# What is the Velocity of M31?

You walk into astronomy class one day and find the following question on the board: "What is the radial velocity of the galaxy M31 with respect to our galaxy?" You had already learned that radial velocity means the velocity in a straight line toward or away from something, so the challenge is to find out how fast M31, also known as the Andromeda galaxy, is moving toward or away from our home galaxy, the Milky Way. Once everyone is in class, your professor says that the first person to solve this question using astronomical experiments and data (instead of looking up the answer on the Internet or in a book) will be excused from exams for the rest of the year.

Your professor tells you that the resources you can use include the University's intro astronomy equipment (for example, an optical telescope), as well as astronomical data available in print and on-line. Use your understanding of the laws of physics to select an experiment which will help you to find the answer.

You immediately think of three possible approaches:

1. Use a lightcurve from M31 and the 1/r2 relationship to determine M31's distance. You think that if the distance to M31 is changing over time, you could use 1/r2 at two different times to determine the change in distance. From that changing distance and the time interval between those measurements, you can determine the velocity.
2. Use a spectrum from M31 and the Doppler shift of emission lines. You remember learning that the observed wavelength of emission lines is shifted when the source is moving with respect to the observer, so maybe you can use this to measure the velocity of M31.
3. Use Hubble's Law. You learned about Hubble's Law earlier in astronomy class, which states that galaxies are all moving away from each other, and the further a galaxy is, the faster it is moving away. You think that you could maybe use this law to determine the velocity of M31.

At least one of the above methods will give you the correct answer. Which one do you want to try?