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.

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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).

### 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 emission law is NOT the RADIATIVE ENERGY absorption law!

Thus, the Planet Effective Temperature Equation:

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

"Greenhouse Effect
the earth, Te, is determined by the need
for infrared emission from the planet to

πR²(1 - A)So = 4πR²σTe, (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
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

could also be applied to the real planet Infrared Emission BEHAVIOR.

Also, a planet surface radiative energy emission behavior should not be confused with the blackbody emission behavior.

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

That it is how everything started! Hansen saw the possibility to THEORETICALLY calculate 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.

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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.

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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.

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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.

Last time updated:

March 22, 2023

### Let's introduce to the very POWERFUL the Solar Irradiated planet surface Rotational Warming Phenomenon.

When comparing the various different planets' and moons' (without-atmosphere, or with a very thin atmosphere, Earth included), when comparing the planetary surface temperatures, the Solar Irradiated Planet Surface Rotational Warming Phenomenon emerges:

Planets' (without atmosphere, or with a thin atmosphere) the mean surface temperatures RELATE (everything else equals) as their (N*cp) products' SIXTEENTH ROOT.

( N*cp ) ^¹∕₁₆

or

[ (N*cp)¹∕ ⁴ ] ¹∕ ⁴

Where:

N - rotations/day, is the planet's axial spin.

cp - cal/gr*oC, is the planet's average surface specific heat.

This discovery has explained the origin of the formerly observed the planets' average surface temperatures comparison discrepancies.

The difference of rotation speed between Earth and its Moon is the most important factor in our computation of their respective warming!

Earth is warmer than Moon because Earth rotates faster than Moon and because Earth’s surface is covered with water.

Earth's /Moon's example

Let's demonstrate the Planet Surface Rotational Warming Phenomenon on the:

Earth's /Moon's example

Earth is on average warmer 68°C than Moon.

Earth and Moon are at the same distance from the sun. But Moon receives 28% more solar energy than Earth, because Moon's average surface Albedo is significantly lower (Moon’s Albedo a =0,11 vs Earth’s Albedo a =0,306).

Yet Earth is on average warmer 68°C than Moon.

The average surface temperature difference of 68°C can be explained only by the Planet Surface Rotational Warming Phenomenon.

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

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

Earth is on average warmer than Moon not only because of the Earth having 29,53 times faster rotational spin.

Earth also has a five (5) times higher average surface specific heat (for Earth cp.earth = 1 cal/gr*oC, it is because Earth has a vast ocean; and for Moon cp.moon = 0,19cal/gr*oC – its soil is a dry regolith).

N.moon = 1 /29,53 rotation /per day, is Moon's rotation spin

cp.moon = 0,19 cal/gr*oC

Earth is warmer than Moon not because of Earth's very thin atmosphere having some trace greenhouse gasses content.

Earth is warmer because its surface has 155,42 times higher the (N*cp) product than Moon’s surface.

Earth(N*cp) /Moon(N*cp) = (1*1) /[(1/29,53)*0,19] =

29,53 /0,19 = 155,42

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

If Moon had Earth's albedo (a=0,306), Moon's mean surface temperature would have been 210K.

As we know, Earth's mean surface temperature is 288K (15°C). Earth is warmer because its surface has 155,42 times higher the (N*cp) product than Moon’s surface.

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

Let's compare the Earth's and Moon's (for equal average Albedo) the mean surface temperatures:

Tmean.earth /Tmean.moon = 288K /210K = 1,3714

and the Earth's and Moon's (N*cp) products sixteenth root:

[ Earth(N*cp) /Moon(N*cp) ]^1/16 = (155,42)^1/16 = 1,3709

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

The results (1,3714) and (1,3709) are almost identical!

It is a demonstration of the Planet Surface Rotational Warming Phenomenon:

Planets' mean surface temperatures relate (everything else equals) as their (N*cp) products' sixteenth root.

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The rightness of the Rotational Warming Phenomenon is many times demonstrated and, also, it has been theoretically explained by the physics first principles.

What we do in our research is to compare the satellite measured planetary temperatures.

There are not two identical planets or moons in solar system.

Nevertheless all of them, all planets and moons in solar system are subjected to the same ROTATIONAL WARMING PHENOMENON!

