The Andromeda galaxy, also known to astronomers by the catalog number M31, is in our local group of galaxies, about 2.5 million light-years from our own Milky Way (MW) galaxy. When using spectrometers to measure the wavelengths of light emitted by stars in M31, astronomers find the redshift to be \(\Delta \lambda / \lambda=-0.001001\), where \(\lambda\) is the wavelength of the spectral line in the laboratory, \(\Delta \lambda\) is the shift in wavelength, and the minus sign indicates that \(\Delta \lambda

(a) If one assumes this change in wavelength is due to the Doppler effect, how fast (in \(\mathrm{km} / \mathrm{s}\) ) is M31 approaching us?

(b) If this velocity were also M31's velocity toward our galactic nucleus, and it did not change with time, how long would it take M31 to collide with the MW? [In fact, M31's velocity toward the MW nucleus is less than the result calculated in part (a), because the

solar system is orbiting around our MW nucleus, with a component of velocity directed towards M31, so in fact M31 is moving only about \(110 \mathrm{~km} / \mathrm{s}\) toward our MW nucleus. We would also expect the M31/MW relative velocity of approach to increase with time due to their mutual gravitational attraction. Taking all this into account predicts they will collide in about 4 billion years.]

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Fig. 2.15 The M31 (Andromeda galaxy) referred to in a problem. Image credit: NASA/JPL-Caltech, from the GALEX mission.