Spectroscopic parallax isn't exactly a parallax (angle) measurement, but it does present a means of getting a distance estimate for a star that is too far away for actual parallax measurement. You do it by examining the spectrum of a star and determining its spectral type. Looking at the Main Sequence band at that type allows you to look to the left of the diagram and get an estimate of the absolute magnitude. Since you always can find m (apparent magnitude) and you have an estimate of M (absolute magnitude), the formula will yield a distance. The Main Sequence does have some width (is not a thin line), so the estimate of M, and therefore the distance, is somewhat uncertain (has an error bar). That is, however, a LOT better than knowing nothing about the distance.
There's only one way to determine the mass of a star directly - measure its gravitational influence on something else. For the Sun it's easy; use the orbits of its planets to find its gravity. For other stars that do not have planets we can see it is a problem. The only thing we are likely to be able to use in finding the star's gravitational influence is another star, and that requires having two stars orbiting each other in a binary star system. Fortunately, over half the stars in the Galaxy are in binary systems, so there are a lot of opportunities.
The masses are determined by studying the orbit of the binary system. Remember that the two stars orbit around the common center of mass (CM). Astronomers will determine the following.
Once masses have been determined for a significant number of stars, we find that mass and luminosity are related. See Figure 10.21 for an indication of the Mass-luminosity relationship (or use this graphic); type O stars are the most massive and type M stars (red dwarfs) are the least massive.
Also note that stellar radius and spectral type are related. The more massive stars are the largest, while the least massive stars are smallest.
Be sure you understand this chapter. Use the questions at the end of the chapter for practice.