The Blue Marble by the crew of Apollo 17 (1972)

### 1. Earth’s Without-Atmosphere Mean Surface Temperature calculation

Tmean.earth

So = 1.361 W/m² (So is the Solar constant)

S (W/m²) is the planet's solar flux.

For Earth S = So

Earth’s albedo: aearth = 0,306

Earth is a smooth rocky planet, Earth’s surface solar irradiation accepting factor Φearth = 0,47

(Accepted by a Smooth Hemisphere with radius r sunlight is S*Φ*π*r²(1-a),

where Φ = 0,47)

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

N = 1 rotation /per day, is Earth’s axial spin

cp.earth = 1 cal/gr*oC, it is because Earth has a vast ocean. Generally speaking almost the whole Earth’s surface is wet. We can call Earth a Planet Ocean.

σ = 5,67*10⁻⁸ W/m²K⁴, the Stefan-Boltzmann constant

Earth’s Without-Atmosphere Mean Surface Temperature Equation Tmean.earth is:

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

Τmean.earth = [ 0,47(1-0,306)1.361 W/m²(150 days*gr*oC/rotation*cal *1rotations/day*1 cal/gr*oC)¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =

Τmean.earth = [ 0,47(1-0,306)1.361 W/m²(150*1*1)¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =

.

.

Τmean.earth = ( 6.854.905.906,50 )¹∕ ⁴ = 287,74 K

Tmean.earth = 287,74 Κ

And we compare it with the

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

These two temperatures, the calculated one, and the measured by satellites are almost identical.

Conclusions:

The planet mean surface temperature equation

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

produces remarkable results.

The calculated planets temperatures are almost identical with the measured by satellites.

Planet…....Tmean….Tsat.mean

Mercury.....325,83 K…..340 K

Earth……....287,74 K…..288 K

Moon……...223,35 Κ…..220 Κ

Mars………..213,21 K…..210 K

Te.correct vs Tsat.mean comparison table

Planet…........Te........Te.correct.......Tmean….Tsat.mean

Mercury....439,6 K…….364 K..........325,83 K…..340 K

Earth……...255 K…......210 K...........287,74 K…..288 K

Moon……..270,4 Κ…....224 K..........223,35 Κ…..220 Κ

Mars……..209,91 K…….174 K..........213,21 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.

There is NO +33°C greenhouse enhancement on the Earth's mean surface temperature.

Both the calculated by equation and the satellite measured Earth's mean surface temperatures are almost identical:

Tmean.earth = 287,74K = 288 K

### CONCLUSION

The planet mean surface temperature equation is for planets WITHOUT ATMOSPHERE the whole planet equilibrium emission concept.

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

When applied to the planets the equation produces remarkable results. The calculated planets temperatures are almost identical with the measured by satellites.

Planet………Te………….Tmean…Tsat.mean

Mercury….439,6 K…….325,83 K…..340 K

Earth………255 K………287,74 K…..288 K

Moon……..270,4 Κ……..223,35 Κ…..220 Κ

Mars……209,91 K……..213,21 K…..210 K

The results speak for themselves – it has become possible to calculate planets mean surface temperatures very closely matching the measured by satellites.

When we compare the results for Planet Earth we realize that there is very small difference between the Tmean = 287,74 K and the Tsat.mean = 288 K.

This observation can only be attributed to the fact that there are only traces of greenhouse gasses in the Earth’s atmosphere.

Also the Earth’s atmosphere is very thin. There is not any significant Greenhouse Gasses Warming effect on the Earth’s surface.

.

https://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

.

“I am not certain Earth would warmer or cooler if its day was 48 hours or 12 hours.”

the temperatures
RELATE, (everything else equals), as their (N*cp) products SIXTEENTH ROOT.

Tmean.1 /Tmean.2 =

= [ (N1*cp1) /(N2*cp2) ]^1/16

Where:
N rotations/day, is the planets axial spin.
cp cal/gr*oC, is the planets average surface specific heat.

Earth rotates N =1rot/day it is N1
Earth Tmean = 288K it is Tmean.1

Now if its day was 12 hoours, N2 =2 rot/day

Everything else equals, in both cases Earth is covered with ocean,

so cp1 = cp2

Let’s calculate for Tmean.2:

Tmean.1 /Tmean.2 = ( N1 /N2 )^1/16

288K /Tmean.2 = ( 1/2 )^1/16 = 0,9576

Tmean.2 = 288K/0,9576 = 300,75K

If Earth’s day was 12 hours, Earth’s average surface temperature would have been 300,75K