The very POWERFUL the Solar Irradiated planet surface Rotational Warming Phenomenon ( N*cp )^1/16

All planets and moons are inevitably subjected to that UNIVERSAL PHENOMENON

because (everything else equals),

(Tsat.planet.1) /(Tsat.planet.2) = 

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

The PLANETARY (Tsat /Te.correct) CRITERION 

Table of data

................HORIZONTAL...............1 GRAPH........2 GRAPH

Planet..Warming factor... Φ.......(Tsat /Te)....(Tsat /Te.correct)

...............(β*N*cp)^1/16                                                 criterion

Mercury........0,895..........0,47........0,773..............0,934

Moon............0,998..........0,47........0,815..............0,982

Earth............1,368..........0,47........1,134..............1,365

Mars.............1,227..........0,47....... 1.....................1,207

Ceres............1,4535...........1............ - ................... - ......

Io..................1,169...........1............1,156..............1,156

Europa.......1,264.........0,47......1,072............1,294

Ganymede....1,209..........0,47........1,028..............1,242

Calisto..........1,147...........1............1,169..............1,169

Enceladus....1,341...........1.............1,340..............1,340

Tethys..........1,315...........1............1,292..............1,292

Titan..............1,1015.........1............1,1086............1,1086

Triton...........1,158..........? .............1,297. ?...........1,297 ?

Pluto............1,116...........1............1,189..............1,189

Charon.........1,218...........1............1,265..............1,265

***********************

I had the impression that I need to work on it.

A lot of things about it were really exciting, the biggest being that you'll potentially discover a new PHENOMENON from the PLANETS TEMPERATURES COMPARISON.

***********************

The carbon dioxide (CO2) is a trace gas in Earth’s thin atmosphere.
The 0,04 % CO2 doesn’t cause any harm to the global climate.
It is obvious for us engineers.

***********************

The Rotational Warming Phenomenon is not only about THE NON-LINEARITY OF THE S-B EMISSION LAW.

It is a much more Powerful Phenomenon.

********************

In the Graph the cause and effect move in the same direction.

The Graph Ratio of Measured Planet Temperature to Corrected Blackbody Temperature (Tsat /Te.correct), as a Quasi-LINEAR  function of the Rotational Warming Factor = (β*N*cp)^1/16

************

What we did in the present research was to compare the different planets and moons surface temperatures in accordance with the incident on the planet surface their respective solar flux (S), with their respective average surface Albedo (a), and, also, in accordance with their respective rate of rotation (N) , and with their respective surface specific heat (cp) and surface roughness features (the light capturing abilities).

-

In this research we have shown, and now we demonstrate that a planet average surface temperature (Tmean K) is determined by those five (5) major parameters:

1. The distance from the sun (solar flux "S" W/m²).

The intensity of the incident on a celestial body solar EM energy is dependent on the distance from the sun the square inverse law value.

Because the intensity of solar EM energy upon a planet or moon is the major factor determiming the planet's or moon's average surface temperature Tmean.

2. The average surface diffuse reflectivity (Albedo "a"),

which is dependent on the planet's or moon's average surface the diffuse reflection properties.

Because the higher the planet's or the moon's Albedo - the less solar EM energy interacts with surface's matter, the less is the average surface temperature Tmean.

3. The surface's spherical shape and the surface's roughness coefficient (the solar irradiation accepting factor "Φ").

Because planets and moons have very distinguished their respective surfaces features - there are the smooth surface planets and moons and there are the rough surface planets and moons.

The rough surface planets and moons almost do not exhibit the specular reflection from their respective surfaces.

4. The rate of rotation ("N" rotations/day),

which is a unique for every planet and moon value.

Because when rotating faster a planet's or moon's surface accumulates more solar energy, and, therefore, the planet or moon average surface temperature Tmean appears to be higher.

5. The average surface specific heat ("cp" cal/gr*oC),

which is determined by the planet the respective average surface chemical composition.

Because when the average surface specific heat cp is higher, there are more atoms streched over the square meter of surface, there are more atoms to interact with the incident solar EM energy.

Therefore the average surface temperature Tmean appears to be higher.

Yes, the same universal laws, but applied to different input parameters.
So the same universal physical laws, but applied to different celestial bodies.

And, there also is, the very POWERFUL the Solar Irradiated planet surface Rotational Warming Phenomenon.

******************************************************

Summary:

A new universal equation for calculating a planet's mean surface temperature is developed here, to provide better estimates than the simple "blackbody" equation which was based on simplifying assumptions.

Recognizing that a real planet does not match the assumptions for an idealized blackbody, Vournas developed an expanded equation with four additional terms to better represent a planet's actual conditions, particularly considering planet axial rotation.

The derivation of the new equation from the planet energy balance is shown below, followed by a description for each of the four new terms in the new equation, including rotation (N), specific heat capacity (cp), solar light reflection and dispersion (Φ, a), and a new universal constant (β) determined empirically.

This new Vournas equation results are compared for twenty (20) solar system bodies (planets and moons), with the equation's calculated temperature closely matching the data, the NASA satellite measured temperature.

********************************************************

The Planet Without-Atmosphere (Tmean) Universal Equation

What we need is a universal equation, when substituting in the equation for every planet's or moon's surface its respective the major characteristic data, because we should be able to theoretically calculate for every planet or moon the average surface temperature (Tmean).

The Planet Surface Rotational Warming Phenomenon should be necessarily present in the Planet Without-Atmosphere (Tmean) Universal Equation, because to this Phenomenon all planets and moons are strongly subjected.

******************

Very well...

***********

The (Tsat /Te) Ratio's Deterministic Relationship

-

Tsat  - is the satellite measured the planet or moon average surface temperature.

Te - is the theoretically calculated the planet or moon  uniform surface temperature (the effective temperature).

 Te = [(1-a) S /4σ ]^1/4 (K) (1)

where

a - is the average surface Albedo.

Albedo is defined as the diffuse reflected portion of the incident on planet surface solar flux.

S - W/m²  the solar flux at the Planet's or moon's average distance from the sun.

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

*************

Whereas, because of its natural occurence, the (Tsat) is all the solar and planetary parameters dependent value, on the other, the theoretically calculated planet effective temperature (Te) is only the Solar flux (S) and the planetary Albedo (a) dependent value.

-

What we see is that for different planets and moons (Tsat) and (Te) do not give the same respective numerical values, hence (Tsat) and (Te) are not physically comparable,

also when we compare for the different planets and moons their respective (Tsat/Te) ratios, the ratios are very different, 

and that implies the effect of some additional planetary physical variables...

therefore, there definitely should be some deterministic relationship between the (Tsat) and (Te) values.

Those two terms,

the measured average surface temperature (Tsat) simply occurs as the result of solar EM energy actual interaction with planet surface

and

the calculated uniform surface temperature (Te) is a result of theoretical approach

both those two terms (the average Tsat and the uniform Te) deal with the entire planetary surface temperature (they both resulting to the average surface temperature), but they are different the average surface temperatures physical terms.

Therefore, they cannot be (the measured Tsat average vs the calculated Te uniform), they cannot be straight-forwardly compared between them...

We note that (Tsat) and (Te) both depend on the same physical properties,

i.e. both (the measured Tsat average) and (the calculated Te uniform) strongly depend on the same two physical properties, namely:

S - the same solar flux (W/m²)

a - the same average Albedo

As we demonstrate further on, Tsat > Te almost for all planets and moons.

So there should be a good reason for that

Tsat > Te 

The measured (Tsat) also necessarily depends on planet spin (N) and on planet surface specific heat (cp).

But for the theoretically calculated (Te) - according to the blackbody planet uniform surface temperature definition - the planet spin (N) and the planet surface specific heat (cp) are being  ignored in the theoretical Te  formula.

Thus, some necessarily expected influence from the planet spin (N), on the planet average surface temperature is whatsoever absent in the theoretical (Te) temperature.

And, some necessarily expected influence from the planet average surface specific heat (cp), on the planet average surface temperature is also whatsoever absent in the theoretical (Te) temperature.

When we compare for the different planets and moons their respective (Tsat/Te) ratio, we are confident we are on the right direction,

because there should be a deterministic relationship on the basis of the newly discovered the Rotational Warming Phenomenon.

Thus, we proceed then, for planets and moons, relating their respective

(Tsat/Te) ratio with their respective Rotational Warming Factor = (β*N*cp)^1/16

where

β = 150 days*gr*oC/rotation*cal –  ( the Rotational Warming Factor constant ),

which relates the rotating planet average surface temperature (Tsat) with the planet effective temperature (Te), and this new  constant (β) is determined empirically.

Below we can see:

The Graph Ratio of Measured Planet Temperature to NOT CORRECTED Blackbody Temperature (Tsat /Te), as a linear function of the Rotational Warming Factor = (β*N*cp)^1/16

The Graph Ratio of Measured Planet Temperature to CORRECTED Blackbody Temperature (Tsat /Te.correct), as a Quasi-LINEAR function of the Rotational Warming Factor = (β*N*cp)^1/16

In the above Graph (Tsat /Te.correct) we distinquish the following scientifical truths:

1). Tsat is planets' or moons' the average surface satellite measured temperatures.

2). N is the planets' or moons' the measured rotational ratio.

3). cp is the planets' or moons' (for the known average surface chemical composition) the specific heat.

4). Earlier we have demonstrated the Powerful Rotational Warming Phenomenon, which is present in the Graph.

