Question 1
The layer model assumes that the temperature of the body in space is all the same. This isn't really very accurate, as you know that it's colder at the poles than it is at the equator. For a bare rock with no atmosphere or ocean, like the moon, the situation is even worse, because fluids like air and water are how heat is carried around on the planet. So let's make the other extreme assumption, that there is no heat transport on a bare rock like the moon. Assume for comparability that the albedo of this world is 0.33, and the solar constant is 1350 Watts/m2, same as for Earth.

What would be the equilibrium temperature of the surface of the moon, where influx equals outflux, on the equator, at local noon, when the sun is directly overhead, in Kelvins?

 The letter s should appear at least 32 times.
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