A planet of radius R _ p is revolving around a star of radius R ^ * , which is at temperature T ^ * . The distance between the star and the planet is d . If the planet's temperature is f ~T ^ * , then f is proportional to

Step-by-step solution

The planet should be in Thermal equilibrium with star. Amount of heat energy emitted by start per second E ₁= ( T ^ * 4 ) (4 R ^ *² ) d = distance between star and planet Hence, amount of energy reaching planet per aligned unit area per second &= E₁ 4 d ² &= ( T ^ * 4 ) (4 R ^ * 2 ) 4 d ² &= T ^ *⁴ R ^ * 2 ~d ² aligned Hence energy received by planet per second E ₂= ( T ^ * 4 R ^ * 2 ~d ² ) R _ P ² ~T = Temperature of planet then amount of energy emitted by planet per second E₃= ( T⁴ ) (4 R_ P ² ) For thermal equil