Question

what of the following options are true?

The masses of galaxies are measured from
I. their rotation curves.
II. the motions of small galaxies orbiting nearby them.
III. the widths of spectral absorption lines from the galaxies.
IV. summing up the light contribution from all of their stars.

Answer 1

The masses of galaxies are found from the orbital motion of their stars. Stars in a more massive galaxy will orbit faster than those in a lower mass galaxy because the greater gravity force of the massive galaxy will cause larger accelerations of its stars. By measuring the star speeds, you find out how much gravity there is in the galaxy. Since gravity depends on mass and distance, knowing the size of the star orbits enables you to derive the galaxy's mass.

For spiral galaxies the rotation curve is used to measure their masses. The rotation curve shows how orbital speeds in a galaxy depend on their distance from the galaxy's center. The mass inside a given distance from the center = (orbital speed)² × (distance from the center)/G. The orbital speed is found from the doppler shifts of the 21-cm line radiation from the atomic hydrogen gas.

Hence , correct options are :

I. Their rotation curves.
II. The motions of small galaxies orbiting nearby them.
III. The widths of spectral absorption lines from the galaxies.