Velocities of galaxies. Measured radial velocities of galaxies } relative to the earth are not isotropic over the sky. Nonisotropy results from the motion of the sun (orbital velocity) with respect to the center of our galaxy, and from our galaxy's own motion with respect to the local extragalactic standard of rest. Let us examine all galaxies at a particular distance, say, $3.26 \times 10^{7}$ light $y r$.
(a) What is the mean radial velocity of these galaxies? Ans. The mean velocity of the galaxies as calculated from the velocity-distance relation is $494 \mathrm{~km} / \mathrm{s}$.
(b) Where in their spectra will be the average location of the $\mathrm{H} \alpha$ line of hydrogen? (In the laboratory, $\lambda_{\mathrm{H}_{\alpha}}=$ $\left.6.563 \times 10^{-5} \mathrm{~cm} .\right)$
Ans. The H $\alpha$ line will be, on the average, at $6.574 \times$ $10^{-5} \mathrm{~cm}$
In our sample we find that in a certain direction the velocities are $300 \mathrm{~km} / \mathrm{s}$ larger than the average and in just the opposite direction they are this much too small.
(c) What is the velocity of the sun in this frame of reference? Ans. $300 \mathrm{~km} / \mathrm{s}$
(d) Is that necessarily the orbital velocity of the sun around the center of our galaxy? Ans. No, for it can include any motion of our galaxy as a whole in this reference frame.
(e) Assuming that this is the orbital velocity, estimate the mass of our galaxy, taking all the mass to be at its center and the orbit of the sun to be circular (the distance to the center of the galaxy is 3500 light yr). Compare with the mass of $8 \times 10^{44} \mathrm{~g}$ quoted for the mass of the galaxy and explain the difference. Ans. $4.5 \times 10^{43} \mathrm{~g} .$ This is less than that usually quoted because much of the mass of our galaxy is not at the center-in fact, much mass lies exterior to the sun, where it would not affect the sun's motion or be detectable in this way.