Earth's Orbital Velocity

CAUTION: Since I made the lab prep video, I have photo-reduced the spectra and
included them in the lab manual.  This means that the plate scale I show in the
video and the shift in spectrum B that I show are not the values you will get.
I have corrected the Power Point slide.  In order to get EXACTLY what I am doing,
I suggest that you actually get out your calculator and run my numbers.  In that
way you will have an example of how to generate each number in the exercise.

The spectra of Arcturus are labeled a and b on the right hand edge.  Notice that
they are absorption spectra as is typical for stars.  A reference spectrum has
been included above and below the spectra of the star.  These help us establish
the wavelength scale. 

The work in the first part of the lab is very similar to setting the scale on a map.
With a sharp pencil draw thin lines connecting the top and bottom of each of the
numbered reference lines.  Measure the distance between reference lines 1 and 7 in
centimeters.  Line one has a wavelength of 4260.48 angstroms and line seven has a
wavelength of 4307.91 angstroms.  Follow the work on page two of the lab to determine
the plate scale (i.e., the map scale).

Each of the reference lines can be found in the spectrum of the star, but they will
be shifted depending on the relative velocity between Arcturus and the Earth on the
date the spectrum was obtained.  The easiest of the reference lines to spot it number
5.  Notice the same line in the spectrum of Arcturus.  Spectrum B is slightly over-
exposed, so the line centers are somewhat washed out.  I have a blown up version around
line five in the write-up and I show with small blocks the shifts you are to measure.

Starting with spectrum A (top) I can tell you that on this date the lines are red
shifted (which way is toward the red on the spectrum?)  For spectrum B (bottom) the
lines are blue shifted.  The shifts are small and a magnifying glass may help.  Measure
the shift of each of the lines in the spctrum from its reference position in cm.  Then
use the Plate Scale to convert the measured shift to angstroms.  Next use the Doppler
Equation to obtain the velocity.  We measure four lines in order to take an average
and reduce our errors.

Do the same procedure for spectrum B.  Remember that now you are dealing with blue
shifts.  Again average the velocities you obtain.

Now that you have VA and VB you can compute the velocity of the star and the Earth
by the equations at the top of page two.

For question 4, we would get maximum velocity if Arcturus were on the ecliptic.
So take its position and drop a vertical (line of the same RA) to the ecliptic.
Read off the declination.

Think about question 5 in light of the discussion I have on the Doppler Effect on the
video.