The Planet Surface Rotational Warming Phenomenon is expressed QUANTITATIVELY.

It appears to be a very POWERFUL the planet surface warming factor.

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The Planet Surface Rotational Warming Phenomenon:

It is well known that when a planet rotates faster its daytime maximum temperature lessens and the night time minimum temperature rises.

But there is something else very interesting happens. When a planet rotates faster it is a warmer planet.

The Earth seen from Apollo_17

Earth is warmer than Moon, because Earth rotates faster!

The planet mean surface temperature (Tmean) is amplified by the Planet Surface Rotational Warming Phenomenon.

### we ended up to the following remarkable results:

Comparison of results the planet's Te calculated by the Incomplete Equation (the Planet Effective Temperature Te):

Te = [ (1-a) S / 4 σ ]¹∕ ⁴ (K)

the planet's mean surface temperature Tmean calculated by the Planet's Without-Atmosphere Mean Surface Temperature New Equation:

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

and the planet's Tsat.mean measured by satellites:

To be honest with you, at the beginning, I got by surprise myself with these results.

Correlation is not causation, but the match is striking.

You see, I was searching for a mathematical approach…

We have collected the results now:

Planet…..Te.incompl....Tmean….Tsat.mean

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

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

Moon……....270,4 K…….223,35 Κ…..220 Κ

Mars……....209,91 K…..213,21 K…..210 K

the calculated with Planet's Without-Atmosphere Mean Surface Temperature Equation and the measured by satellites are almost the same, very much alike.

It is a situation that happens once in a lifetime in science.

The Planet Effective Temperature Equation

Te = [ (1-a) S / 4 σ ]¹∕ ⁴ (K)

is incomplete because it is based only on two parameters:

1. On the average solar flux S (W/m²) on the top of a planet’s atmosphere and

2. The planet’s average Albedo "a".

The planet's without-atmosphere mean surface temperature equation has to include all the planet surface major properties and all the characteristic parameters.

3. The planet's axial spin N (rotations/day).

4. The thermal property of the surface (the average specific heat cp).

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

Altogether these parameters are combined in the Planet's Without-Atmosphere Mean Surface Temperature New Equation:

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

Consequently, the planet mean surface temperature Tmean is based on Stefan-Boltzmann emission law,

πr²Φ*S*(1-a)  (W)

and on precise estimation by planet surface the total amount of emitted energy

and on the different for each planet the energy emission distribution (the  temperatures distribution) over surface area - resulting in the very POWERFUL

the Planet Surface Rotational Warming Phenomenon.

( ...on the way the energy emission is distributed over the entire planetary surface – the Planet Surface Rotational Warming Phenomenon. )

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Let's consider another pair of planets and their satellite measured mean surface temperatures:

Moon and Mars (220K vs 210K)

Mars is at 1,5 AU from the sun, thus Mars receives 2,32 times less solar energy on its surface than Moon.
Also Mars has higher than Moon average Albedo (0,25 vs 0,11). It can be shown that if Moon had the same as Mars Albedo, Moon's mean surface temperature would also be 210K, therefore it would be equal to Mars' mean surface temperature of 210K.

Thus Mars receives 2,32 times less solar energy than Moon, yet Mars and Moon would have (for equal average Albedo) the same mean surface temperature 210K.
-
Therefore, there is only the Rotational Warming Phenomenon what justifies for Earth and for Moon, the measured, but the so very much the different, the mean surface temperatures (288K vs 220K).

And also, therefore, there is only the Rotational Warming Phenomenon what also justifies, now in the case of Moon and Mars, the measured, but this time the so very much the proximate, the mean surface temperatures (220K vs 210K).

Rotational Warming Phenomenon justifies for Earth and for Moon, the measured, but the so very much the different, the mean surface temperatures (288K vs 220K).

-

Rotational Warming Phenomenon also justifies, in the case of Moon and Mars, the measured, but this time the so very much the proximate, the mean surface temperatures (220K vs 210K).

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The rightness of the Rotational Warming Phenomenon is many times demonstrated and, also, it has been theoretically explained by the physics first principles.

-

The planet Radiative "Energy In" is ruled by the three major parameters:

1. The intensity of Solar flux "S" (W/m²), which is defined as the solar energy intensity perpendicular to the planet cross-section cycle (it is the proximity to the sun dependent value).

