Halliday, Resnick & Walker — Gravitation: Problem 56

56 The presence of an unseen planet orbiting a distant star can sometimes be inferred from the motion of the star as we see it. As the star and planet orbit the center of mass of the star–planet system, the star moves toward and away from us with what is called the line of sight velocity, a motion that can be detected. Figure 13-38 shows a graph of the line of sight velocity versus time for the star 14 Herculis. The star’s mass is believed to be 0.90 of the mass of our Sun. Assume that only one planet orbits the star and that our view is along the plane of the orbit. Then approximate (a) the planet’s mass in terms of Jupiter’s mass \(m_J\) and (b) the planet’s orbital radius in terms of Earth’s orbital radius \(r_E\).