5). When the planets' or moons' effective temperature (Te) is calculated, it is based on the measured solar flux upon the planet and it is based on the measured average surface Albedo.

6). When the effective temperature (Te) was corrected, the six planets and moons, which are known for their smooth surface features, were aligned with the rough surface planets and moons.

Consequently, all data used in above Graph are measured values.

Also, all data used in above Graph are independently measured values.

The six smooth surface planets and moons alignment with the rough surface planets and moons testifies for the rightness of the 

Solar Irradiation Accepting Factor

(Φ = 0,47) - the planet surface spherical shape and roughness coefficient.

Thus the Solar Irradiation Accepting Factor

(for smooth surface Φ = 0,47) - the planet surface spherical shape and roughness coefficient - is of the major importance for the planets' or moons' the Radiative Energy balance

Energy in = Energy out

the very much precise estimation.

*****************

***************************

The Theoretical Equation

The theoretical equation we seek for, the theoretical equation Tmean should have its calculated results to be very close to the satellite measured temperatures Tsat, because it is exactly what we are looking for, so we shall have:

Tmean = Tsat = ~ Te.correct*(β*N*cp)^1/16

Tmean  =    Te.correct   *   (β*N*cp)^1/16

Tmean = [ Φ (1-a) S /4σ ]^1/4 * (β*N*cp)^1/16

or

Tmean = [ Φ (1-a) S (β*N*cp)^1/4 /4σ ]^1/4 (K) (3)

and

Tmean = [ Φ (1-a) S (β*N*cp)^1/4 /4σ ]^1/4 (K) (3)

************

So, a planet surface responses to the (interacts with), responses to the incident solar energy, and because of that there is an average surface temperature.

The Planet Surface Rotational Warming Phenomenon what it does is to modulate (to rise) the planet average surface temperature. Because the higher the planet's (N*cp) product - the higher the planet average surface (Tmean) temperature.

–
The EM energy comes from sun. There is the

“energy in =energy out” the equilibrium energy balance axiom to be met.

So, there is the Solar flux (S), surface Albedo (a), the solar irradiation accepting factor (the spherical shape and roughness coefficient (Φ) ), and also, there is the Planet Surface Rotational Warming Phenomenon.

Therefore, we have formulated the Planet Mean Surface Temperature Theoretical Equation:

Tmean = [ Φ (1-a) S (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴ (K)   (3)

Equation is building in the actual Rotational Warming Phenomenon.

The Phenomenon correlates spin (N) and average surface specific heat (cp) with average surface temperature (Tmean).

**************

************

**********

We shall proceed by calculating the planets' and moons' Mean Surface Temperatures by the use of the Planet Mean Surface Temperature Theoretical Equation:

1. Earth's Without-Atmosphere Mean Surface Temperature Calculation.

R = 1 AU, is the Earth's distance from the sun in astronomical units (R = 150.000.000 km, which is Earth's average distance from the sun).

Earth’s albedo: aearth= 0,306

Albedo is defined as the diffuse reflected portion of the incident on planet surface solar flux.

Earth is a smooth rocky planet, Earth’s surface solar irradiation accepting factor is:

Φearth= 0,47

Φ - is the planet surface solar irradiation accepting factor (the planet surface spherical shape and the planet surface roughness coefficient).

Φ(1 - a) - is the planet surface coupled term (it represents the NOT REFLECTED portion of the incident on planet surface solar flux, it is the portion of solar flux which gets in INTERACTION processes with the planet surface).

β = 150 days*gr*oC/rotation*cal – ( the Rotational Warming Factor constant ).

N = 1 rotation /per day, is Earth’s rate of rotation in reference to the sun. Earth's day equals 24 hours= 1 earthen day.

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

So = 1.361 W/m² (So - it is the Solar constant - the solar flux at the Earth's average distance from the sun).

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 =

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.

.................................................

2. Moon’s Mean Surface Temperature calculation.

Tmean.moon

Surface temp..Tmin..Tmean..Tmax Kelvin

........................100.K...220.K...390.K

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

Moon’s albedo: amoon = 0,11

Moon’s sidereal rotation period in reference to the stars is 27,32 earthen days. But Moon also orbits sun, so the lunar day is 29,5 earthen days.

Moon does

N = 1/29,5 rotations/per day

Moon is a rocky planet, Moon’s surface irradiation accepting factor Φmoon = 0,47

(Accepted by a Smooth Hemisphere with radius r sunlight is S* Φ*π*r²*(1-a), where Φ = 0,47)

cp.moon = 0,19cal/gr oC, moon’s surface specific heat (moon’s surface is considered as a dry soil)

β = 150 days*gr*oC/rotation*cal – ( the Rotational Warming Factor constant ).

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

Moon’s Mean Surface Temperature Equation Tmean.moon:

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

Tmean.moon = { 0,47 (1 - 0,11) 1.361 W/m² [150* (1/29,5)*0,19]¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ }¹∕ ⁴ =

Tmean.moon = ( 2.488.581.418,96 )¹∕ ⁴ = 223,35 K

Tmean.moon = 223,35 Κ

The newly calculated Moon’s Mean Surface Temperature differs only by 1,54% from that measured by satellites!

Tsat.mean.moon = 220 K, measured by satellites.

.................................................

3. Mars’ Mean Surface Temperature calculation.

Tmean.mars

Surface temp..Tmin..Tmean..Tmax

Kelvin............130.K...210.K...308.K

(1/R²) = (1/1,524²) = 1/2,32

Mars has 2,32 times less solar irradiation intensity than Earth has

Mars’ albedo: amars = 0,25

Mars performs 1 rotation every 1,028 day

For Mars

N = 1 /1,028 = 0,9728 rotations /day (or 0,9728 marsian day /per an earthen day)

Mars is a rocky planet, Mars’ surface irradiation accepting factor: Φmars = 0,47

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

β = 150 days*gr*oC/rotation*cal – ( the Rotational Warming Factor constant ).

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

Mars' Mean Surface Temperature Equation is:

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

Tmean.mars = [ 0,47 (1-0,25) 1.361 W/m²*(1/2,32)*(150*0,9728*0,18)¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =

=( 2.066.635.457,46 )¹∕ ⁴ = 213,21 K

Tmean.mars = 213,21 K

The calculated Mars’ mean surface temperature

Tmean.mars = 213,21 K is only by 1,53% higher than that measured by satellites

Tsat.mean.mars = 210 K !

................................................

So, we know how to calculate the PLANETARY TEMPERATURES.

After the initial insights, in the present research we demonstrate a typical scientific analysis.

And we have calculated the planet mean surface temperatures for all planets and moons. The calculations are in the next pages of the present site.

Table 1. Comparison of Predicted (Tmean) vs. Measured (Tsat) Temperature for All Planets and moons in solar system

Tmean = [ Φ (1-a) S (β*N*cp)^1/4 /4σ ]^1/4 (K)  (3)

Table 1. Comparison of Predicted vs. Measured Temperature for All Planets

               Distance      Flux      Factor       Bond        rot /day      surface      cal /gr.°C  Warming.Factor   °K        °K           °K       °K

                   ( AU )     ( W/m² )      Φ         Albedo        N Spin          Type               Cp              (β*N*cp)¹∕ ⁴   Te  Te.correct Tmean Tsat

Mercury    0,387      9082,7      0,47         0,068        0,00568         basalt            0,20             0,64250        439,6   364,0    325,83   340

Venus        0,723      2601,3      1              0,77         60/243           gases             0,19             1,6287           226,6   255,98       -       737

Earth         1,0          1361         0,47         0,306         1,0               ocean             1                 3,4996            254     210      287,74    288

Moon         1,0          1361         0,47        0,11           0,0339          regolith         0,19             0,99141       270,4    224      223,35    220

Mars          1,524        586,4      0,47        0,25           0,9728           rock              0,18             2,26495       209,8    174      213,11    210

Ceres         2,77         177,38     1             0,09           2,645             ice                1                  4,463            162,9  162,9     236          -

Jupiter       5,20          50,37     1              0,503        2,417            gases               -                     -                102     102           -         165 at 1 bar level

Io               5,20          50,37      1             0,63          0,5559            rock             0,145           1,8647          95,16   95,16     111,5     110

Europa      5,20          50,37      0,47         0,63          0,2816           ice                1                  2,5494         95,16    78,83     99,56     102

Ganymede 5,20         50,37      0,47        0,41          0,1398           ice                 1                  2,14           107,08   88,59    107,14    110

Calisto      5,20          50,37      1              0,22          0,0599          ice                 1                 1,7313        114,66  114,66  131,52    134±11

Saturn       9,58         14,84      1             0,342        2,273             gases               -                     -              81         81           -        134 at 1 bar level

Enceladus 9,58         14,84      1             0,85           0,7299           ice                1                  3,2347      55,97     55,97     75,06      75

Tethys       9,58         14,84      1            0,70            0,52971         ice                1                  2,9856      66,55     66,55     87,48     86 ± 1

Titan         9,58         14,84      1            0,22            0,06289        gases            0,4980         1,47223     84,52     84,52     93,10      93,7

Uranus    19,22          3,687     1            0,30           1,389             gases              -                      -       58 MM *      -             -         76 at 1 bar level

Neptune  30,33         1,48       1            0,29           1,493              gases             -                      -          46,4       46,4          -         72 at 1 bar level

Triton      30,33         1,48      0,47 (?)   0,76            0,17021          rock           0,4116           1,800          35,4      29,29     33,92       38

2) Triton  30,33         1,48     1 (?)         0,76            0,17021         rock            0,4116          1,800           35,4      35,4      40,97       38

Pluto        39,48        0,874     1             0,50           0,1565            rock            0,248            1,5533         37         37         41,6         44

Charon    39,48         0,874     1            0,2              0,1565            ice                1                 2,2014         41,90    41,90    51,04       53

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"This new Vournas equation results are compared for twenty (20) solar system bodies (planets and moons), with the equation's calculated temperature closely matching the data, the NASA satellite measured temperature."

