Binary stars:
(a) About half of the visible “stars” are actually binary star systems, two stars that orbit each other with no other objects
nearby. Describe the motion of the center of mass of a binary star system. Briefly explain your reasoning.
(b) For a particular binary star system, telescopic observations repeated over many years show that one of the stars
(whose unknown mass we'll call M1) has a circular orbit with radius R1 = 6 × 1011 m, while the other star (whose
unknown mass we'll call M2) has a circular orbit of radius R2 = 9 × 1011 m about the same point. Make a sketch of
the orbits, and show the positions of the two stars on these orbits at some instant. Label the two stars as to which is
which, and label their orbital radii. Indicate on your sketch the location of the center of mass of the system, and
explain how you know its location, using the concepts and results of this chapter.
(c) This double star system is observed to complete one revolution in 40 years. What are the masses of the two stars?
(For comparison, the distance from Sun to Earth is about 1.5 × 1011 m, and the mass of the Sun is about 2 × 1030
kg.) This method is often used to determine the masses of stars. The mass of a star largely determines many of the
other properties of a star, which is why astrophysicists need a method for measuring the mass.