# Measuring the Distance to Nearby Galaxies

This activity is originally from the Introductory Astronomy Clearinghouse,

created and maintained by the Astronomy Department at the University of Washington.

## Procedure

1. Print out the worksheet and download the excel workbook from the astronomy 214 Laboratory website .
2. From the Galaxy List, choose a galaxy from the list on your worksheet.
3. Find the angular size of the galaxy using its image. The images used in this lab are negatives, so that bright objects -- such as stars and galaxies -- appear dark. There may be more than one galaxy in the image; the galaxy of interest is always the one closest to the center. To measure the size, click on opposite ends of the galaxy, at either end of the longest diameter. Be sure to measure all the way to the faint outer edges. Otherwise, you will dramatically underestimate the size of the galaxy, and introduce a systematic error. The angular size of the galaxy (in milliradians; 1 mrad = 0.057 degrees = 206 arcseconds) will be displayed; record this number on your worksheet.
4. Repeat step 2 for all 10 of the galaxies on the worksheet.
5. The full optical spectrum of the galaxy is shown at the top of the spectrum page. Below it are enlarged portions of the same spectrum, in the vicinity of some common spectral features. The small dark bar near the lower left corner of the sub-spectrum indicates the rest wavelength of the line. Measure the wavelength by clicking at the middle of the spectral line in the galaxy's spectrum. Find the red-shifted wavelength for Ca K, Ca H and H-alpha lines for each galaxy on the worksheet using its spectrum.
6. Repeat step 4 for all 10 of the galaxies on the worksheet.
7. Calculate the redshift, z for each of the lines, and enter these data in the z boxes on the worksheet.
8. Find the average of the redshifts for each galaxy, and enter it in the table.
9. Use this average redshift to find the velocity: v = c z,
and enter this in the table under Velocity.
10. We will assume that all of these galaxies are about the same size. From other methods we know that galaxies of the type used in this lab are about 22 kpc (1 kpc = 1000 pc) across. Find the distance to each galaxy using the small angle formula, adapted for the units we are using here:
d (Mpc) = s (kpc) / a (mrad),
and record this distance in your data table under Distance.
11. Record your velocities and distances in the excel workbook. Make a graph of your data with distance on the x-axis, and velocity on the y-axis. Using the math functions in excel calculate the slope of the best fit straight line to your data. This slope is just the Hubble constant, H. Record this on the excel spreadsheet. Make a second plot, using the second set of data in the workbook, which comes from the Hubble Space Telescope Key project to determine the Hubble constant. Recalculate the slope of the line, with this added data. Finally, make a third plot with the data for the 14 galaxy clusters included with your lab results and the Hubble data. Again calculate the slope of the best fit straight line.
12. And now for the age of the universe! If the universe has been expanding at a constant speed since its beginning, the universe's age would simply be 1/Ho. Convert Ho to inverse-seconds (1/sec) by cancelling out the distance units: 1 Mpc = 3.09 x 1019 km.
13. The "expansion age" of the universe is t = 1/Ho. This is a very simple model for the expansion of the universe.
14. A better model would account for the deceleration caused by gravity. Models like this predict the age of the universe to be: t = 2/(3Ho). Re-calculate the age using this relation.
15. Print out the excel spread sheet and your three graphs. Make sure your graphs are annotated appropriately.