So we have a compelling argument that the temperature of planets, among the other parameters, also is strongly related to their speed of rotation, and to their average surface specific heat.

******************

So we have concluded:

Earth's average surface temperature is much higher than Moon's average surface temperature, and it is so because of a good reason.

Earth's average surface temperature is much higher than Moon's average surface temperature, because Earth rotates very much faster than Moon.

Actually Earth rotates 29,5 times faster than our Moon.

And also, because

the earth's surface is everywhere full of water, and so it has

cp =1 cal/gr*oC

which is five (5) times higher than that of moon's regolith surface, which has

cp =0,19 cal/gr*oC.

Opponent:

"Have you eliminated other variables such as the atmosphere and the oceanic heat sink?

There’s also the problem that 70% of the Earth’s surface is smooth ocean while the Moon’s surface is rough regolith. By your own logic the Moon should be warmer than the Earth because the Moon reflects less radiation.

Thank you, for your response.
-
The other variables, the earthern atmosphere, is very thin, that is why it doesn't make any significant difference (when comparing with the satellite measured Earth's Tsat =288K)

when we theoretically calculate earth's average surface temperature without atmosphere.

By the way, the theoretically "eliminating" any planet's surface atmosphere commenced with the theoretical effective temperature (Te) definition implementation.

-

"The 70% of the Earth's surface is smooth ocean while the Moon's surface is rough regolith."
-
Yes, but for Earth, Moon, Mars, Mercury, Europa and Ganymede the
Solar Irradiation Accepting Factor "Φ" is very much close
to the Φ =0,47

All the six the above mentioned celestial bodies reflect solar light very much close to a perfectly smooth spherical body.
-

"The Moon would be warmer than the Earth because the Moon reflects less radiation".
-
Yes, Moon reflects less solar energy, because
Moon's Albedo is a =0,11 vs Earth's

a =0,306

Nevertheless, Moon is on average much colder than Earth, because Moon rotates 29,5 times slower, and, also, moon's regolith has
cp =0,19 cal/gr*oC, which is five (5) times smaller, than that of earth's.
-

******************

The planet specular reflection was neglected

In the billions of years of their existence, planets and moons surfaces were subjected to natural influences (which were different for every planet and moon). Those continuous influences had developed either the smooth surface pattern, or the heavy cratered (rough surface) pattern.

There is not a 100% smooth surface planet or a 100% smooth surface moon.

And when we say a 100% smooth surface, what we mean by that is that the incident EM energy flux interacts with matter in a single one-touch strike.

When, for theoretical reasons, we consider a 100% smooth surface planet or a 100% smooth surface moon, then we (only theoretically), then we are dealing with the EM energy one-touch strike on the matter.

And when one-touch striking the matter, part of the incoming EM energy gets ("absorbed"), and part gets specularly reflected.

The reflection's outcome is a directional EM energy flux, but it has weakened, compared to the incoming incident solar EM energy flux, because some of the incident EM energy being ("absorbed").

When solar flux strikes a real planetary surface, it is not a one-touch interaction with matter process.

The directional (because of the large distance) EM energy flux from the sun, when interacting with planetary surface matter is subjected to multiple tiny specular reflections, as the EM energy first gets scattered upon the surface's matter.

And the macroscopic outcome is the outgoing diffuse reflection, "in which light is scattered away from the surface in a range of directions."

What we observe, when solar flux interacts with planetary surface's matter, what we observe as the macroscopic outcome is the surface's the diffuse reflection - it is what we see from some distance when looking at that surface. And that diffuse reflection is measured and determined as Planetary Albedo.

But, for smooth surface planets and moons (not 100% smooth), for those planets and moons there is also a strong directional constituent, because it originates from the incoming solar flux's EM energy, which enters from the opposite direction. 

Thus,  

for planets and moons with smooth surface, the surface's specular reflection is not negligible.

The smooth surface planets and moons have a very strong the surface's specular reflection.

The specular reflection is not included in albedo.

So we had (for those planets and moons with smooth surface, and, therefore, with surface's strong specular reflection), we had to correct their respective the planet effective temperature Te.

Thus, for Earth, the Te =255K, when corrected, became Te.correct =210K.

But, notice, it is very important:

The planet effective temperature, even when it is corrected, the planet effective temperature does not exist, the planet effective temperature is a mathematical abstraction.

*****************

The First Conclusions

Conclusions:

1). We have written the theoretically exact the planet mean surface temperature equation as a very much reliable theoretical formula:

Tmean = [ Φ (1-a) S (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴  (K)     (3)

The theoretically calculated planets temperatures (Tmean) are almost identical with the measured by satellites (Tsat.mean).

2). We shall now compare the theoretically calculated Earth's (without-atmosphere) the average surface temperature (Tmean) with the satellite measured one, the (Tsat), because we are very much interested to estimate the magnitude of the atmospheric greenhouse effect.

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

Mercury....440 K......364 K........325,83 K…..340 K

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

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

Mars……….210 K......174 K........213,11 K…..210 K

The planet mean surface temperature New equation is written for planets and moons WITHOUT atmosphere.

When applied to Earth (Without Atmosphere) the New equation calculates Earth's mean surface temperature as 287,74K, which is very much close to the satellite measured 288K.

3). Thus for the planet Earth the  288 K – 255 K = 33 oC difference does not exist in the real world.

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.

........................

Also, there is not any +33C atmospheric greenhouse effect on Earth’s surface.

Because we have written a Universal Equation which is valid for all planets and moons in solar system.

Earth is a planet, thus when the Equation calculates for Earth's surface the mean surface temperature Tmean = 287,4 K and the satellite measured the Earth's average surface temperature

Tsat =288K,

Then there is no room for any significant atmospheric greenhouse effect, much more there is not any +33 °C atmospheric greenhouse effect on Earth's surface,

and there can’t be any other significant warming because the new theoretical Planet Mean Surface Temperature Equation (Tmean) and the followed calculations don’t allow it.

*****************

It is all explained further on below.

*****************

Also, we are explaining about the actual reasons of Global Warming at the bottom side of this page.

Opponent:

"Does your “Universal Equation” apply to Phobos?"

The unknown nature of phenomena makes us to consider them as "black boxes".

It is what a small child does. A child tests everything, because a child doesn't know how everything works and why.
-
It is the only way we are learning.

-

When considering Earth’s average surface temperature behavior as a
“black box”.

And when comparing it with the rest planets, also considered as

“black boxes”.

And when they all (Earth included) appear with the same average surface temperature behavior…

There is the only conclusion:

Earth’s atmosphere doesn’t have any significant influence on the Earth’s average surface temperature.

So, there is not any +33C atmospheric greenhouse effect on Earth’s surface.

-

-

Also, we are explaining about the actual reasons of Global Warming at the bottom side of this page.

November 1, 2024

Opponent:
“While your result of 33 °C warming is farcical, as is your hubris to claim there can’t be any other significant warming because your (copied?) hypothesis and calculations don’t allow it."
–
Answer:

Yes, thank you.
I never said there is a 33 °C rotational warming.

What I said is, there is not any 33 °C greenhouse warming effect on Earth’s surface.

Also I said Earth’s average surface temperature (288K) is 68 °C higher than Moon’s average surface temperature (220K) because of the Rotational Warming Phenomenon.

Yes,  you know what I have valued in your comment most?
The “…claim there can’t be any other significant warming because your (copied?) hypothesis and calculations don’t allow it.”

Because it is exactly that – the new theoretical Planet Mean Surface Temperature Equation doesn’t allow it.

And that is the best saying!
Thank you, again,
Christos

Now, about Φ -factor:

Φ - is the solar irradiation accepting factor (the planet surface spherical shape and planet surface roughness coefficient).

Φ =0,47 for smooth surface planets and moons without-atmosphere, (or with a thin atmosphere, Earth included), assumes the similarity with the measured
Drag Coefficient =0,47 for smooth spheres in the parallel flow fluids.

Link:

Drag coefficient - Wikipedia

We have Φ for different planets’ or moon's surfaces varying

0,47 ≤ Φ ≤ 1

For ideal smooth planet or moon surface

the  Φ = 0,47

And for a planet or moon with a very rough surface, which surface doesn’t exhibit specular reflection, (which is also idealistic)
the Φ = 1.

Planets and moons with a smooth surface have

Φ -factor very close to
Φ =0,47.

And planets or moons with a rough surface have

Φ -factor very close to
Φ = 1.

Only Triton (Neptune's moon), presumably, has Φ -factor somewhere in between, thus it is not possible for us to estimate its exact value.

Wikipedia

https://en.wikipedia.org/wiki/Albedo

Albedo (/lˈbiːdoʊ/ al-BEE-doh; from Latin albedo ‘whiteness’) is the fraction of sunlight that is diffusely reflected by a body.