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2. The planet average surface Albedo "a".

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3. The planet surface Solar Irradiation Accepting Factor "Φ" (in other words - the planet surface spherical shape and the planet surface roughness coefficient).

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All those three major parameters are combined in the Radiative

"Energy In" Equation:

Energy In = Φ*(1-a)*S (W/m²)

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Also, the planet mean surface temperature Tmean is amplified by the Planet Surface Rotational Warming Phenomenon.

-

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Recognizing the difference between what theory suggests and practical knowledge demonstrates is critical.

Academics have the luxury of focusing on one or a limited number of parameters at a time. The traditional scientific method of hypothesis testing through experimentation is better suited to studies involving limited numbers of variables. Wicked complex systems full of all sorts of inconvenient interactions and feedback tend not to always work as might be suggested by theory from the "settled" sciences.

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The planet blackbody equilibrium temperature Te (the planet effective temperature) was the first scientifically supported attempt  to theoretically estimate the expected planet mean surface temperature Tmean.

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It was the brilliant insight - to apply the planet radiative energy ballance (Energy in = Energy out), and to attribute to the "Energy out" the planet mean surface temperature Tmean THE TOTAL infrared outgoing radiative energy.

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This brilliant approach had two serious basic science cavets though.

1. Planets are not blackbodies.

2. The Stefan-Boltzmann emission law cannot be applied wice-versa (we cannot calculate the radiated surface's temperature by simply measuring the incident on the surface radiative energy flux.)

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Also it was omitted that the planets have spherical shape and that the planets' surfaces have different levels of roughness. The planets' spherical shape and the planets' surface roughness play a major role in solar irradiation- planet surface interaction processes.

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We shall proceed by demonstrating the New Equation for the planets mean surface temperatures precise calculation.

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

Tmean.earth

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 here 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 – is the Rotating Planet Surface Solar Irradiation INTERACTING-Emitting Universal Law constant

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

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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 – it is a Rotating Planet Surface Solar Irradiation INTERACTING-Emitting Universal Law 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.

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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 – it is a Rotating Planet Surface Solar Irradiation INTERACTING-Emitting Universal Law 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 !

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We have calculated The Planet Mean Surface Temperatures by the use of the New Equation:

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

for all the twenty (20) major planets and moons in solar system. The results are very close to the satellite measurements.

The detailed Mean Surface Temperatures calculations for each and every planet and moon in solar system, by the use of the New Equation, are posted in the next pages of this site.

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How much of the incident on a planet surface solar flux’s radiative energy a planet can absorb?

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What portion of the incident on planet surface solar flux's radiative energy gets transformed from SW incident into the IR emitted (the IR outgoing) energy?

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Io (Jupiter’s satellite), Io’s Albedo a =0,62

Moon (Earth’s satellite), Moon’s Albedo a =0,11

Why those Albedo are so much different?

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Earth’s Albedo without clouds is a =0,08

Venus' Albedo a =0,77

Why there is so much difference?

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Yes, we are approaching now the second very much important concept of this research:

Planets and moons (without-atmosphere, or with a very thin atmosphere, Earth included) may have very smooth planetary surfaces, or they may have very much cratered (the heavy cratered) planetary surfaces.

The smooth surface planets, when solar irradiated, exhibit a very strong specular reflection, which cannot be measured by satellites (as a supplementary portion of Bond Albedo), because the specular reflected portion of solar flux does not enter into the satellite's sensor.

The heavy cratered surface planets, when solar irradiated, do not exhibit specular reflection, because the incident solar flux is subjected there to multiple reflections within the planetary surface craters, and thus, its radiative energy  being captured and absorbed - not having the ability to escape as a specular reflection.

-

Planets and moons with a  low Albedo tend not to appear as Lambertian scatterers, in fact they tend to scatter more light into the oblique angles than a Lambertian scatterer.
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The-not reflected-portion = It is the what has left after reflection and dispersion of the incident solar flux

In the E-in versus E-out radiation balance, you always see on the left side of the equation:

π * r²

The total solar irradiance hitting a hemisphere of 2*π*r² is obtained by weighting the 1.362 W/m² by the square of the cosine of the incidence angle; that gives π*r².

