The distance d between the sun and the earth is increasing very slowly. This means the earth's average temperature T will go down. The fraction of the power radiated by the sun that is received on earth is proportional to d21 ; the power radiated by the earth is proportional to T4 .
a. Deduce the dependence of the temperature T of the earth on the distance d .
b. Hence estimate the expected drop in temperature if the distance increases by 1.0%. Take the average temperature of the earth to be 288 K.
c. Can you think of a reason why the sun–earth distance might be increasing?
d. The distance is actually increasing at a rate of 1.5 cm per year. This distance is now 1.5×1011 m. After how many years will the distance increase by 1%?