Final answer:
To determine the mass of a star, astronomers primarily rely on measuring the orbital periods and velocities of stars in binary systems. This method allows for precise calculations, which are much more reliable than guesses based on luminosity or apparent brightness. The correct option that explains how we know how massive stars are is D) We measure the orbital periods and velocities of stars in binary systems.
Step-by-step explanation:
Understanding the mass of a star is crucial for deducing its lifespan and eventual fate; however, this is not an easy task. The common method to measure stellar masses involves observing binary star systems. In these systems, two stars orbit around a shared center of mass. This can be seen directly with visual binaries or deduced from spectral lines in spectroscopic binaries. By analyzing the orbital periods and velocities of these stars, especially through the Doppler effect in velocity curves, astronomers can calculate their masses.
It's important to emphasize that directly measuring luminosity or apparent brightness of a star is not sufficient since stars vary greatly in intrinsic luminosity. Thus, observing a star's dimness doesn't necessarily indicate its mass, as it could either be of low luminosity or simply far away. However, the mass-luminosity relation aids in inferring that typically, more massive stars are more luminous.
Finally, it's the binary systems that provide the clearest method for mass measurement, leading to the correct option, D) We measure the orbital periods and velocities of stars in binary systems, as the way to determine how massive stars are.