Thus the total solar irradiance hitting a hemisphere is:

π*r²*So = π*r²*1.362 W/m²

-
The next very important step is to determine what has left of
the total solar irradiance hitting a hemisphere

for the planet radiation balance left side of the equation

E-in versus E-out

Because it is one thing the E-in and it is another thing
the
E-in- the-not reflected-portion of
the total solar irradiance hitting a hemisphere” .

In other words- it is about of the -what has left after reflection and dispersion of the incident solar flux.

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Let's introduce to the Φ -Factor

It is very important!

Φ - is the dimensionless Solar Irradiation accepting factor - very important.

It is a realizing that a sphere's surface "absorbs" the incident solar irradiation not as a disk of the same diameter, but accordingly to its spherical shape.

For a smooth spherical surface

Φ = 0,47

What a smooth enough planet surface is for the incident solar light's specular reflection to occur?

Here it is an interesting insight we share with you !

We shine a light on a wall (from a fair way back).

Then we place a tennis ball in front of the wall, thus reducing the amount of light striking the wall.

Next to the ball we fix a disc of opaque material to the wall, with radius equal to the radius of the ball.

Ignoring minor effects due to non-parallel rays, which object blocks the most light from hitting the wall?

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The tennis ball’s shadow on the wall is the same size as the disk’s shadow on the wall…

So they block the same exactly amount of light from hitting the wall!

Now, which one of the above described objects, reflects the most light, and which one absorbs the most light?

If the surfaces are made of the same material, and provided that reflection is isotropic, they each reflect the same total amount of light.

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Near the “edge” of the earth (as seen from the sun) the surface flux of an incoming “sunbeam” reduced by exactly the same percentage as the area of that surface increases.

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In our example we were comparing a disk to a sphere assuming all other parameters were constant.

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What same material?

Also the material can be a smooth layer, or the material can form a rough surface...

What exactly the rough planet surface can be defined for - in order for the surface to be capable capturing some of the specular reflected solar energy?

What makes planet surface smooth, and what makes it rough?

Also, there should be a gradation of the planet surface smoothness, or, of the planet surface roughness.

And  (it is demonstrated in this site) the smoothness is limited to some level, which doesn't make the more smooth surface to reflect more.

And, likewise, the roughness is limited to some level, beyond which the more rough planet surface does not absorb more solar radiative energy.

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A heavy cratered planet surface has a resemblance with a dence urban area, where high buildings form the deep-down streets-canjons. Solar rays are subjected to multiple reflections and absorptions there...

Heavy cratered planet surface reflects less and absorbs more of the incident solar radiative energy.

Consequently, when planet surface is a heavy cratered, everything else equals, the heavy cratered planet develops a warmer surface (a higher average surface temperature).

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Earth also has glint.

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The Earth is actually a smooth planet.

Yes, they are made from the same material.

But we should be very careful here, because the reflection of light is not an isotropic phenomenon.

The reflection of light is a complex phenomenon, in most cases it appears as a diffuse reflection, but diffuse reflection (it looks like), but it is not an isotropic reflection...

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Actually reflection is not isotropic, reflection is resulting from the radiative flux’s interaction with matter.

Flux is a directional radiative energy. Reflection cannot be characterized as a 100% isotropic phenomenon.

***

The following question arises:

What a smooth enough planet surface is for the incident solar light's specular reflection to occur?

### Φ factor explanation

The Φ - solar irradiation accepting factor - how it "works".

It is not a planet specular reflection coefficient itself. There is a need to focus on the Φ factor explanation. Φ factor emerges from the realization that a sphere reflects differently than a flat surface perpendicular to the Solar rays.

Φ – is the dimensionless Solar Irradiation accepting factor.

"Φ" is an important factor in the Planet Mean Surface Temperature Equation:

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

It is very important the understanding what is really going on with by planets the solar irradiation reflection. There is the specular reflection and there is the diffuse reflection. The planet's surface Albedo "a" accounts only for the planet's surface diffuse reflection.

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The importance of the Solar Irradiation Accepting Factor Φ.

For smooth surface planets (like Earth) the Φ =0,47

So = 1362 W/m² - is the solar flux on the TOA (the top of atmosphere). It is also called the Solar Constant.

a = 0,306 - is the Earth's average surface Albedo.

