Question

Assume a planet with a solar constant S=2000 W/m2, an albedo α=0.4 and radius of 3,000 km. What is the planet’s surface temperature? What would happen to the temperature if the planet’s radius doubles?

Answer 1

heat absorbed by planet = (1 - α) πR²S

_{= (1-0.4)*3.14*(3*10^6)^2 * 2000}

   _{= 3.393*10^16 J}

heat radiated from planet = (4πR²) σT⁴

σ is Stefan-Boltzmann constant = 5.670373 x 10^-8 watts / m² K⁴

^{This must equal heat absorbed}

^so,

3.393*10^16 =  (4πR²) σT⁴

3.393*10^16 = (4*3.14*(3*10^6)^2)*5.670373 x 10^-8*T^4

3.393*10^16 = 1.13*10^14 * 5.670373 x 10^-8*T^4

T = 269.7 K