What property of stars can be measured only by using binary-star systems?

mass

Explanation:

To expect an understanding of the nature and evolution of the stars, astronomers had to try to determine an important parameter: its mass. This is difficult to determine because neither the luminosity measurements nor the spectral analysis are of any help. The only solution is to resort to astrometry, the precise measurement of stellar positions, and apply it to what is called binary systems, that is, pairs of stars linked by their mutual gravitational attraction and in orbit around each other.

In the solar system there is a law, called the third law of Kepler, that connects the size and period of each planetary orbit and that makes the Sun's mass intervene. This law can be generalized in all bodies in orbit, in particular the members of a binary system. Instead of the mass of the Sun, it is the total mass of the couple that counts. Thus, if it was possible to measure the period and size of a binary system by observation, it would be enough to apply this law in order to calculate the total mass of the pair.

To determine the mass of each star, not just that of the couple, the astronomer had to study in more detail the relative movement of the two members. This allowed him to determine the proportion of each star in the total of the couple and finally obtain the mass of each body.