Thus the incident on Earth solar energy not reflected from the planetary cross-section disk is:

1362 W/m² *Φ(1 - a) = 1362 W/m² *0,47(1 - 0,306) = 444 W/m²

This not reflected energy doesn’t get distributed over the hemisphere or over the sphere.

The not reflected portion of 444 W/m² is INTERACTING with planet’s surface matter on the very instant of incidence.

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In short, the Φ -Factor is not the planet specular reflection portion itself. The Φ -Factor is the Solar Irradiation Accepting Factor (in other words, Φ is the planet surface spherical shape and planet surface roughness coefficient).

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How to formally prove Φ -Factor's correctness in the

Ein = Eout formula.

Ein = (1-a)S W/m²

used in the blackbody planet effective temperature Te is an empirical assertion, which is not based on any theoretical research, not to say, its correctness has not been demonstrated, quite the opposite…

– The Energy in:

Ein = Φ(1-a)S W/m²

is based on measurements (the Drag Coefficient for smooth spheres in a parallel fluid flow Cd = 0,47), and it is demonstrated to be the correct one.

The Φ -Factor's importance is explained in every detail in next pages in this site.

### The 4th root powers twice

The 4th root powers twice is an observed the Rotational Warming (N*cp) in sixteenth root power phenomenon when planet mean surface temperatures comparison ratios with the coefficients is compared.

Please visit the page “Earth/Mars 288K/210K”

The entire thread there is devoted to the planets’ mean surface temperatures comparison. And every time for the compared planets’ the (N*cp) in sixteenth root is necessarily present.

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Earth / Mars satellite measured mean surface temperatures 288 K and 210 K comparison.

It is a demonstration of the Planet Surface Rotational Warming Phenomenon!

These ( Tmean, R, N, cp and albedo ) planets' parameters are all satellites measured. These planets' parameters are all observations.

Planet…....Earth.….Moon….Mars

Tsat.mean.288 K….220 K…210 K

R…...............1... AU..1 AU..1,525 AU

1/R²…..........1…........1….…0,430

N…..............1....1 /29,531..0,9747

cp................1.........0,19.......0,18

a..............0,306......0,11......0,250

1-a…........0,694……0,89…….0,75

(1-a)¹∕ ⁴…0,9127....0,9713…0,9306

coeff...........1...................0,72748

As we can see Earth and Mars have very close values for

(1-a)¹∕ ⁴ term; For Earth (1-a)¹∕ ⁴ = 0,9127 and for Mars (1-a)¹∕ ⁴ = 0,9306.

Also Earth and Mars have very close N; for Earth N = 1 rotation /day, and for Mars N = 0,9747 rotation /day.

Earth and Mars both have the same Φ = 0,47 solar irradiation accepting factor.

Thus the comparison coefficient can be limited as follows:

Comparison coefficient calculation

[ (1/R²) (cp)¹∕ ⁴ ]¹∕ ⁴

Earth: Tsat.mean = 288 K

[ (1/R²)*(cp)¹∕ ⁴ ]¹∕ ⁴ =

= [ 1*(1)¹∕ ⁴ ] ¹∕ ⁴ = 1

Mars: Tsat.mean = 210 K

[ (1/R²)*(cp)¹∕ ⁴ ]¹∕ ⁴ =

= [ 0,430*(0,18)¹∕ ⁴ ] ¹∕ ⁴ = ( 0,430*0,65136 )¹∕ ⁴ =

= ( 0,2801 )¹∕ ⁴ = 0,72748

Let's compare

Earth coeff. / Mars coeff. =

= 1 /0,72748 = 1,3746

And

Tmean.earth /Tmean.mars =

= 288 K /210 K = 1,3714

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

The results (1,3746) and (1,3714) are almost identical! .

Conclusion:

Everything is all right. It is a demonstration of the Planet Surface Rotational Warming Phenomenon!

And It is the confirmation that the planet surface specific heat "cp" should be considered in the (Tmean) planet mean surface temperature equation in the sixteenth root:

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

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Earth / Europa (Jupiter's moon) satellite measured mean surface temperatures 288 K and 102 K comparison.

It is a demonstration of the Planet Surface Rotational Warming Phenomenon!

All the data below are satellite measurements. All the data below are observations.

