The Planet's Surface Mean 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 Planet Mercury’s Φ = 0,47 Paradigm Confirmation

We have now chosen the planet Mercury for its very low albedo a=0,088 and for its very slow rotation spin N=1/175,938 rotations/day.

The planet 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=0,088) plays little role in planet's energy budget.

These (Tmean, R, N, and albedo) planets' parameters are all satellites measured. These planets' parameters 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......0,088......0,136......0,250

1-a…0,912……0,864…….0,75

Let’s calculate, for comparison reason, the Planet Mercury’s effective temperature with the old incomplete formula:

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

We have

(1-a) = 0,912

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 = [ 0,912* 1.362 W/m² * 6,6769 /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =

Te.incomplete.mercury = ( 36.568.215.492,06 )¹∕ ⁴ = 437,296 K

Te.incomplete.mercury = 437,296 K

And we compare it with the

Tsat.mean.mercury = 340 K - the satellite measured Mercury’s mean temperature

Amazing, isn’t it? Why there is such a big difference between the measured Mercury’s mean 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 formula calculation Te = 437 K?

Let’s put these two temperatures together:

Te.incomplete.mercury = 437 K

Tsat.mean.mercury = 340 K

Very big difference, nearly 100°C higher!

But why the incomplete effective temperature formula 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 = 437 K

Very big difference, nearly 100°C higher!

The Planet 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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