The runaway conundrum
Like the perpetual motion machine
lacks a basis in reality due to the laws of thermodynamics.
In the case of earth this means that the planet is unable to get any hotter than the amount of energy it is getting from the sun [* apart from a minuscule amount of energy conducted from the hot earth center].
A conceptual problem is that the earth is not a flat non moving disc but a rotating sphere. This affects the discussion of how much energy actually reaches any point on the earths surface.
The second is that unlike smaller planets the earth surface is a mixture of solid and liquid with an overlying atmosphere. The atmosphere also takes in water vapor and other gases from the solid and liquid surfaces
Thirdly some heat can move through the atmosphere and liquid, very little through the solid surface layer, to the dark side apart from the effect of rotation.
There is thus an upper bound on the temperature that the atmosphere can rise to which is the maximum temperature the sun can heat the underlying earth surface to.
This equates to the temperature on the surface of the moon at peak sunshine as the earth /moon is a coupled dipole at roughly the same distance average from the sun as they rotate around each other in their rotation from the sun.
This is given as 200 degrees centigrade.
It is impossible, no matter what the composition of the earth atmosphere , to get above 200 degrees Centigrade at the middle of day from an incoming 1034 W/M squared of solar energy at the hottest point on earth [barring volcanoes etc].
But this is the hottest point and everything goes downhill from there.
In the first place the albedo of the earth without clouds and aerosols reflects 28% of the energy from ever reaching the earth.
Since we are considering temperatures the temperature of the earth would not be 200 degrees celsius but 473.15 Kelvin.
28% 0f this is 132.4 So the hottest point on earth can only ever be 340.25 K or 67.1 C.
The average global temperature is about 14.8 degrees centigrade [287.95 K] but is never put up anywhere.
The TOA is about 6 km out. The earth has a solid liquid diameter of 12.8 Km but an effective diameter accepting energy of 13.1 KM.
The total energy incident on the true earth is therefore higher than that usually used.