Planet….Earth….Europa

Tsat.mean 288 K….102 K

R…...........1 AU…5,2044 AU

1/R²………1…….0,0369

N………....1……1/3,5512 rot./day

a…………..0,306……0,63

(1-a)………0,694……0,37

coeff...0,9127...0,3158

Comparison coefficient calculation

[ (1-a) (1/R²) (N)¹∕ ⁴ ]¹∕ ⁴

Earth: Tsat.mean = 288 K

[ (1-a)*(1/R²)*(N)¹∕ ⁴ ]¹∕ ⁴ =

= ( 0,694 * 1 * 1 )¹∕ ⁴ = 0,9127

Europa: Tsat.mean = 102 K

[ (1-a)*(1/R²)*(N)¹∕ ⁴ ]¹∕ ⁴ =

= [ 0,37*0,0369*(1/3,5512)¹∕ ⁴ ] ¹∕ ⁴ = 0,3158

Let's compare

Earth coeff. /Europa coeff. =

= 0.9127 /0,3158 = 2,8902

And

Tmean.earth /Tmean.europa =

= 288 K /102 K = 2,8235

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

The results (2,8902) and (2,8235) are almost identical! .

Conclusion:

Everything is all right. It is a demonstration of the Planet Surface Rotational Warming Phenomenon!

Notice:

We could successfully compare Earth /Europa ( 288 K /102 K ) satellite measured mean surface temperatures because both Earth and Europa have two identical major features.

Φearth = 0,47 because Earth has a smooth surface and Φeuropa = 0,47 because Europa also has a smooth surface.

cp.earth = 1 cal/gr*°C, 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.

Europa is an ice-crust planet without atmosphere, Europa’s surface consists of water ice crust,

cp.europa = 1cal/gr*°C.

Conclusion:

Everything is all right. It is a demonstration of the Planet Surface Rotational Warming Phenomenon!

And It is a confirmation that the planet axial spin (rotations per day) "N" should be considered in the (Tmean) planet mean surface temperature equation in the sixteenth root:

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

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

The rightness of the Rotational Warming Phenomenon is many times demonstrated and, also, it has been theoretically explained by the physics first principles.

Planet Surface Rotational Warming Phenomenon

The faster rotation - the warmer the planet!

### The first steps

At the very first look at the data table we distinguish the following:

Planet..Tsat.mean..Rotations..Tmin..Tmax

...........measured...per day......................

Mercury..340 K.....1/176....100 K...700 K

Earth.....288 K........1.............................

Moon....220 Κ.....1/29,5.....100 K...390 K

Mars.....210 K....0,9747.....130 K...308 K

The Earth's and Mars' by satellites temperatures measurements, in relation to the incident solar irradiation intensity, appear to be higher,

and it happens because of Earth's and Mars' faster rotation.

I should say here that I believe in NASA satellites temperatures measurements. None of my discoveries would be possible without NASA satellites very precise planet temperatures measurements.

It is the "magic" of the planet's spin. When it is understood, it becomes science.

The closest to the sun planet Mercury receives 15,47 times stronger solar irradiation intensity than the planet Mars does.

However on the Mercury's dark side Tmin.mercury = 100 K, when on the Mars' dark side Tmin.mars = 130 K.

These are observations, these are the by satellite the planet surfaces temperatures measurements.

And they cannot be explained otherwise but by the planet Mars' 171,5 times faster rotation than planet Mercury's spin.

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

Let's study the table of data above.

Interesting, very interesting what we see there

- Earth and Moon are at the same distance from the Sun

R = 1 AU.

Earth and Mars have almost the same axial spin

N = 1rotation /day.

Moon and Mars have almost the same satellite measured average temperatures

220 K and 210 K.

Mercury and Moon have the same minimum temperature

100 K.

Mars' minimum temperature is 130 K, which is much higher than for the closer to the Sun Mercury's and Moon's minimum temperature 100 K.

And the faster rotating Earth and Mars appear to be relatively warmer planets.

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

Two planets with the same mean surface temperature can emit dramatically different amounts of energy.

Moon's average surface temperature is Tmoon = 220 K

Mars' average surface temperature is Tmars = 210 K

Moon's average surface Albedo a =0,11

Mars' average surface Albedo a =0,25

It can be demonstrated that for the same Albedo Mars and Moon would have had the same average surface temperature.

