Astronomers can deduce the existence of a binary star system even if the two stars cannot be visually resolved by noting an alternating Doppler shift of a spectral line. Suppose that an astronomical observation shows that the source of light is eclipsed once every 18 h. The wavelength of the spectral line observed changes from a maximum of 563 nm to a minimum of 539 nm. Assume that the double star system consists of a very massive, dark object and a relatively light star that radiates the observed spectral line. Use the data to determine the separation between the two objects (assume that the light object is in a circular orbit about the massive one) and the mass of the massive object. (Use the approximation ∆f / f0 ≈ v/c.