Specular reflection - Wikipedia

"Specular reflection, or regular reflection, is the mirror-like reflection of waves, such as light, from a surface.^[1]

The law of reflection states that a reflected ray of light emerges from the reflecting surface at the same angle to the surface normal as the incident ray, but on the opposing side of the surface normal in the plane formed by the incident and reflected rays. This behavior was first described by Hero of Alexandria (ADc. 10–70).^[2]

Later, Alhazen gave a complete statement of the law of reflection.^[3][4][5]He was first to state that the incident ray, the reflected ray, and the normal to the surface all lie in a same plane perpendicular to reflecting plane.^[6][7]

Specular reflection may be contrasted with diffuse reflection, in which light is scattered away from the surface in a range of directions."

-

*****

********

An example would be specular reflections from water, which can only be perceived from a particular direction. Or sunlight reflected by a mirror. You cannot measure how much light is being reflected unless it is shining on your instrument.

-

An instrument flying on a satellite cannot detect reflection that is outside its view angle. Even with direct reflection, the angle of reflection could be outside the instrument’s view angle.

-

*************

“Bond Albedo is the fraction of power in the total electromagnetic radiation incident on an astronomical body that is scattered back out into space.

Because the Bond albedo accounts for all of the light scattered from a body at all wavelengths and all phase angles, it is a necessary quantity for determining how much energy a body absorbs. ”
–
–
“it is a necessary quantity for determining how much energy a body absorbs.”

But Albedo doesn’t account for the entire fraction of electromagnetic radiation incident on an astronomical body that is scattered back out into space.

The measured by satellites planetary Albedo accounts only on the (isotropical-like part of the scattered diffuse reflection), which can be seen by the satellite sensors, since it falls upon them.

But Albedo doesn’t account on the (directional-like part of the diffuse reflection) which escapes the satellite sensors orientation.

And it is the (directional-like part of the diffuse reflection) which resemblances with the "pure" specular reflection, which is always directional. 

We observe that directional-like reflection on the Earth all the time.

And we usually see it as a kind of specular reflection.

Sun emits EM energy as a diffuse outgoing flux.

We are used to see our world in a diffuselly reflected illumination.

We see our Moon in a diffuselly reflected solar light.

What we see as 

Specular reflection is the elementary light reflection when EM energy hits matter.

Part of EM energy gets specularly reflected and part is not reflected - ("absorbed").

-

Diffuse reflection consists of numerous tiny specular reflections.

-

Sun emits EM energy as a diffuse outgoing flux, sun emits EM energy as an almost isotropic outgoing flux.

The incoming to planetary surface solar EM energy, because of the large distance from the source (sun), the solar incoming EM energy appears as a directional flux of energy (rays). 

When hitting a smooth surface area, some EM energy gets ("absorbed"), and some gets in its entity reflected in a simple (elementary reflection) way, the specular reflection - which is the one-touch interaction process. The elementary specular reflection outcome also consists from a directional EM energy outgoing flux.

-

Some planets and moons have smooth surfaces, though they are not 100% perfectly smooth. Thus, because of their surface being smooth, they may have along with the diffuse reflection a very strong specular reflection constituent.

-

Those smooth surface planets and moons, and therefore with a very strong specular reflection constituent, those smooth surface planets and moons  are:

1). Mercury

2). Earth

3). Moon

4). Mars

5). Europa (Jupiter's satellite)

6). Ganymede (Jupiter's satellite)

-

The planet surface specular reflection constituent is a directional flux of EM energy. And, an instrument flying on a satellite cannot detect reflection that is outside its view angle. And, that is the reason, because the Strong Planetary Specular reflection was Neglected.

*************************

Whether a mirror is large or small, it reflects in a specular fashion – otherwise it would not be a mirror.

Again, because the planet specular reflection issue is very important:

-

Every infinitesimal point reflects specularly.

And every infinitesimal point reflects specularly according to its respective infinitesimal orientation to the incident solar flux.

As a result, an observer sees a scattered light, which looks like a diffuse reflection.

Since the incoming solar flux is directional, there always is a stronger scattering of reflected light towards the opposite direction. Thus the reflection of solar light is always a combination of diffuse and specular reflection.

Some planets and moons have surfaces which permit that infinitesimal point reflection to escape the planet surface. Those are the smooth surface planets and moons (Mercury, Earth, Moon, Mars, Europa and Ganymede).

The rest planets and moons have surfaces' features, which capture that primer infinitesimal point reflection (because, on those surfaces, the primer reflected light gets reflected multiple times, and only after, what is not absorbed, finally escapes surface) ,

thus those planets and moons do not let the directional reflection out, so their respective the out reflected light is entirely diffuse reflection.

Albedo is the measure of diffuse reflection. Thus for those planets and moons the

"radiative energy in" = (1-a)S.

But for the smooth surface planets and moons the

"radiative energy in" = Φ*(1-a)S.

-

*************************

Also, more about specular reflection at:

https://www.rp-photonics.com/specular_reflection.html

It is very important what it says:

” There can be also a combination of specular and diffuse reflection; an object with such properties exhibits specular highlights (depending on the illumination conditions) in addition to the appearance generated by diffuse scattering.

Specular reflections can appear much brighter than diffuse reflections, when seen from a large distance because the reflected light is concentrated to a smaller range of directions. (That can be a problem in the context of laser safety.) On the other hand, specular reflections remain unnoticed for an absorber if the reflected light misses his or her eyes.”

****************

It is not "a hypothetical solar irradiation accepting factor."

By "accepting" means how much energy a spherical shape body may "stop".

A spherical shape body may stop a flow of energy. Because of spherical shape a sphere

may stop Φ(1-a)S of total incident energy.

Φ varies from 0,47 to 1.

The smoother the surface is the closer to 0,47 the Φ is.

Thus, a smooth surface sphere with Albedo a = 0
should "absorb" 0,47*S.

A sphere with rough surface (Φ = 1) and

a = 0 should "absorb" a 100% S.

And a sphere with Albedo a = 1 should not "absorb" EM energy, regardless the values of Φ.

****************

Some surfaces exhibit almost “Lambertian reflectance”, where the diffuse reflection is almost the same in all directions.

-
https://en.wikipedia.org/wiki/File:Lambert6.gif

It looks like, but it isn’t. There is not a 100% "Lambertian reflection".

There are surfaces that exhibit almost "Lambertian reflectance", Moon doesn't. But there are celestial bodies, which exhibit the almost "Lambertian reflectance".

There are surfaces with "Not Lambertian reflectance" and there are surfaces with almost "Lambertian reflectance".

When solar energy hits surface's matter, the solar energy partly gets reflected-scattered.

1). The one-touch scattering is when the reflected solar energy is subjected to only one single reflection and then escapes from the surface. Because surface is smooth enough not to stop the reflected solar energy to leave.
Those surfaces exhibit the "Not Lambertian reflectance".

2). The multi-touch scattering is when the reflected solar energy is subjected to multiple-times reflections in the surface's "folds" and only then, the not absorbed solar energy escapes from the surface.
Those surfaces exhibit the almost "Lambertian reflectance".
-

***************

There is not a 100% "Lambertian reflection".
-
Planets and moons which exhibit the "not Lambertian reflection" have along with the diffuse reflection, also a strong specular-like reflection. So they have Φ = 0,47 (the solar irradiation accepting factor).
Those planets and moons are:

Mercury
Earth
Moon
Mars
Europa
Ganymede

All other planets and moons exhibit the almost "Lambertian reflection". This includes the 4 gaseous planets and Venus and Titan, which also exhibit "Lambertian reflection".
So for them the Φ = 1.
-

The incoming solar EM energy averaging is a mistaken thought experiment

“340W/m² reaches Earth from the Sun.”

Ok,

1360W/m² /4 = 340W/m²

But we cannot average the perpendicular to the planet cros-section cycle the incoming solar flux of So =1360W/m² , because there is neither solar radiation, nor Albedo at the planet dark-side area.

"Not a problem. Just accept that the solar flux and albedo on the night side of the Earth are zero. Then calculate the averages as usual."

-

Of course, I can do that.

But it is a mistaken theoretical thought experiment.

Solar EM energy doesn't "go" to the planet dark-side area. It is the planet rotating, and, while rotating, there is always half of the globe faces the sun.

Solar energy only interacts with the matter it is fallen on, solar energy doesn't interact when the surface is out of view, solar energy doesn't interact when the surface is on the planet's dark -side area.

Thus, we cannot average the incident on a planet solar energy's interaction result with the planet surface matter, we are not justified to average it over the entire planet surface, because solar EM energy interacts with surface only on the solar lit side area.

Solar EM energy at the instant of incidence on the planet surface what it does is to interact with the surface's matter.

At every point of incidence solar EM energy produces at that point the EM/surface interaction result.

The EM/surface interaction result is localized at that very point of EM energy incidence.

We cannot average the incident on a planet solar EM energy over some planet surface areas, because solar EM energy interacts with surface only at the point of incidence.

Because when the incident solar EM energy averaging, the new EM/surface interaction layout changes the actual EM/surface interaction result.

Solar flux cannot theoretically be averaged over some area, because solar flux what it does is to interact with matter.

When solar flux is averaged, the averaged flux is four (4) times weaker, therefore there would be a new interaction result, which would be very different from the actual one.

Solar flux cannot theoretically be averaged over some area.

Yes, because solar flux interacts with matter, it vanishes then.

And there has no much energy of the initial incidence left to be averaged then.

Like-wise we cannot average snow over the entire Global area, because snow belongs where it has fallen on.

Snow also vanishes at spring, but you cannot average the amounts of snow over the entire planet surface.

Of course the math would be correct, but in reality there is not snow at most of the planet surface areas.

Solar flux cannot theoretically be averaged over some area, because solar flux what it does is to interact with matter.

