Halliday, Resnick & Walker — Gravitation: Problem 35

35 Hunting a black hole. Observations of the light from a certain star indicate that it is part of a binary (two-star) system. This visible star has orbital speed \(v = 270 \text{ km/s}\), orbital period \(T = 1.70 \text{ days}\), and approximate mass \(m_1 = 6 M_s\), where \(M_s\) is the Sun's mass, \(1.99 \times 10^{30} \text{ kg}\). Assume that the visible star and its companion star, which is dark and unseen, are both in circular orbits (Fig. 13-31). What integer multiple of \(M_s\) gives the approximate mass \(m_2\) of the dark star?