A planet of negligible atmosphere orbits a distant star at a fixed distance
PHYSICS · Subjective · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter
Problem
A planet of negligible atmosphere orbits a distant star at a fixed distance d. Treat the planet and the star as perfect black bodies. The equilibrium temperature Tp of the planet is reached when the rate at which it absorbs stellar radiation equals the rate at which it emits radiation.
(i) Derive an expression for Tp in terms of the star’s radius Rs, its surface temperature Ts, and the orbital distance d of the planet.
(ii) Suppose the star undergoes changes such that its radius becomes 21Rs while its surface temperature becomes 2Ts. The orbital distance of the planet remains unchanged. Calculate the ratio of the new planetary temperature to the original one, i.e. Tp(old)Tp(new).