Corrected Effective Temperatures of the Planets' and the Mean Surface Temperature Equation: Tmean = [ Φ (1-a) S (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴

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Mercury in color

Φ - dimensionless solar irradiation accepting factor

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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