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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Venus real color

The Earth seen from Apollo 17

This section will be for planets with atmosphere. The wonderful thing is that when calculating, for planet Venus we obtain the Venus' mean surface temperature T.atmo.mean.venus = 733,66 K

This section will be for planets with atmosphere.

As we can see, planets with thin atmosphere have a very small addition to the surface mean temperature caused by their traces greenhouse gases.

But when it comes to the Venus, or to the gases giants - they have very strong greenhouse effects.

Consequently, when interracting with the emitted back to surface from the greenhouse gases IR emission energy the surface gets additionally warmed in the same exactly way as it gets warmed from the solar flux without atmosphere.

So what we have here is the surface getting warmed from two different sources, the solar flux and the greenhouse gases IR emission energy.

And the wonderful thing is that when calculating, for planet Venus we obtain the Venus' mean surface temperature

T.atmo.mean.venus = 733,66 K.

Venus' Without-Atmosphere Mean Surface Temperature calculation

R = 0,723 AU, is the Venus’ distance from the sun in astronomical units

1/R² = 1,9130

Venus’ albedo: avenus = 0,76 Bond

Venus is a gases planet, Venus’ surface solar irradiation accepting factor Φvenus = 1

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

1/243 rotations /per day, is the planet's Venus sidereal rotation spin.

On the Venus atmosphere winds are 60 times faster than the planet's Venus sidereal rotation spin. Since Venus has very thick atmosphere and being considered a gases planet, the Venus' surface rotation spin will be calculated as

N = 60* 1/243 = 60/243 = 0,24691 rotations per day

cp.venus = 0,19 cal/gr*oC, it is because the surface is regolith – dry soil

σ = 5,67*10⁻⁸ W/m²K⁴, the Stefan-Boltzmann constant So = 1.362 W/m² (So is the Solar constant)

Venus’ Without-Atmosphere Mean Surface Temperature Equation Tmean.venus is:

 

Tmean.venus = [ Φ (1-a) So (1/R²) (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴

 

Τmean.venus = [ 1(1-0,76)1.362 W/m² 1,9130*(150 days*gr*oC/rotation*cal *0,24691rotations/day*0,19 cal/gr*oC)¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =

Τmean.venus = [ 0,24*1.362 W/m²1,9130*(150*0,24691*0,19)¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =

= [ 0,24*1.362 W/m²1,9130*(1,6287) /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =

Τmean.venus = ( 4.490.620.150,82 )¹∕ ⁴ =

Tmean.venus = 258,87 K

 

And we compare it with the

Tsat.mean.venus = 735 K, measured by satellites.

 

What we see here is that planet Venus having a strong greenhouse warming effect due to the greenhouse gas CO2 96,5 % high content in the Venus' atmosphere.

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D * X /Y is the atmosphere Greenhouse gases warming effect parameter. Τmean.atmo.venus = 733,66 K

The new equation is completed now with the atmospheric terms and again gives remarkable results:

It is the greenhouse gases' partial density...

Tmean.atmo - is the planet's surface mean temperature ( with or without atmosphere ) equation

D - is atmosphere's ground density kg/m3

X - is the sum of greenhouse gases % content multilplied by mole weight

Y - is the sum of all the gases % content multiplied by mole weight

X /Y - is the atmosphere Greenhouse gases content coefficient

D * X /Y - is the atmosphere Greenhouse gases warming effect parameter

Tmean = [ Φ (1 - a) S (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴

And

Tmean.atmo = { Φ (1 - a) S (β*N*cp)¹∕ ⁴ ( 1 + D *X/Y ) /4σ }¹∕ ⁴ =

Tmean.atmo = { Φ (1 - a) S (β*N*cp)¹∕ ⁴ [ 1 + D *( Gr.coeff.) ] /4σ }¹∕ ⁴ =

Tmean.atmo = { Φ (1 - a) S (β*N*cp)¹∕ ⁴  [ 1 + D *( Greenhouse coefficient) ] /4σ }¹∕ ⁴

 

Tmean.atmo = { Φ (1 - a) S (β*N*cp)¹∕ ⁴  [ 1 + D kg/m³ *( X%* mole weight of greenhouse gas) mol / (sum of Y% * mole weight of all atmosphere gases content) mol*kg/m³ ] /4σ }¹∕ ⁴ =

 

Examples:

Earth's atmosphere composition:

78,98 % N2 (14*2 = 28),

20,95 % O2 (16*2 = 32),

1 % H2O (1*2 + 16 = 18) water is a greenhouse gas,

0,04 % CO2 (12 + 2*16 = 44) carbon dioxide is a greenhouse gas

Earth's atmosphere ground density is D = 1,23 kg/m3

 

Τmean.atmo.earth =

= Tmean.earth * { 1 + D kg/m³ [ (1% * 18 + 0,04% * 44) mol / (78,98% * 28 + 20,95% * 32 + 1% * 18 + 0,04% * 44) mol*kg/m³ ] }¹∕ ⁴ =

