C2
1.00
Suppose an exoplanet of mass $ m $ orbits a star of mass $ M $ in a circular orbit of a radius $ R $ and the period of revolution is $ T $. The orbital plane is at an angle $ \theta $ to the direction to Earth. Estimate the accuracy of the relative frequency measurement, $ \Delta \omega / \omega $, required to detect such an exoplanet by your method. In your answer express $ \Delta \omega / \omega $ in terms of the fundamental constants, $ R, T, \theta, m $, and $ M $.