The Rotation of Saturn

The Rotation of Saturn exercise comes in two pieces: one is the lab manual write-up
and the other is the Sky and Telescope exercise that I included in you supplemental
lab packet.  The S&T exercise contains the spectrum of Saturn, which is essential to
doing the exercise.

The work is quite similar to other things we have done.  It begins by establishing a
scale.  Notice the little notches on the top and bottom of the spectrum.  These are
actually reference lines that are recorded at the same time that the spectrum was taken.
The numbers above the notches are wavelengths in angstroms.  From these I hope you see
that the "red" end is on the right.  The entire spectrum, however, covers only about 175
angstroms.  You begin by connecting the reference lines top to bottom with a thin,
straight line.  Measure the distance between the lines in mm (that's the smallest
division on your millimeter ruler) and put the distances in the first table.  Try to
make your measurements to the nearest 0.1 mm if possible.  I use a table top magnifier
to do this kind of work.  The first table now has a column for wavelength differences
and mm distances between these reference lines.  Total the columns and divide the totals
to give the plate scale (Angstroms/mm).

Now look at the spectrum.  You have the spectrum of the rings as well as the ball of
the planet.  Refer to the sketch on page two.  As you drop a vertical line through the
spectrum, you first come to the spectrum of the rings on one side of Saturn, a gap,
the spectrum of the planet, another gap, and the ring spectrum on the other side.
We are only concerned with the spectrum of the planet in this exercise.  Notice that
the lines are tilted.  This is the Doppler Effect at work.  I have a discussion of this in
one of the early lectures on the solar system.

Select eight spectral lines using the following criteria: easily visible but not too
thick; evenly distributed in wavelength.  Avoid the lines on the right side of the
spectrum that do not appear tilted.  These are from molecules in our atmosphere (called
telleric lines) and have nothing to do with Saturn.  You will be measuring distances
(mm) from the top of the spectral line to a nearby reference and from the bottom of
the line to the same reference.  Subtracting these distances gives us some measure of
the tilt of the line.  Caution - the planet shows limb darkening and the edges of the
spectrum fade as a result.  I have found that if you place your eye and sight across
the page, you get a good idea of where the edges are.  Perhaps you should use a ruler
and draw a line where the edges occur.  When you look face onto the page you get a
different impression of where the edges are.  We measure eight lines to reduce the error.

I've laid out the calculations so just follow the form.  The average doppler shift is
called delta lambda and is a single number (not two variables multiplied together).
You can consult your text to find the textbook value for the rotation rate.

This is the last lab - are you glad?!