Earth’s Without-Atmosphere Corrected Effective Temperature calculation Te.correct.earth = 210 Κ
Earth's Corrected Effective Temperature is Te.correct.earth = 210 Κ
To calculate Earth's Corrected Effective Temperature we should use the following data values
σ = 5,67*10⁻⁸ W/m²K⁴, the Stefan-Boltzmann constant
Φ = 0,47 solar irradiation accepting factor (dimensionless)
a = 0,306 Earth's average albedo
So = 1.361 W/m², solar flux on the top of the Earth's atmosphere
Earth’s Without-Atmosphere Corrected Effective Temperature Equation Te.correct.earth is:
Te.correct.earth = [ Φ (1-a) So /4σ ]¹∕ ⁴
Te.correct.earth = [ 0,47 (1-0,306) 1.361 W/m² /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =
Te.correct.earth = [ 0,47 (0,694) 1.361 W/m² /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =
Te.correct.earth = ( 1,957.367.636,68 )¹∕ ⁴ = 210,34 K
Te.correct.earth = 210,34 K or Te.correct.earth = 210 K
The Planet Corrected Effective Temperature : Te.correct = [ Φ (1-a) S /4σ ]¹∕ ⁴
Te - planet effective temperature Te = [ (1-a) S /4σ ]¹∕ ⁴
Te.correct - the planet corrected effective temperature
Te.correct = [ Φ (1-a) S /4σ ]¹∕ ⁴
Φ - is the solar irradiation accepting factor (it is the planet surface spherical shape, and planet surface roughness coefficient)
Φ = 0,47 - for smooth surface planets without atmosphere
Φ = 1 - for heavy cratered without atmosphere planets
Φ = 1 - for gases planets
.......................................
Te.correct = [ Φ (1-a) S /4σ ]¹∕ ⁴
Tmean = [ Φ (1-a) So (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴
Or Tmean = Te.correct * [ (β*N*cp)¹∕ ⁴ ]¹∕ ⁴
Table 1.
Comparison of Predicted (Tmean) vs. Measured (Tsat) Temperature for All Rock-type Planets
......................Φ....Te.correct ..[(β*N*cp)¹∕ ⁴]¹∕ ⁴..Tmean ...Tsat
...................................°K ........................................°K .........°K
Mercury .....0,47....364,0 ........0,8953............. 325,83 ...340
Earth ..........0,47....210 ...........1,368................287,74 ....288.
Moon ..........0,47....224 ...........0.9978.............223,35 .....220
Mars ...........0,47....174 ...........1,227..............213,11 .....210
Io ..................1.......95,16 ........1,169..............111,55 .....110
Europa ........0,47....78,83 ........1,2636.............99,56 .....102
Ganymede...0,47....88,59 ........1,209.............107,14 ....110
Calisto ..........1.....114,66 ........1,1471...........131,52 ....134 ±11
Enceladus .... 1 ......55,97 ........1,3411............75,06 .......75
Tethys ..........1.......66,55 .........1,3145 ...........87,48 .......86 ± 1
Titan .............1.......84,52 .........1,1015 ...........96,03 .......93,7
Pluto .............1.......37 ..............1,1164 ...........41,6 .........44
Charon .........1......41,90 ...........1,2181 ...........51,04 .......53
Conclusion:
We can calculate planet mean surface temperature obtaining very close to the satellite measured results.
Tmean = Te.correct * [ (β*N*cp)¹∕ ⁴ ]¹∕ ⁴ where [ (β*N*cp)¹∕ ⁴ ]¹∕ ⁴ - is the planet surface warming factor
Warming Factor = (β*N*cp)¹∕₁₆
Why is (for Earth Te =255K) NASA calculation so inaccurate – too high?
Earth without-atmosphere and higher than Moon Albedo (a=0,306), when measured by NASA the Earthen equilibrium temperature should be even less than 210K.
Why is (for Earth Te =255K) NASA calculation so inaccurate – too high?
And Tse – Te = 288K - 210K = 78C the measured GHE then?
The planet effective temperature Te is not the limit to the avg. temperature rise.
There is a deeply established concept that "The avg. planetary temperature changes with rotation speed rising to equilibrium temperature as the spin rate increases.”
This concept determines the planet effective (equilibrium) temperature Te as a kind of cut-off point. This concept states, planet avg. temperature (the avg. surface without-atmosphere temperature) cannot exceed the planet effective (equilibrium) temperature Te, no matter how fast the planet rotational spin.
What we actually observe is the following:
The avg. planetary temperature changes with rotation speed rising to equilibrium temperature and overgoing it as the spin rate increases...
Notice, there is a limit to the avg. planetary temperature rise, but it is not the Te or the Te.corrected.
Also the calculated Te and Te.corrected assume planet having reached uniform surface temperature, which is impossible, because planets always are solar irradiated by one side, and, no matter how fast they rotate, the solar lit side is always warmer…
And there are not measured data for planets' blackbody temperatures, because planet blackbody temperatures, (either the not corrected Te and the corrected Te.corrected) are only mathematical abstractions.
When rotating faster – more areas get exposed to solar flux in unit of time.
(Orphan planet is a planet not having a mother star to orbit).
Orphan planet is not solar energy irradiated, therefore it has a surface temperature because of its own internal heat sources.
Two orphan planets may have the same average surface temperature, but the more differentiated surface temperatures orphan planet has the greater amount of IR outgoing radiative energy the orphan planet emits. (It is in accordance with Stephan-Boltzmann emission law nonlinearity.)
Let’s consider two orphan planets emitting the same amount of IR outgoing radiative energy. The more surface temperatures differentiated orphan planet – the colder on average surface temperature planet.
An orphan planet with uniform surface temperature would have approached the planet effective radiative temperature Te. Te is the highest possible average surface temperature for an orphan planet.
When rotating the planet surface has larger surface areas get exposed to solar flux in unit of time. When rotating faster – more areas get exposed.
Since surface's the slower ability to accumulate HEAT than emit IR, the faster rotating planet is capable to TRANSFORM larger amounts of SW EM radiative solar energy into HEAT.
Thus the faster rotating planet (everything else equals) is capable to accumulate larger amounts of transformed into HEAT solar EM energy.
That is what makes a faster rotating planet on average surface a warmer planet.