When solar flux is averaged, the averaged flux is four (4) times weaker, therefore there would be a new interaction result, which would be very different from the actual one.

The solar flux /Earth's surface interaction result comes up with  the actual

Tmean = 288K.

The averaged solar flux's the new interaction result comes up with the impossible  Te = 255K.

***********************************

Specular and diffuse reflection cannot be averaged over the entire planet surface – the dark side doesn’t reflect solar light.
–
The reflection happens on the solar lit hemisphere.

The solar flux, when perpendicular to the surface is ~1360 W/m².

It takes place somewhere around equator at local noon.
When Eqinox, it takes place at local noon on equator.

The sun is exactly above then, at that one particular point.

For the rest of solar lit hemisphere, sun is not exactly above.

At any given time sun's rays are perpendicular to planet surface only on one particular point.

The angle of incidence changes for all directions away from that one particular point, towards the terminator, and not only pole-ward.

So, there is only one particular point on Earth’s solar lit hemisphere surface every given moment, where sun is exactly above.

Thus the entire solar lit hemisphere reflects specularly, the lower is the sun the higher is the specular reflection ratio.

The lower is the sun, the larger is the cycle on the hemisphere, at which cycle the stronger is the specular reflection.

–
For more visit page: "Φ = 0,47 and FRESNEL"

**********************

How A Planet Retains The Solar Energy

There is the Solar flux (S), surface Albedo (a), the solar irradiation accepting factor

(the spherical shape and roughness

coefficient (Φ) ), and also, there is the Planet Surface Rotational Warming Phenomenon.

Solar flux (S) and surface Albedo (a) are two well-known and generally accepted physical terms when for the solar irradiated surface of a planet the

ENERGY IN = ENERGY OUT

equilibrium radiation balance is considered.

What is new in present research are

The solar irradiation accepting factor

(the spherical shape and roughness

coefficient (Φ) ), which is thoroughly explained further below,

and

The Planet Surface Rotational Warming Phenomenon

1). The faster rotation (N), the less differentiated the surface temperature - the higher the planet average surface temperature.

And, also, the faster rotating planet absorbs more solar energy.

************

2). A planet with a higher surface specific heat (cp) has also less differentiated the surface temperature - the higher the planet average surface temperature.

And, also, the higher is the surface specific heat, the more solar energy the planet absorbs.

************

Where The Additional Solar Energy Comes From

There is no additional solar energy involved in the Rotational Warming Phenomenon.

Here it is what happens:

Solar energy arrives at a planet's (Earth’s) orbit distance from the sun, falls on the spherical shape surface a planet has and interacts with the matter.
–
When interacting with matter there are three processes occur:

(SW) reflection,

(LW) emission and

(HEAT) absorption.

1). Some of solar energy is reflected at the same wavelengths it has arrived (as SW EM energy). It gets reflected both diffuselly and specularly.

2). Some gets transformed into (LW) EM energy and at that very instant gets emitted (without being absorbed).

( When solar energy interacting with the surface's the very upper skin layer, the not reflected solar energy goes both ways - some is (LW) emitted and some is conducted as HEAT into the surface's inner layers. )

3). And some gets transformed into HEAT and gets conducted as HEAT into the surface's inner layers and absorbed in the inner layers.

The not reflected portion of the incident solar flux (S) can be calculated as:

Φ*(1-a)*S (W/m²)

where

S - the solar flux (W/m²)

a - the satellite measured average Albedo

Φ - the solar irradiation accepting factor (the planet spherical shape and planet surface roughness coefficient)

Now, the quantity of transformed into heat and absorbed in inner layers portion of solar energy is expressed as:

(absorbed) = (Not reflected) - (LW emitted) (W/m²)

or

(absorbed) = Φ*(1-a)*S – [ 2). the (LW)] (W/m²)

***********

The portion of solar energy that instantly gets transformed into a (LW) and instantly emitted

the amount of

(LW emitted)

or

[ 2). the (LW)] (W/m²)

varies because of the Rotational Warming Phenomenon.

When a planet rotates faster (N), and when a planet has a higher the surface specific heat (cp), (everything else equals),

the amount of

(LW emitted)

or

[ 2). the (LW)] (W/m²)

is smaller, and the amount of the absorbed solar energy in form of HEAT is higher.

And that is how the Rotational Warming Phenomenon makes a planet (Earth) warmer.

Thus, there is no additional solar energy involved in the Rotational Warming Phenomenon.

It is that the warmer planet is able to retain more energy from the incident on its surface solar flux.

It is that the warmer planet, at the instant of solar flux' incidence, emits less outgoing (LW) EM energy, at the instant of solar flux' incidence, the warmer planet emits less outgoing (LW) EM energy than a colder one.

Notice:

The W/m² is referred (in every planet case) to an area which is perpendicular to the arriving solar flux’ intensity W/m².

************

***************

The Polar latitudinal areas' role

A planet absorbs only a small portion of the incident SW EM energy W/m² as  heat.

Some of that heat gets transported to the poles.

The planet average surface temperature (Tmean) is fundamentally determined by the Radiative energy balance's quantitative magnitude (on how much  EM energy enters and leaves the planetary boundaries):

Energy in = Energy out.

The Polar latitudinal areas' participation in Planet Radiative energy balance is very insignificant.

******************

**************************

**********************************

It is time to look elsewhere and retool.

So far, in present research, we have corrected the two mistakenly assumed observations.

1). A planet reflects the incident solar SW EM energy not only diffuselly, but also specularly. The specular reflection was neglected in planet radiative

Energy in = Energy out

balance equation, and thus the specularly reflected SW EM energy was mistakenly considered as part of the "Energy in".

2). When solar irradiated, a planet surface not only reflects and absorbs the incident SW EM solar energy, but at the instance of the SW EM solar energy incidence, a planet also emits (LW) EM energy.

Thus, the at the instance of the SW EM solar energy incidence, the by planet surface emitted (LW) EM energy was mistakenly considered as part of the "Absorbed".

Also visit page:

A NEW UNIVERSAL LAW

------------------------------------------------------------------------------

Earth is warmer than Moon, because Earth rotates faster.

At the same distance from the sun, Earth receives 28% less solar energy (higher Albedo), but Earth rotates

very much faster...

Earth's average surface temperature, in comparison with Moon's, is much HIGHER!

The planet or moon average surface temperature (Tmean) is dependent on the distance from the sun (the solar flux) and on the celestial body's average surface Albedo.

-

But there is something else very interesting happens!

What is new, is that the average surface temperature (Tmean) is SIGNIFICANTLY amplified by the Planet Surface ROTATIONAL WARMING PHENOMENON.

-

*****

-

Things get hot when placed in sunlight.

Surface IR emission is isotropic, and is emitted back into the free space around it. 
And there is only a “portion” that gets converted to heat and absorbed in the inner layers.

-

********

The specularly reflected solar energy should be considered in the planetary radiative energy balance estimation.

-

*****

-

The Planet Surface Rotational Warming Phenomenon is a UNIVERSAL PHENOMENON.

-

All planets and moons are INEVITABLY subjected to that UNIVERSAL PHENOMENON.

-

*****

-

Here it is a very well known scientific observation:

-

Earth’s surface is warmer than Moon’s on average +68°C.
–
But it happens so not because of Earth’s thin atmosphere very insignificant greenhouse effect.
–
Earth’s surface is warmer than Moon’s on average +68°C, because of the Planet Surface Rotational Warming Phenomenon!

********

-

We examine here the full scope of the issues. 

-

“What is an average?”

Because not all the measurements are the same, we can average them, to see what we shall have (on average).
–
Now, when we have for two different celestial bodies the average surface temperatures so much different

Earth Tmean =288K

Moon Tmean =220K

We have to find out why it is happening so.
Is Earth on average warmer than Moon?

Yes, Earth is on average warmer than Moon.

But why Earth is on average warmer than Moon?

Because Earth rotates faster, and Earth is able to absorb much more solar energy, than Moon.

When a planet rotates faster, its surface absorbs more solar energy. Thus the planet becomes on average warmer.

When atoms are larger.

When surface has a lower thermal capacity, when solar irradiated, surface will intesify emitting more intensively, because it gets warmed at higher temperatures.

I am here referring to the EM energy/surface skin layer’s interaction process.

When surface consists from a material with a lower thermal capacity, it is because the surface is made of larger atoms.

When atoms are larger, there are much less atoms streched on the surface skin layer of 1 m².

When there are less atoms to interact with, the incident EM energy (W/m²) is shared between a lesser number of atoms, so they interact more intensively (W).

And, yes, the surface temperature is induced to higher levels.

It is the same EM energy/interaction process.

But there are less EM energy degraded to heat.

So, there are less EM energy conserved as heat.

Two basic physics planetary AXIOMS

We shall start our narrative with two very simple, but nevertheless very important basic physics planetary axioms.

1. The planet's equatorial mean surface temperature (Tmean.equatorial) is always higher than the entire planet's the global mean surface temperature (Tmean.global).

and

2. The faster a planet rotates, the bigger is the difference

Δt = Tmean.equatorial - Tmean.global

and, likewise, the slower a planet rotates, the smaller is the difference

Δt = Tmean.equatorial - Tmean.global.

-

*******

These two simple axioms led us to the following very important conclusions:

1. No matter how fast a planet rotates, planet surface never approaches a uniform surface temperature (Tmean.uniform).

and

2. For a very slow rotating planet the 

Δt = Tmean.equatorial - Tmean.global

the difference "Δt" is very small, and for the entire planet surface, the global mean surface temperature (Tmean.global) is very close to the equatorial mean surface temperature value (Tmean.equatorial).

