How did astronomers determine the relationship between spectral type and mass for main sequence stars?

Astronomers established the relationship between spectral type and mass for main sequence stars by measuring the masses and spectral types of stars in binary systems. Binary systems, where two stars orbit each other, provide a unique opportunity to determine the masses of stars directly through gravitational interactions. When one star's mass can be accurately measured, its companion's spectral type can also be obtained by examining its light spectrum. This correlation allows astronomers to identify a consistent relationship between mass and spectral type.

The spectral type of a star reflects its temperature and, consequently, its characteristics such as color and luminosity. By analyzing numerous binary systems, astronomers were able to compile data that linked specific spectral types to corresponding masses, leading to a clearer understanding of how mass influences stellar evolution and characteristics throughout the main sequence phase.

While the other options provide insights into different aspects of stellar characteristics or methods of studying stars, they do not directly address the specific relationship between spectral type and mass for main sequence stars as effectively as the method involving binary systems.