Question A planet recives energy only from sun and loses energy due to radiation. Planet's temperature as a function of the distance bewtween between them(D) is?

• propD^-2
• propD^-0.5
• propD^-1
• None

Solution

This is a straight forward one not too complex, we just need to equate the energy lost and the energy gained by the planet.

Let the radius of planet be R, P the heat energy released by sun

So we can write:

Energy recieved by planet as =P/4pid^2*piR^2

Energy radiated by the planet as =4piR^2sigmaT^4

At equilibrium they are same so we get:

P/(4piD^2)*piR^2=4piR^2sigmaT^4

T^4prop1/D^2

TpropD^-0.5