Astronomers detect a natural satellite orbiting an exoplanet in a distant stellar system. The satellite’s nearly circular orbit has a radius of 9.0×107m and a period of 2.50×105s. It is further assumed, on the basis of spectroscopic evidence, that the exoplanet has the same average density as the Earth (5510kgm−3).
(i) Derive an expression for the mass of the exoplanet in terms of the orbital radius r and period T of its satellite.
(ii) Calculate the numerical value of this mass.
(iii) Using the assumed density, determine the radius of the exoplanet.
(iv) Compare the radius obtained in part (iii) with the Earth’s radius (6.37×106m) and state whether the exoplanet is larger or smaller than Earth.