### The Mercury’s Φ = 0,47 Paradigm Confirmation

**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 incomplete effective temperature formula 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, for comparison reason, the Mercury’s effective temperature with the old incomplete equation:**

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

** We have**

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

**1/R² = 6,6769**

** So = 1.362 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.incomplete.mercury = [ 0,932* 1.362 W/m² * 6,6769 /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =**

** Te.incomplete.mercury = ( 37.369.999.608,40 )¹∕ ⁴ = 439,67 K**

** Te.incomplete.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**

** Amazing, isn’t it? Why there is such a big difference between the measured Mercury’s mean surface temperature, Tmean = 340 K, which is the correct, ( I have not any doubt about the preciseness of satellite planets' temperatures measurements ) and the Mercury's Te by the effective temperature incomplete equation calculation Te = 440 K?**

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

** Te.incomplete.mercury = 440 K**

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

**Very big difference, a 100°C higher!**

** But why the incomplete effective temperature equation gives such a wrongly higher result?**

** The answer is simple – it happens because the incomplete formula 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 0,53*S of the incident solar irradiation. **

**Imagine a completely black planet; imagine a completely invisible planet, a planet with a zero albedo. **

**This planet still reflects 53 % of the incident on its surface solar irradiation.**

**The satellite measurements have confirmed it.**

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

**Te.incomplete.mercury = 440 K**

** Very big difference, a 100°C higher!**

**The Mercury’s Φ = 0,47 Paradigm has confirmed it:**

** Φ = 1 - 0,53 = 0,47 **

**Φ = 0,47**

**Φ - is the dimensionless planet surface solar irradiation accepting factor**

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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……….437 K……….346,11 K……..340 K**

** Earth…………..255 K………..288,36 K……..288 K**

** Moon…………..271 Κ………..221,74 Κ……..220 Κ**

** Mars…………209,91 K……..213,42 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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