Halliday, Resnick & Walker — Gravitation: Problem Problem_54

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 \( T = 1.70 \text{ days} \text{,} \) and approximate mass \( m_1 = 6M_s \text{,} \) 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. 13.27). What integer multiple of \( M_s \) gives the approximate mass \( m_2 \) of the dark star?