College Physics with MasteringPhysics 7th Edition by Jerry Wilson,Anthony Buffa,Bo Lou

Exercise 60

To see in principle how astronomers determine stellar masses, consider the following. Unlike our solar system, many systems have two or more stars. If there are two, it is a binary star system. The simplest possible case is that of two identical stars in a circular orbit about then common center of mass midway between them (small black dot in Fig.). Using telescopic measurements, it is sometimes possible to measure the distance, D , between the star's centers and the time (orbital period), T , for one orbit. Assume uniform circular motion and the following data. The stars have the same mass, the distance between them is one billion km (1.0 × 10 9 km), and the time each takes for one orbit is 10.0 Earth years. Determine the mass of each star.

FIGURE Binary stars See Exercise.