### Φ - factor is proven by the observed quantities

** Φ - factor is proven by the observed quantities**

** I know what was missing in my syllogisms. There was a need of observed quantities. **

**I have to offer observed numbers to prove that a planet (a sphere) follows the basic law of the parallel solar rays energy reflection /absorption ratio. **

**The observed numbers should be very convincing.**

** We have chosen Mercury for its very low albedo a=0,068 and for its very slow rotational spin N = 1/175,938 rotations/day. **

**Mercury is most suitable for the blackbody effective temperature equation definition - a not rotating planet, or very slow rotating. Also it is a planet where albedo (a=0,068) plays little role in planet's energy budget.**

** These (Tmean, R, N, and albedo) parameters of the planets are all satellite measured. These parameters of the planets are all observations.**

** Planet….Mercury….Moon….Mars**

** Tsat.mean.340 K….220 K…210 K**

** R…......0,387 AU....1 AU...1,525 AU**

** 1/R²…..6.6769….....1….…0,430**

** N…1 /175,938..1 /29,531..0,9747**

** a.........0,068.........0,11......0,250**

** 1-a…...0,932….....0,89......0,75**

** Let’s calculate the Mercury’s effective temperature with the old blackbody equation:**

** Te.mercury = [ (1-a) So (1/R²) /4σ ]¹∕ ⁴ **

**We have**

** (1-a) = 0,932 **

**1/R² = 6,6769 **

**So = 1.361 W/m² - it is the Solar constant ( the solar flux on the top of Earth’s atmosphere )**

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

**Te.mercury = [ 0,932* 1.361 W/m² * 6,6769 /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =**

** Te.mercury = ( 37.369.999.608,40 )¹∕ ⁴ =**

** 439,67 K Te.mercury = 439,67 K = 440 K **

**And we compare it with the Tsat.mean.mercury = 340 K - the satellite measured Mercury’s mean surface temperature**

** Let's analyze what we have here.**

** Because of Mercury having a very low albedo (a = 0,68) the what is left to absorb for Mercury's surface is (1-a) = 0,932 or 93,2 % of the incident solar flux on the Mercury (according to the theory of planets absorbing the incoming parallel solar rays as a cross section disk).**

** So it was thought that the 93,2 % is absorbed. **

**Te.mercury = 440 K**

** Tsat.mean.mercury = 340 K**

** Let's calculate the Mercury's corrected effective temperature by inserting in the above equation the Φ = 0,47**

** Te.mercury.correct = [ Φ (1-a) So (1/R²) /4σ ]¹∕ ⁴**

** Te.mercury.correct = [ 0,47*0,932* 1.361 W/m² * 6,6769 /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =**

** Te.mercury.correct = ( 17.536.114.624,63 )¹∕ ⁴ = 363,9 K **

**Te.mercury.correct = 363,9 K = 364 K **

**Let’s put these temperatures together:**

** Te.mercury = 440 K **

**Te.mercury.correct = 364 K**

** Tsat.mean.mercury = 340 K **

**The difference is 440 K - 364 K = 76°C**

**This difference is due to the absence of the Φ(1-a) coupled term.**

** And Te.mercury.correct = 364 K is very much closer to Tsat.mean.mercury = 340 K measured by satellite, and it is due to the Φ = 0,47 for the smooth surface planets.**

**The answer is simple – it happens because the old equation (Te.mercury = 440 K) assumes planet absorbing solar energy as a disk and not as a sphere.**

** We know now that even a planet with a zero albedo reflects a**

**[1 - Φ(1-a)]S portion of the incident on it's surface solar irradiation.**

** Imagine a completely black smooth surface planet; imagine a completely invisible planet, a planet with a smooth surface and with a zero albedo. This planet still reflects [1 - Φ(1-a)]S portion of the incident on its surface solar irradiation. **

**The satellite measurements have confirmed it.**

**https://en.wikipedia.org/wiki/Mercury_(planet)**

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**Conclusions: **

**The Planet's Surface Mean Temperature Equation produces remarkable results. The calculated planets’ temperatures are almost identical with the measured by satellites.**

** Planet..…Te.incomplete…Tmean…Tsat.mean**

** Mercury……….440 K……….325,83 K……..340 K**

** Earth…………..255 K………..287,74 K……..288 K**

** Moon…………..270,4 Κ…....223,35 Κ……..220 Κ**

** Mars…………209,91 K……..213,21 K……..210 K**

** The 288 K – 255 K = 33 oC difference does not exist in the real world.**

** There are only traces of greenhouse gasses. The Earth’s atmosphere is very thin. There is not any measurable Greenhouse Gasses Warming effect on the Earth’s surface.**

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