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

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Mars: Pictured in natural color in 2007

The Earth seen from Apollo 17

Planet’s Mars Te misfortunate coincidence

Comparison of results planet's Mars Tsat.mean.mars measured by satellites,

planet's Mars Te.mars.incomplete calculated,

and the planet's Mars Tmean calculated by the mean surface temperature equation :

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

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

 

We have here planet's Mars mean temperature measured by satellites:

Tsat.mean.mars = 210 K

calculated by incomplete:

Te.mars.incompl = [ (1-a) S /4 σ ]¹∕ ⁴ = 209,91 K

and the planet's Mars Tmean calculated by the mean surface temperature equation:

Tmean.mars = [ Φ (1-a) S (β* N*cp)¹∕ ⁴ /4σ]¹∕ ⁴ = 213,21 K

 

The difference between Incomplete  Effective Temperature and the planet's Mars Tmean surface temperature calculation equations is:

*[ Φ (β* N*cp)¹∕ ⁴ ]¹∕ ⁴

 

For planet Mars we have:

Mars performs 1 rotation every ( 24,622hours / 24hours/day ) = 1,026 day

N = 1 /1,026 = 0,9747 rotations /day

Mars is a rocky planet, Mars’ surface solar irradiation accepting factor:

Φmars = 0,47

cp.mars = 0,18 cal/gr oC, on Mars’ surface is prevalent the iron oxide Fe2O3

β = 150 days*gr*oC/rotation*cal – it is a Rotating Planet Surface Solar Irradiation Absorbing-Emitting Universal Law constant

(β* N*cp)¹∕ ⁴ = (150*0,9747*0,18)¹∕ ⁴ =

=(26,3169) ¹∕ ⁴ = 2,265

Φ = 0,47

[ Φ (β* N*cp)¹∕ ⁴ ]¹∕ ⁴ =

=( 0,47* 2,265 )¹∕ ⁴ =

=( 1,06455)¹∕ ⁴ = 1,01576

So the difference between these two equations for planet Mars is only 1,576 % !

And it is a coincident.

It is a coincident, but with very important consequences.

 

Let's explain:

Tsat.mean.mars = 210 K measured by satellites

is almost equal with

Te.mars.incomplete = 209,91 K

and Tmean.mars = 213,21 K.

 

When measuring by satellites the Tsat.mean.mars = 210 K

and calculating with incomplete effective temperature equation

Te.mars.incomplete = 209,91 K

scientist were led to mistaken conclusions.

First they concluded that the planet's effective and mean temperatures should normally be equal, which is wrong.

Secondly they concluded that Earth without atmosphere should have effective temperature, according to the incomplete equation calculation,

Te.earth.incomplete = 255 K.

The measured by satellites Tsat.mean.earth = 288 K.

The difference of Δ 33 oC was then attributed to the Earth’s atmosphere greenhouse warming effect.

 

Now we have the planet mean surface temperature equation that gives

Tmean.mars = 213,21 K.

This result is almost identical to the measured by satellites

Tsat.mean.mars = 210 K.

And the Equation gives very reasonable results for all the other planets without-atmosphere in the solar system.

We know now the Δ 33 oC does not exist.

The Tmean.earth = 288,36 K = Tsat.mean.earth = 288 K.

Te.earth = 255 K does not exist.

 

And I dare to assume now, that this Complete Equation may be applied to all the planets without atmosphere in the whole Universe.

And I am convinced there is not any measurable greenhouse effect in Earth's atmosphere. Earth's atmosphere is very thin to have a detectable greenhouse effect.

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Comparison of Te and Te.Φ for planets Mars, Earth, Moon and Mercury

 Φ = 0,47 is the for smooth without atmosphere planet's surface solar irradiation accepting factor

Planet...Tsat.mean.....Te….......Te.Φ

Mars …....210 K ....209,91 K …174 Κ

Earth.......288 K.......255..K......211K

Moon.......220 K.......270..K......224 K

Mercury....340 K......440 K......364 K

Let's explain:

Tsat = 210 K measured by satellites is almost equal with Te = 209,91 K

So scientist were led to mistaken conclusions.

First they assumed that the planet's effective and mean surface temperatures were equal, which is wrong.

Second, Earth's effective temperature was calculated as

Te.earth = 255 K

The measured by satellites

Tsat.mean.earth = 288 K.

The difference of Δ 33 oC was attributed to the Earth’s atmosphere greenhouse warming effect.

Now we have calculated planet's Mars effective temperature

Te.Φ = 174 K

So the assumption that planet's

Tsat.mean = Te is wrong.

Planet's Mars Tsat = 210 K.

We can conclude now that planet's Earth

Te.earth = 255 K is not equal with the planet's Earth Tmean.earth.

Thus the difference of Δ33 oC does not exist.

Also we have calculated the planet's Earth Te.Φ = 211 K

which is much less than the previously estimated Te.earth = 255 K.

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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 ← Tmax

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