The very POWERFUL the Solar Irradiated planet surface Rotational Warming Phenomenon: ( N*cp )^1/16

The planet corrected effective temperature equation Te = [ Φ (1-a) S / 4 σ ]¹∕ ⁴

We know, that the on the smooth without atmosphere planet's surface the "absorbed" incident solar flux fraction is Φ (1 - a) S.

Φ (1 - a) S - is what is left to "absorb".

Φ (1 - a) S - is the basis for estimating the planet's theoretical uniform emission temperature. 

Te - is the planet's emission temperature calculated by the improved equation:

Te = [ Φ (1-a) S / 4 σ ]¹∕ ⁴

here:

a - is the planet's surface average albedo

Φ - is the spherical surface solar irradiation accepting factor

S - is the solar flux W/m²

σ = 5,67*10⁻⁸ W/m²K⁴, the Stefan-Boltzmann constant

Φ (1 - a) S - is the "absorbed" fraction of the solar flux

(1 - Φ + Φ*a) S - is the reflected fraction of the solar flux

Planet ......Te........ Tmean...... Tsat......... N

............emission equation measured rot /day

.........theoretical..... new.... from orbit

Mercury.. 364 K.... 325,83 K.. 340 K... 1 /176

Earth....... 211 K.... 287,74 K.. 288 K....... 1

Moon .......224 Κ.... 223,35 Κ.. 220 Κ.... 1 /29,5

Mars ........174 K.... 213,21 K.. 210 K .......1

And we observe here that Te is depended only on solar flux and albedo, but with the same Φ = 0,47 gradually subsides from Mercury to Mars from 364 K to 174 K.

Eath and Moon, having the same solar flux, have different Te because Earth has a higher than Moon albedo.