# Temperature of planet

**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!!