Opponent:

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

Bond Albedo is intended to include ALL reflections.

There is not some 47% correction needed for “smooth” planets.

Answer:

Satellite Era moved  planet surface temperatures measurements at a New Level!

The NASA spacecrafts very precise measurements

The present research is based on NASA spacecrafts the solar system planets and moons the surface temperatures very precise measurements.

-

Also it is based on NASA spacecrafts the solar system planets and moons the surface reflectivity (Albedo) very precise measurements.

-

NASA has precisely measured the solar system planets and moons the rates of rotation.

-

Also NASA spacecrafts  missions have determined for the solar system the various planets and moons the planetary surface's the different chemical composition.

-

******

A satellite orbiting planet measures the planet's every point surface temperature.

At day-time the satellite measures the instantly induced by sun the surface temperature.

At night-time the satellite measures the planet surface "the warmth" temperature.

When the measured temperatures being averaged over the entire planet surface - it is the planet average surface temperature (Tmean) - it is the mean surface temperature.

-

******

Yes, planets and moons do obey to the same universal laws, it is an axiom, but applied to different input parameters.

What we did in the present research was to compare the different planets and moons surface temperatures in accordance with the incident on the planet surface their respective solar flux (S), with their respective average surface Albedo (a), and, also, in accordance with their respective rate of rotation (N) , and with their respective surface specific heat (cp) and surface roughness features (the light capturing abilities).

-

In this research we have shown, and now we demonstrate that a planet average surface temperature (Tmean K) is determined by those five (5) major parameters:

1. The distance from the sun (solar flux "S" W/m²).

The intensity of the incident on a celestial body solar EM energy is dependent on the distance from the sun the square inverse law value.

2. The average surface diffuse reflectivity (Albedo "a"),

which is dependent on the planet's or moon's average surface the diffuse reflection properties.

3. The surface's spherical shape and the surface's roughness coefficient (the solar irradiation accepting factor "Φ").

Because planets and moons have very distinguished their respective surfaces features - there are the smooth surface planets and moons and there are the rough surface planets and moons.

The rough surface planets and moons almost do not exhibit the specular reflection from their respective surfaces.

4. The rate of rotation ("N" rotations/day),

which is a unique for every planet and moon value.

5. The average surface specific heat ("cp" cal/gr*oC),

which is determined by the planet the respective average surface chemical composition.

Yes, the same universal laws, but applied to different input parameters.
So the same universal physical laws, but applied to different celestial bodies.

And, there also is, the very POWERFUL the Solar Irradiated planet surface Rotational Warming Phenomenon.

*********

You can have all the theory in the world, but sometimes you’ll come across a problem that defies all logic and any theory you have learned.

When comparing the various different planets' and moons' (without-atmosphere, or with a very thin atmosphere, Earth included), when comparing the planetary surface temperatures, a very persistent question needs to be answered:

How can the planet average surface temperature (Tmean) increase without the radiation increasing?

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And here it is when a major basic physics concept BREAKS THRU!

The importance of the proper use, and the importance of the proper understanding of the STEFAN-BOLTZMANN BLACKBODY EMISSION LAW!

Jemit = σT⁴ W/m²

The Stefan-Boltzmann blackbody emission law actually is THE RADIATIVE ENERGY EMISSION LAW!

The Stefan-Boltzmann blackbody emission law is a mathematical abstraction, which has a relation with some real bodies' emission intensity at some higher temperatures.

When the Stefan-Boltzmann blackbody emission law is applied to various material bodies there is a physics need to be considered those bodies as non perfect emitters, so those are gray bodies.

In order to continue applying the Stefan-Boltzmann emission law to the non perfect emitters - the gray bodies,  the term emissivity (ε) was invented.

After applying the theoretical Stefan-Boltzmann emission law formula to the different for every material or surface condition (oxidized or polished etc...) after applying the different and empirically estimated (measured) emissivity (ε), the theoretical Stefan-Boltzmann emission law was established as the UNIVERSAL FORMULA when the bodies' and surfaces' the EM emission intensity was theoretically calculated.

-

What we conclude is that every material body and every material surface emits EM energy according to its absolute temperature fourth power ( T⁴ ) followed by a coupled coefficient (ε*σ), so it takes the final form of:

Jemit = εσT⁴ W/m²

The empirically estimated (measured) the emissivity coefficient (ε) depends on the emitting surfaces' content. 

What exactly atoms and what exactly molecules are streched upon the m² of emitting surface.

The (ε) also depends on the atoms' and molecules' dimensions - how small or how large they are.

When there are more atoms are streched over the

m² of emitting surface, there are much more emitters, so the emissivity coefficient (ε) is higher.

When surface consists of larger atoms, there are much less emitters, so the emissivity coefficient (ε) is lower.

The Stefan-Boltzmann emission law is limited to the hotter bodies and surfaces.

When bodies and their respective surfaces are not hot enough, there is not enough thermal energy available to be transformed and emitted as EM energy in accordance to what the Stefan-Boltzmann emission law

Jemit = εσT⁴ W/m²

for those bodies and for those surfaces dictates.

The colder bodies still do emit EM energy, but their emission is much weaker, the colder bodies' EM energy emission intensities are much lower than the S-B emission law intensities.

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The Stefan-Boltzmann emission law cannot be applied as it is to the EM energy (to the solar energy) irradiated surfaces.

-

The notion on a 2-way transfer of heat via radiation is wrong.

What they have done is apply the Stefan-Boltzmann equation in both directions, but the S-B equation is not about heat transfer, only radiation intensity of a surface at a temperature T.

They also have contradicted the basic quantum theory as laid out by Bohr in 1913. Bohr said that Electrons in atoms are the only particles that can transmit or absorb radiative energy, which is electromagnetic energy.

In fact, when a body radiates EM it loses heat at the same rate it emits the EM. Therefore the process IS A ONE WAY process.

When EM radiation of the same intensity hits another body, the resulting INTERACTION  with matter doesn't put-in the same amount of heat being lost in the emission process by the first body.

The notion that heat can be transferred two ways using EM is an anachronism dating back to the 19th century, when scientists believed heat was transmitted through space via heat rays. Bohr proved that idea wrong in 1913.

Here is a definition of S-B which might suffice:

The amount of radiation emitted per unit time from an area A of a black body at absolute temperature T is directly proportional to the fourth power of the temperature T.

***

Says nothing about radiation or heat transfers, just relates the temperature of a surface to the radiation intensity it emits.

-

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The Stefan-Boltzmann emission law is NOT the RADIATIVE ENERGY absorption law!

It was mistakenly believed that we are scientifically justified when directly converting the solar EM flux into temperature! 

Thus, the Planet Effective Temperature Equation:

Te = [ (1-a) S / 4 σ ]¹∕ ⁴ (K)  Hansen et. al., (1981), Link: [22]

"Greenhouse Effect
The effective radiating temperature of
the earth, Te, is determined by the need
for infrared emission from the planet to
balance absorbed solar radiation:

πR²(1 - A)So = 4πR²σTe⁴, (1)
or
Te = [So(1 -A)/4σ]¹∕ ⁴ (2)

where R is the radius of the earth, A the
albedo of the earth, So the flux of solar
radiation, and σ the Stefan-Boltzmann
constant. For A ~ 0.3 and So = 1367
watts per square meter, this yields
Te ~255 K.
The mean surface temperature is
Ts ~288 K. The excess, Ts - Te, is the
greenhouse effect of gases and clouds,"

which is based on the mistaken assumption, that the Stefan-Boltzmann Blackbody Radiative Energy Emission Law FORMULA

Jemit = σT⁴ W/m²

which describes the blackbody surface at absolute temperature (T) the blackbody surface emission intensity in (W/m²)

It was mistakenly assumed that an irradiated with the same intensity  (W/m²) a blackbody will develop the same absolute temperature (T).

 Thus the above S-B Formula was very mistakenly

re-written as:

T = [S / σ ]¹∕ ⁴ (K)

and it was very much mistakenly applied to the real planet Infrared Emission BEHAVIOR.

Thus they had a planet surface radiative energy emission behavior being confused with the blackbody emission behavior.

(Which is very much different, because what a blackbody does is to emit EM radiative energy at absolute temperature (T), when what a planet does is to INTERACT WITH THE INCIDENT SOLAR FLUX.

***

*****

It is the matter's property to spontaneously get rid of energy. The matter gets rid of energy by the spontaneous EM (Electromagnetic) emission. And, the warmer (hotter) the object is, the more intensively the object emits EM energy.

So, the matter spontaneously emits EM energy in order to get rid of energy. When irradiated, the matter does not welcome the incident on its surface the incoming EM energy. 

So, when EM irradiated, the matter does everything in its powers not to let in the incident energy. It does what ever it takes to absorb as little as possible.

Yes, when irradiated, the matter (on the very instant of incidence) reflects, emits and absorbs. And absorbs as little as possible.

When a planet surface is solar irradiated with some amount of EM energy, at the same very instant the surface INTERACTS WITH THAT AMOUNT of EM energy, and by doing so, the surface (on the very instant)  SW reflects a portion of the incident EM energy, and (on the very instant) transforms some other portion from the SW into IR  and emits it as IR outgoing EM energy, and what EM energy is left from SW reflection and IR emission, the planet surface (on the very instant) transforms it into heat and absorbs it in the inner layers.

