Hubble's Law

In this exercise we use actual photos and spectra of galaxies to "rediscover"
Hubble's Law.  Hubble found that the more distant the galaxy, the faster the
galaxy is moving away from us.  The logical conclusion of this discovery is
that the universe is expanding.  In the lecture I call this the first pillar
of modern cosmology.

Hubble's Law is usually presented as a graph (see page 80).  It is a plot of
recessional velocity as measured from the Doppler Effect vs. distance.  The
lab goes into considerable detail on how we will measure the distance and the
red shift.  Distance can be measured because the sample galaxies are all about
the same size.  This means, of course, that galaxies nearby will appear large
and those farther away will appear smaller.  We measure the diameters of the
galaxies in millimeters (S) and use the equation in step 4 (page 84) to get
the distances.  We generated this equation specifically for the scale of the
photos in the Sky and Telescope exercise.  In the case of elliptical galaxies,
take an average of the major and minor axes.

The recessional velocity is computed using the Doppler equation and the
measured red shift.  In steps 1 and 2 on page 83, we are creating the scale 
for the spectra in much the same way we did in the Earth's Orbital Velocity
lab.  We measure the distances between two reference lines of known wavelength
(L) and compare that to the distance from one of these reference lines to the
H line of ionized Calcium in the spectra of the galaxies (x).  Notice that
"comparing" here means dividing x by L.  Here also we determined the equation
for the observed wavelength on page 83 based on the scale of the spectra of
the galaxies.  Once we have the observed wavelength, we can use the Doppler
equation (also on page 83).  In case you were wondering, we give you
wavelengths for the reference lines and the H line in nm (nanometers).

Once you get through page 83 of the exercise, you have generated the data
to make the Hubble's Law plot.  Put the recessional velocities (last column
of Data Table) on the y-axis and the distance (column 3 of the Data Table)
on the x-axis.  The note at the top of page 84 cautions you to include the 
Milky Way on the plot. Now, what is the distance and recessional velocity
of our home galaxy?

You should see that the graph is a straight line, if you did your measurements
correctly.  Now you need to measure the slope of the best fitting straight
line.  How do we do that?  Look at the excellent web pages at

http://www.saburchill.com/physics/chapters/0073.html

Hubble's Law is the ultimate in distance measuring techniques.  In astronomy
we bootstrap our way to more and more distant objects.  Early in the course
you learned about Stellar Parallax, which itself is based on the length of
the astronomical unit.  Parallax is the only direct distance technique.  Once
we had accurate distances from Stellar Parallax, we could make an H-R diagram
and get distances to open clusters (see the Pleiades lab or the Star Clusters
lab).  In lecture I talked about using RR Lyrae or Cepheid variables to get
distances.  Each technique gets us farther out in the universe.  Hubble's Law
allows us to determine the distance to any galaxy whose spectrum we can obtain.
Question 2 has you practice this useful technique.

In the final question you use your value for Hubble's constant (the slope of
the straight line graph) to determine the age of the universe.  The units of
Ho are km/sec/Mpc.  The reciprocal of Ho has units of (Mpc X sec)/km.  Yes,
this is a unit of time, since both Mpc and km measure distance.  But it is a
horribly mixed time unit.  So we give you some conversions so you can either
convert the km to Mpc or the Mpc to km.  Then you will have the age of the
universe in seconds, which is fairly meaningless.  Convert the seconds into
billions of years.