Final answer:
The claim that Harlow Shapley used the 21-cm hydrogen line to work out the position of the Sun in the Milky Way is false; instead, Shapley utilized RR Lyrae variable stars in globular clusters to map the galaxy and ascertain our Sun's position relative to the galactic center.
Step-by-step explanation:
The statement that Harlow Shapley used the 21-cm hydrogen line to determine the position of the Sun in the Milky Way is false. Shapley's groundbreaking work in the early 20th century utilized the observation of RR Lyrae variable stars within globular clusters to estimate the distance of these clusters from the Sun. By doing so, he was able to construct a map of the Milky Way and deduce that our Sun was not at the center of the galaxy, as previously thought by many astronomers but instead located towards the outskirts.
Conversely, the 21-cm hydrogen line was used by other astronomers, such as Tully and Fisher, to determine the rotation velocities and the mass of galaxies by measuring the width of the 21-cm line from the hydrogen within these galaxies. This line, which is emitted by neutral hydrogen atoms, allows astronomers to track the distribution and movement of hydrogen in the galaxy. These measurements can indirectly give insight into the size and mass distribution within galaxies.
Shapley's method did not involve the 21-cm hydrogen line but rather the properties of variable stars to measure distances. And while the 21-cm line can now be used to map the Milky Way's structure and the location of the Sun within it, this was not the technique Shapley applied in his pioneering work.