the galaxy’s spectra. On the left hand side you can find the calcium K and H lines.
The absorption lines due to calcium will be some of the strongest (deepest) of the spectral lines. At the bottom of the image are two black lines that show the actual position of where the calcium lines show up in laboratory spectra (that is, here on Earth). The wavelengths of these black lines are listed at the top of the spectra image. You will need to click on each of the red-shifted absorption lines in order to measure the wavelength at which these lines are observed in the galaxy.
You will also do the same thing on the right hand size in measure the hydrogen α line. Generally there are one or two strong emission lines to the right of the H-α laboratory wavelength. The line you want to measure is the one with the shortest wavelength (the bluest) of them.
• To get the velocity, use your shifted wavelengths and the Doppler formula for the redshift (see "background and theory" section).
• Find the redshift for ALL of the lines you measured (this means doing this calculation three times for every galaxy you selected ). Then average the redshifts and multiply the average times the speed of light ( 3×105 km/s) to get the recessional velocity of the galaxy.
Plot the recessional velocity of each galaxy as a function of its distance from us.
• The Hubble constant is equal to the slope of this line. Draw a best fit line through your data to estimate the Hubble constant. Your line should go through (0,0). The slope of this line is your estimated value of the Hubble Constant.
• Now estimate the associated uncertainty for the Hubble Constant. For the uncertainty, draw in the steepest and shallowest lines that still fit your data. Measure the slopes of the steepest and shallowest lines and average the difference between H and those two slopes (see the last page of the data table worksheet for the formula).
• Quote your answer as H ± uncertainty in H.