Thus, when planet surface is solar irradiated:

at the same very instant the surface INTERACTS WITH THAT AMOUNT of EM energy and as a result

1). Some of SW gets reflected as SW

2). Some of SW gets transformed straight into IR (by omitting to decay as heat) which IR instantly gets emitted as IR

3). And the rest of the incident SW EM energy, gets transformed into HEAT, and that heat is what gets absorbed in the inner layers.

***

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*****

This special application (Te) derived from Stefan-Boltzmann, what Hansen calls the “Planet Effective Temperature Equation”, was used to recover the planet without-atmosphere the global average surface temperature (Tmean).
–
Yes, the (Te) “a special application derived from Stefan-Boltzmann” it is a good “working” name. Maybe to call it “the Hansen’s Equation”…

The

Te = [So(1 -A)/4σ]¹∕ ⁴ (2)

is based on a brilliant insight Hansen had, "The effective radiating temperature of
the earth, Te, is determined by the need for infrared emission from the planet to
balance absorbed solar radiation".

That it is how everything started! Hansen saw the possibility to THEORETICALLY calculate for a planet without-atmosphere the average surface temperature (Tmean).

It was neglected though, that a planet surface radiative energy emission behavior should not be confused with the blackbody emission behavior.

The EFFECTIVE RADIATING TEMPERATURE is the temperature of a body with a single approximate emission temperature that radiates the same power over its whole spherical surface as it receives as a disk from the sun, based on the albedo-reduced SOLAR FLUX.

This  emission temperature should not be confused with any NORMAL planet average SURFACE temperature, because the Stefan-Boltzmann emission law cannot be applied to any kind of average surface temperature!

The solar FLUX's ratio of the PLANET’s surface area to its cross-sectional area is 4:1.  Once again, the EFFECTIVE RADIATING TEMPERATURE is an equivalent uniform surface temperature, based on the SIMPLIFYING ASSUMPTION that a PLANET radiates like a STAR.

*******

The Planet Effective Temperature is only the FIRST STEP to mathematical APPROACH, and, therefore, the FORMULA:

Te = [So(1 -A)/4σ]¹∕ ⁴ (2)

is an IMPERFECT, and it is an INCOMPLETE equation for the Planet the Mean Surface Temperature (Tmean) the THEORETICAL calculation.

*******

A planet surface in radiative equilibrium with the sun has NOT any resemblance with the radiative equilibrium in the cavity with a small hole.
–
The planet average surface temperature (Tmean) is not a blackbody’s temperature.
–
Planet does not have a blackbody temperature, because planet has not a uniform temperature, and because planet is not a blackbody.

*******

It was used saying:

“NET incoming solar (what will be absorbed by the surface, incoming minus reflected away).”
–
We should say now:

NET absorbed solar (what will be absorbed by the surface, incoming minus reflected away, minus at the spot instantly IR emitted away).

*******

I mean, at the instant of the SW solar energy incidence to the surface, the IR emission takes place without an absorption. The incident SW solar energy gets IR emitted on that very spot, without being accumulated in inner layers as heat.
–
The result is that only

 a special part of the incident solar energy, which is conserved as heat - it is the heat which gets absorbed by the planetary surface matter.

It is accumulated as heat and gets IR emitted later at night, or at different times.
–
Thus it is impossible to consider the incident solar flux to be averaged over the entire planet surface, because it is not averageble – the incident solar energy mostly is getting out from the sunlit side of a planet. Only a  part is conserved as heat and gets accumulated.

The 240 W/m² has no physical meaning, has no physical analog, for radiative energy subjected spheroids (planet Earth) and, therefore, the planet Te =255K is simply a mathematical abstraction, and cannot be a comparison model for planet average surface temperature.

When based on the blackbody-planet theory, it was wrongly calculated:

"The earth's surface emits on average 240 W/m². "
-

Also it was very much wrongly concluded:

"Without greenhouse effect, Earth’s surface would be some 33°C (59°F) cooler.”

*********

Clearly there is something wrong

By accepting the 255K as an approximation, you accept the 255K or -18°C to emit the impossible

240 W/m².

Because the generally accepted physics say so. They have averaged the incident on Earth solar flux over the entire planet surface and came up with the 240 W/m².

It is known, from our everyday's practice, that a body does not emit the impossible high 240 W/m² at the very low temperature of -18°C.

In our homes, it is the fridges what produce to that very low temperature.

When outside in winter, at -18°C, there it is a deadly cold, there is nowhere any 240 W/m² emission to warm our bones a little bit.

Clearly there is something wrong.

Also, the inference is that ice, at 0°C, can transfer an energy of 315 W/m² of energy to a nearby body. So, if you have a square of ice 1 metre square, you should be able to put a body above it that is 1 metre square and warm it from the ice.

Clearly there is something wrong. The Stefan-Boltzmann emission law cannot describe the matter's EM emission at low temperatures.

-

And there is not any Back-calculatiǹg method permitted by the use of the Stefan-Boltzmann law.

Stefan-Boltzmann law is about a hot body's at uniform temperature the EM energy emission intensity.

Stefan-Boltzmann law doesn't describe the incident EM energy/ surfase matter interaction processes.

Also, the Stefan-Boltzmann law doesn't "work" at terrestrial temperatures, because it gives very much overestimated results.

Example:

It is said Earth, according to S-B law, as a uniform surface temperature sphere
emits 240 W/m² at Te=255K or -18°C.

I have experienced the -18°C what it is like. When outdoors at -18°C it is a deadly cold. There is nowhere 240 W/m² emitting.

A small 3m x3m x3m room at -18C according to S-B should emit:

3m x3m x6 = 9m^2 x6 = 54m²

54m² x240W/m² = 12.960 W or ~ 13 kW

Have you experienced 13 Kw heater in a small 3m x3m x3m room ?

Have you experienced how it is inside a refrigerator the size of 3m x3m x3m room at -18°C ?

Therefore the Stefan-Boltzmann law doesn't work at terrestrial temperatures, because it gives very much overestimated results.

****************

*******

The actual matter, which is made from atoms and molecules, does not have the necessary energy to support the expected IR EM emission levels the Stefan-Boltzmann theoretical equation dictates for the terrestrial and for lower than terrestrial temperatures.

***

***************

*******

Hot bodies do not radiate heat, they radiate electromagnetic energy (EM). If nothing intercept that radiation nothing can warm.

Therefore a planet interacts only with radiation. Should not get confused between interaction with radiation, and the thermal energy (heat) input.

The properties of EM are very different than the properties of heat. EM has no mass and is an electric field orthogonal to a magnetic field. It has a frequency. Heat has no frequency and cannot exist without mass. The two energies are of different physics behavior, thus when interacting with matter not the entire EM energy gets put in (not the entire EM energy gets absorbed).
–

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*******

The low temperature bodies have much less heat, and, therefore, they are not capable to emit their, according to Stefan-Boltzmann emmission law, the respective intensity EM radiation, those that the S-B law dictates.
–
And that is why, when S-B law is applied to planets and moons the IR emission intensities, the S-B respective to their absolute temperatures, the result is very much mistaken.

Thus we have the laughable 255K (-18C) emitting the impossible
240 W/m² !!!
–
Conclusion:
The S-B emission law application is limited by the energy a body is capable to give up.
If a body is over-loaded with energy, the energy is pouring out by EM radiation according to the S-B emission law, because at the emitting surface there is an instant equilibrium of energy transfer gets established – and establishing that equilibrium is what the Stefan-Boltzmann emission law is all about.
–
When there is much less energy in the body (at lower temperatures), it cannot support the IR emission intensity the S-B emission law dictates to emit at body’s respective low temperatures.

-

When deeping a thermometer in the lower temperature matter, thermometer is adjusted to the matter's temperature (the kinetic energy of molecules).

Molecules do vibrate at lower temperatures, but there is not enough energy to exitate the  electrons in atoms, and they, the electrons, cannot emit the respective amounts of EM energy the S-B emission law dictates. 
–

There’s nothing wrong with the Stefan-Boltzmann Law. It’s just that it is limited on the hotter bodies.

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******

The Temperature Graph (from Diviner) Of The Lunar Equator

This is a temperature graph (from Diviner) of the Lunar equator. As the sun light angle decreases to night it looks as if the temperature drops rapidly (much higher rate of radiant heat loss vs incoming solar energy).

Then at night, when cold, it does drop but much slower as the radiant loss is reduced significantly.

Links:

 Lunar Surface Temperature Graph  1
–

 Lunar Surface Temperature Graph  2

-

 Lunar Surface Temperature Graph  3

-

 Lunar Surface Temperature Graph  4

-

Let's analyse

As the sun light angle decreases to night it looks as if the temperature drops rapidly (much higher rate of radiant heat loss vs incoming solar energy).
–
What I think is that while the solar EM energy hits the surface, the solar EM energy interacts with the matter.

When interacting with matter:

1). Some of solar energy is reflected at the same wavelengths it has arrived (as SW EM energy). It gets reflected both diffuselly and specularly.

2). Some gets transformed into (LW) EM energy and at that very instant gets emitted (without being absorbed).

3). And some gets transformed into HEAT and gets absorbed in the inner layers.

********************
Thus, while the solar EM energy interacts with matter, it induces the skin layer’s measured the very high ~400 K temperature.

At the very moment the solar EM energy stops interacting with matter, the temperature instantly drops, because there isn’t any significant amount of heat being absorbed during the solar lit hours…

And

Then at night, when cold, temperature does drop but much slower as the radiant loss is reduced significantly.