= Tmean.earth * { 1 + D kg/m³ [ (0,01 * 18 + 0,0004 * 44) mol / (0,7898 * 28 + 0,2095 * 32 + 0,01 * 18 + 0,0004 * 44) mol*kg/m³ ] }¹∕ ⁴ =

= 288 K * { 1 + 1,23 kg/m³ [ (0,18 + 0,0176 ) mol / (22,1144 + 6,704 + 0,18 + 0,0176) mol*kg/m³ ] }¹∕ ⁴ =

= 288 K * { 1 + 1,23 kg/m³ [ (0,1976 ) mol / (29,016) mol*kg/m³ ] }¹∕ ⁴ =

= 288 K * { 1 + 0,00681 ] }¹∕ ⁴ =

= 288 K * { 1,00681 }¹∕ ⁴ =

= 288 K * 1,0016982 = 288,49 K

Earth has a small content of greenhouse gasses in the atmosphere. Also Earth's atmosphere density is low. That is why Earth's the D * X/Y parameter is very low.

 

Titan's atmosphere composition:

95 % N2 (2*14 = 28),

5 % CH4 (12 + 1*4 = 16) methane is a greenhouse gas

Titan's atmosphere ground density

D = 1,48*1,23 kg/m³ = 1,8204 kg/m³

because the atmosphere pressure on the Titan's ground is 1,48 of that of Earth's.

Τmean.atmo.titan =

= Tmean.titan * { 1 + D kg/m³ [ (5% * 16) mol / (95% * 28 + 5% * 16) mol*kg/m³ ] }¹∕ ⁴ =

= Tmean.titan * { 1 + D kg/m³ [ (0,05 * 16) mol / (0,95 * 28 + 0,05 * 16) mol*kg/m³ ] }¹∕ ⁴ =

= 93,10 K*{ 1 + 1,48*1,23 kg/m³ [ (0,80 ) mol / (26,60 + 0,80) mol*kg/m³ ] }¹∕ ⁴ =

= 93,10 K*{ 1 + 1,8204 kg/m³ [ (0,80 ) mol / (27,4 ) mol*kg/m³ ] }¹∕ ⁴ =

= 93,10 K*{ 1 + 0,05315 }¹∕ ⁴ =

= 93,10 K*{ 1,05315 }¹∕ ⁴ =

= 93,10 K*1,01303 = 94,31 K

( 93,7 K is the measured )

Titan has a small content of greenhouse gasses in the atmosphere. Also Titan's atmosphere density is low. That is why Titan's the D * X/Y parameter is very low.

 

Venus' atmosphere composition:

96,5 % CO2 (12 + 16*2 = 44) carbon dioxide is a greenhouse gas

3,5 % N2 (14*2 = 28)

Venus' atmosphere ground density D = 65 kg/m3

 

The Tmean.venus is calculated with the rotational spin of Venusian winds velosity, which is 60 times faster than Venus' planet rotational spin, so

N.venus = 60/243 = 0,24691 rot /day

when calculated without atmosphere

Tmean.venus = [ Φ (1 - a) S (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴

Tmean.venus = 258,85 K

 

Τmean.atmo.venus =

= Tmean.venus * { 1 + D kg/m³[ 96,5% * 44 mol / (3,5% * 28 + 96,5% * 44) mol*kg/m³ ] }¹∕ ⁴ =

= Tmean.venus * { 1 + D kg/m³[ 0,965 * 44 mol / (0,035 * 28 + 0,965 * 44) mol*kg/m³ ] }¹∕ ⁴ =

= 258,85 K * {1 + 65 kg/m³ [ 0,965 * 44 mol / (0,035 * 28 + 0,965 * 44) mol*kg/m³ ] }¹∕ ⁴ =

= 258,85 K * {1 + 65 kg/m³ [ 42,46 mol /(0,98 + 42,46) mol*kg/m³ ] }¹∕ ⁴ =

= 258,85 K * {1 + 65 kg/m³ [ 42,46 mol /(43,44) mol*kg/m³ ] }¹∕ ⁴ =

= 258,85 K * { 1 + 63,534 }¹∕ ⁴ =

= 258,85 K * { 64,534 }¹∕ ⁴ =

= 258,85 K * 2,8343 = 733,66 K

 

Τmean.atmo.venus = 733,66 K

(The measured is 735 K or 737 K)

 

Venus has a high content of greenhouse gasses in the atmosphere. Also Venus has a high atmosphere ground density.

That is why Venus' the D * X/Y parameter is very high.

Important notice:

The Tmean.venus is calculated with the rotational spin of Venusian winds velosity, which is 60 times faster than Venus' planet rotational spin

N.venus = 60/243 = 0,24691 rot /day

This information is essential to calculate Venus' without atmosphere surface mean temperature Tmean.venus = 258,85 K

The Gases planets Jupiter, Saturn, Uranus and Neptune have a small content of greenhouse gasses in their atmosphere.

Nevertheless, these planets have very strong greenhouse effect, because their atmosphere density D is very high. Thus the D * X/Y parameter for gases planets appears to be very much high.  

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