### 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.

**I **

**http://www.cristos-vournas.com**

** The faster a planet rotates (n2>n1) the higher is the planet’s average (mean) temperature T↑mean:**

** Tmin↑→ T↑mean ← T↓max**