How would the equilibrium temperature be modified if the planet always kept the

Question

How would the equilibrium temperature be modified if the planet always kept the same side towards the sun?

The power absorbed by the Earth is given by:

a = Earth's albedo (~0.29)

d = diameter of Earth

I know that the amount of power radiated from the Earth would remain the same as given by:

e = emissivity

Equating these and solving for the equilibrium temperature of the planet gives:

I don't see how this equation would account for a change in the equilibrium temperature of the Earth, because I don't see any parameter for rotation included in it (I understand that by not rotating, one side of the Earth receives all of the solar flux and the temperature would increase, but the other side that did not receive any solar radiation would drop in temperature, and the equilibrium temperature would not be affected, right?). If somebody could explain how not rotating would effect the Earth's equilibrium temperature, I would really appreciate it.

Explanation / Answer

the problem is that the temperature of the hotter part will be higher but because the heat cant not be transfered from the hotter half to the cooler half that easy so we can assume that the "cooler" part is now seperated from the "hotter" part. so that the amount of heat radiated is halve. (area is halve) so that T is increase T=2^1/4*T0

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