Consider an eclipsing binary whose orbital plane is parallel to our line of sight. Doppler measurements of the radial velocity of each component of the binary are shown in Figure 13-36. Assume that the mass m₁ > m₂ and that the orbits of each component about the center of mass are circular.

(a) What is the period T and the angular frequency ω of the binary?

(b) Show that in this case (m₁ + m₂) = (ω² r³) /G, where r = separation of the binary.

(c) Compute the values of m₁, m₂, and r from the data in the v versus t graph.

Figure 13-36

v, km/s 200 0 -200 5 10 M 15 t, days m