Final answer:
Rotation curves of spiral galaxies beyond radii where starlight can be detected are determined through observations of the 21 cm line of atomic hydrogen.
Step-by-step explanation:
The rotation curves of spiral galaxies beyond radii where starlight can be detected are determined through observations of the 21 cm line of atomic hydrogen (option B).
Astronomers use the 21 cm radiation emitted by rotating hydrogen gas in the galaxies. The width of the 21 cm line indicates the range of orbital velocities of the gas, with broader lines suggesting faster rotation and more massive galaxies.