Measuring the Distance to Nearby Galaxies
This activity is originally from the Introductory
created and maintained by the Astronomy Department at the
University of Washington.
- Print out the worksheet
download the excel
from the astronomy 214 Laboratory website .
- From the Galaxy List, choose a galaxy from the list on your
- 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
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.
- Repeat step 2 for all 10 of the galaxies on the worksheet.
- 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.
- Repeat step 4 for all 10 of the galaxies on the worksheet.
- Calculate the redshift, z for each of the lines, and
enter these data in the z boxes on the worksheet.
- Find the average of the redshifts for each galaxy, and enter it
in the table.
Use this average redshift to find the velocity: v
= c z,
and enter this in the table under Velocity.
- 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
d (Mpc) = s (kpc) / a
and record this distance in your data table under Distance.
- 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
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.
- 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.
- The "expansion age" of the universe is t = 1/Ho.
This is a very simple model for the expansion of the universe.
- 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.
- Print out the excel spread sheet and your three graphs. Make
sure your graphs are annotated appropriately.