Lightcurve of M31
Recap: Your astronomy professor has tasked the class with determining the velocity of Andromeda with respect to the Milky Way. You thought of three possible ways to do this, one of which will give you the right answer. You've decided to try using the 1/r2 relationship to find the distance to M31 at two different times and then calculate the velocity from the difference in the two distances.
Here is a graph of the light curve of M31, as observed with a ground telescope at the local university.