At night the temperature drops in a linear relation, because the energy absorbed in inner layers during the day, the absobed heat, provided from inner layers, comes up to the surface according to the lunar surface regolith’s conductivity.

At night the lunar surface radiative cooling rate is determined by the regolith’s upgoing conductivity – there is not any other source of energy to support the night hours EM energy radiative emission.
–
The close analyse of the Graph confirms that the solar EM SW energy portion, which is not reflected as SW, it mostly doesn’t get absorbed in the lunar surface's inner layers.

The major part of not reflected SW EM energy gets at the instant transformed into the LW outgoing EM energy, which leaves to outer space.

Only a portion gets absorbed as heat and, later at night, it is IR emitted to outer space.
–
Also we see in the Graph, that at almost the very instant of solar incidence at the next morning, the surface temperature rises at a tremendous high rate from ~100 K to ~ 400 K.

Thus we can conclude, that the arriving solar SW EM energy on the instant of incidence induces the skin layers high temperature, with very little of that EM energy being absorbed.

****************

********

*****

The faster rotation prevents a planet to get much warmed at day-time. Thus it prevents it from emitting during the day-time hours much IR outgoing EM energy.

Now, please compare the above lunar, at the local lunar noon the upwelling IR, with the very important  (Godwin-Creek-MS-upwelling-IR-).

https://i.postimg.cc/sXhYqDNR/SURFRAD-Godwin-Creek-MS-upwelling-IR-050423.png

Because…. The faster rotation (EARTH) prevents a planet to get much warmed at day-time. Thus it prevents it from emitting during the day-time hours much IR outgoing EM energy.

***************

********

*****

I think planets and moons absorb some of the not reflected portion of solar EM energy at solar lit hours by transforming part of it into HEAT and get warmed, and release EM energy at dark hours at night and get cooled.
–
The rate of cooling slows the cooler surface gets. The S-B emission law is limited to work on much higher than terrestrial temperatures, when an abundance of thermal energy makes it pouring out

at its highest rate of  ~ ε*σT⁴.
–
The emittance from surfaces at lower temperatures doesn’t happen
at the highest ~ σT⁴ rate.
–
And I think that is the reason why planets and moons in solar system (Earth included) still hold enough of their primordial thermal energy.

****************

********

*****

Quote:

“If there is something very slightly wrong in our definition of the theories, then the full mathematical rigor may convert these errors into ridiculous conclusions.”

Richard Feynman

Also, something else I have to quote is Gandhi's saying...

"A mistake does not become truth because it is widespread, nor does truth become wrong because no one sees it."

-

And:

"Because everything is cognized in comparison."

It means you can only know this or that thing for real if you compare it to something else.

The authorship of the phrase "everything is cognized in comparison" belongs to the great French philosopher-Cartesian Rene Descartes.

-

**************

No, the Earth does not emit on average 240 W/m².

-

In addition, Earth is a planet. A planet is irradiated from one direction only, and a planet rotates. A planet's average surface temperature cannot be estimated by simply averaging over the entire planet surface the not reflected portion of the incident solar flux.

-

No, without greenhouse effect, Earth’s surface would NOT be some 33°C (59°F) cooler.

Because there is not a 33°C (59°F) greenhouse effect on Earth's surface.

-
When solar irradiated, a planet surface does not absorb the entire not reflected portion of the incident solar energy.
What planet surface does is to INTERACT with the incident solar flux.
Only a portion of the incident solar energy a planet surface absorbs in inner layers.

***

-

So, it is actually a completely different approach, it is a completely different mechanism when describing the planet radiative energy balance, the

Energy in = Energy out

which (in radiative equilibrium) should be necessarily met.
–
The above naturally begs for the question:

Where to goes the not absorbed solar energy then?

The not absorbed SW solar energy, when interacting with planetary surface’s matter, the surface’s skin layer gets warmed, and instantly transforms the SW solar energy into the LW (IR) outgoing radiative EM energy.

The temperature (at every spot) developed by the surface’s skin layer is measured by satellite sensors and that skin layer’s temperature is considered as the spot’s surface temperature.

The spot’s skin layer’s temperature is a superficial temperature. That temperature doesn’t represent the temperature the surface’s inner layers are at.

Because the not reflected SW solar energy is not entirely absorbed in surface’s inner layers.

-
***

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The Rotational Warming Phenomenon is not only about THE NON-LINEARITY OF THE S-B EMISSION LAW.

When a planet rotates faster, its surface temperatures are less differentiated.

Also, when a planet rotates faster, its surface absorbs more solar energy (a higher thermal energy (heat) input).

Thus the planet becomes on average warmer.

But when a planet rotates faster, its day-time temperatures lessen and the night-time temperatures rise. So there is the self limiting factor:

The planet average surface temperature (Tmean) is always less than the day-time average temperature.

So when N2 > N1

Tnight↑→ T↑mean ← T↓day
-

But, the night-time temperatures rise more (the night-time temperatures AMPLIFICATION - because of the non-linearity of EM energy emission law), than the day-time temperatures lessen. Thus on average (as a whole), when faster rotating, the planet surface is always warmer.

But there is more to it:

The Rotational Warming Phenomenon DOESN'T APPEAR AS THE EXCLUSIVE RESULT OF THE NON-LINEARITY OF THE S-B EMISSION LAW.

The Rotational Warming Phenomenon is a much more powerful Phenomenon, than the S-B non-linearity suggests, because when a planet has a higher (N*cp) product, the planet surface is subjected to a higher thermal energy (heat) input.

************

There is a widely known MATHEMATICAL CONSTRAINT

For identical spheres emitting the same exactly amount of IR EM energy, for those with higher differentiated surface temperatures, the average surface temperature (Tmean) will be lower.

Thus, the higher  the spheres' differentiated surface temperatures, the lower their average surface temperature.

So, consequently, the spheres with UNIFORM (not differentiated) surface temperatures will have the highest (the maximum) AVERAGE surface temperature.

For them, 

Tmean(maximum) ≤ Tuniform

-

It is true for identical spheres emitting the same exactly amount of IR EM energy.

-

We should mention here, that those spheres emit the same exactly amount of IR EM energy, but the source (or sources) of that emitted energy are originated from the spheres' inner layers. That energy comes from the inside of the spheres.

Thus that mathematical constraint cannot be applied to the planets and moons the surfaces' temperatures estimation.

Because, for planets and moons, the source of emitted  IR EM energy is very much different: for planets and moons, the source of emitted IR EM energy originates from the INTERACTION with SOLAR IRRADIATION.

-

The widely known and the widely used, when considering the real bodies' the emission temperature - the physical term emissivity (ε), cannot be applied when the source of EM radiative emission energy originates from the EM/surface INTERACTION PROCESS from the incident on that surface an outer EM radiative energy.

Thus,

The Planet Effective Temperature FORMULA:

Te = [So(1 -A)/4εσ]¹∕ ⁴ (1)

is always written with ε =1,  that is why, after simplification, it has its usual form of appearance as:

Te = [So(1 -A)/4σ]¹∕ ⁴ (1)

and which calculates for Earth the theoretical effective temperature as:

Te = 255 K

but the ε = 1 is for spheres emitting their inner source's heat transformed on their surface into IR EM radiative energy.

For planets and moons, their source of energy is already radiative energy, what they emit as IR EM radiative energy is the result of interaction of the incident radiation with the surface (with the matter).

-

There is NOT for the EM energy interaction process, which results in the surface's IR emission, there is NOT any kind of surface emissivity term to be applied.

So, under those, very much different circumstances, there is NOT any room for the real planets the average surface temperatures to be compared with their respective theoretical effective temperatures.

-

Earth's oceanic waters do have emissivity close to    ε = 1 , but there is NOT possible to the term emissivity being applied, when incident solar EM energy induces the waters to emit IR (to re-emit the SW as IR) - there is NOT any room for the emissivity term to be applied.

Therefore, the above MATHEMATICAL CONSTRAINT also cannot be applied, when we consider for real planets and moons the actual emission behavior.

The planet (or moon) EFFECTIVE TEMPERATURE, which is a pure theoretical ABSTRACTION, cannot be accepted as the planets' (or moons') Mathematical CONSTRAINT

Teffective = Tmean(maximum),

which mistakenly led to the very much confusing conclusion, that planet (or moon) without-atmosphere, the average surface temperature (Tmean) would be constrained to be less than or equal to the Teffective:

Tmean ≤ Teffective   

-

***

Of course, (everything else equals), for planets and moons, the less their surface temperatures are differentiated, the higher their average surface temperatures are.

But the theoretical Teffective does not pose any Mathematical CONSTRAINT to planets' and moons' the average surface temperatures (Tmean).
-
***

The real subject matter is the reality of a dynamic process of a fast spinning ball lit by incoming radiation of 1.362 W/m² from one direction.

*******

A larger question presents itself. Why don’t we just observe the real-time physical processes as they occur on the Solar System's the Various Planets' surfaces and then draw our conclusions from those direct observations, ones being made in real time as the physical processes themselves are happening?

Said differently, the planets' surfaces themselves, as they exist in the real world, might become the ‘computational computer’ which, by the use of planet surface's major parameters will be able to theoretically calculate the expected global mean surface temperatures very much close to those measured by satellites.

Instead of plugging numbers into a physics-based, hand-tuned models, we look at all planets surface's major parameters as an interconnected vector fields.

Last time updated: 

October 31, 2024

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We do the planets surface temperatures comparison as our method