A Planet Effective Temperature Complete Formula Te = [ Φ (1-a) S (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴

Plus the introduction to the Reversed Milankovitch Cycle. Click on the box for more

The first step

Comparison of results the planet Te calculated by the Incomplete Formula:

Te = [ (1-a) S / 4 σ ]¹∕ ⁴

the planet Te calculated by the Complete Formula: 

Te = [ Φ (1-a) S (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴     (1)

and the planet Te (Tsat.mean) measured by satellites:

Planet or         Te.incomplete       Te.complete      Te.satellites

moon                  formula                   formula            measured

Mercury       437 K              346,11 K         340 K

Earth            255 K              288,36 K         288 K

Moon           271 Κ              221,74 Κ         220 Κ

Mars            211,52 K         215,23 K         210 K

 

At very first look at the data table we distiquish the following:

Planet or        Te.incomplete     Te.satellites      Rotations

moon                    formula           measured          per day 

Mercury        437 K            340 K            1/58 

Earth             255 K            288 K               1 

Moon            271 Κ            220 Κ            1/29,5 

Mars             211,52 K       210 K               1 

For the slow rotating Mercury and Moon the Incomplete Formula: Te = [ (1-a) S / 4 σ ]¹∕ ⁴ 

gives us much higher results comparing to measured by satellites.

For the fast rotating Earth and Mars the Incomplete Formula: Te = [ (1-a) S / 4 σ ]¹∕ ⁴ 

gives us much lower result for Earth and almost alike for Mars.

 

The first conclusion is that the Incomplete Formula:

Te = [ (1-a) S / 4 σ ]¹∕ ⁴ 

should be abandoned because it gives us very confusing results, or it should be completed, as we already did. The Mercury's and Moon's higher calculated temperatures were because we hadn't inserted the factor Φ = 0,47 in formula yet.

The incomplete formula "was ignorant" of the spherical surface solar irradiation geometrical dependent absorption. That is why the absorbed by insolated planet hemisphere fraction of solar flux was overestimated.

That is why Mercury's and Moon's by incomplete formula calculated temperatures appeared higher than the measured by satellites. 

The second conclusion is that the faster rotating Earth and Mars according to satellites measurements appear to be warmer, and we conclude it happens because of their fast rotation period. We already have "N" (rotations/per day) in our Complete Formula.

I should mention here again that I believe in NASA satellites temperatures measurements. None of my discoveries would be possible without NASA satellites very precise planet temperatures measurements.