The solar flux on Moon is So =1361W/m²

The solar flux on Mars is S =586W/m²

It is obvious, that for the same average surface temperature, the emitted amounts of energy from Moon are dramatically higher than the emitted amounts of energy from Mars.

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

To continue with the solar system's coincidences, which would  be very useful in the further research, there is another very interesting observation shouldn't be neglected:

I have the gaseous planets at 1 bar level the satellite measured temperatures comparison in relation to the gaseous planets’ rotational spins.

Gaseous planets (Jupiter, Saturn, Uranus, Neptune) have, between them, similar atmospheric gases content.

The more close the content is, the better the satellite measured temperatures relate in accordance to the Rotational Warming Phenomenon.

### There has to be a PROCESS.

Somehow, someway a transformation has to be generated to affect the planet’s surface temperature.

You can’t just say RADIATIVE energy get converted into Heat. It’s more likely it stays Radiative energy.

There has to be a PROCESS.

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

Planets and moons do everything differently.

Βy DEFINITION, the planet theoretical effective radiative temperature’s formula doesn’t consider planet rotating. The formula is for planet with uniform surface temperature, and it is for planet with uniform surface irradiance.

Te = [ (1-a) S /4σ ]¹∕ ⁴

The Te cannot be some kind of a theoretical limitation for planets and moons without-atmosphere the mean surface temperatures not to exceed their theoretical Te calculated temperature.

Planets and moons do not have uniform surface temperature; and they do not have uniform surface irradiance either. And planets and moons do ROTATE.

Consequently, the  Te = [ (1-a) S /4σ ]¹∕ ⁴ is not capable to describe the real planets’ and moons’ the mean surface temperatures.

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

Planet mean surface temperature cannot be associated with any kind of BB profile spectrum.

The BB (black body) profile spectrum is associated with a single BB emitting temperature.

A planet doesn’t have a uniform surface temperature. The planet’s mean surface temperature doesn’t have a BB profile spectrum, because planet doesn’t emit at mean surface temperature…

Every spot on the planet’s surface at every given instant has a different emitting temperature…

Every spot at that given instant emits with its own spectrum profile…

A planet’s mean surface temperature’s BB profile spectrum (theoretically expected) cannot be considered as the planet’s mean BB profile spectrum.

Planet mean surface temperature cannot be associated with any kind of BB profile spectrum.

————–

Two planets with the same mean surface temperature may emit dramatically different amounts of IR outgoing EM energy.

Earthrise, taken in 1968 Dec 24 by William Anders, an astronaut on board Apollo 8

Moon and Earth - so close to each other - and so much different...

We may conclude that for a faster rotating planet there is the phenomenon of its warmer surface...

### The Planet Surface Rotational Warming Phenomenon

I’ll try here in few simple sentences explain the very essence of how the Planet Surface Rotational Warming Phenomenon occurs.

A planet surface doesn't absorb solar energy first, gets warmed and only then emits IR EM energy.

No, a planet surface emits IR EM energy at the very instant solar flux hits the matter.

Lets consider two identical planets F and S at the same distance from the sun.

Let’s assume the planet F spins on its axis Faster, and the planet S spins on its axis Slower.

Both planets F and S get the same intensity solar flux on their sunlit hemispheres. Consequently both planets receive the same exactly amount of solar radiative energy.

The slower rotating planet’s S sunlit hemisphere surface gets warmed at higher temperatures than the faster rotating planet’s F sunlit hemisphere.

The surfaces emit at σT⁴ intensity – it is the Stefan-Boltzmann emission law.

Thus the planet S emits more intensively from the sunlit side than the planet F.

There is more energy left for the planet F to accumulate then.

That is what makes the faster rotating planet F on the average a warmer planet.

That is how the Planet Surface Rotational Warming Phenomenon occurs.

And it states:

Planets’ (without atmosphere, or with a thin atmosphere) the mean surface temperatures relate (everything else equals) according to their (N*cp) products’ sixteenth root.

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

Here it is what I have also to say.

1). The faster rotating planet has a less differentiated surface temperatures distribution. Thus, for the same amount of solar energy transformed into HEAT and accumulated in inner layers, the faster rotating planet has a higher average surface temperature.

2). The not reflected portion of the incident SW EM energy is NOT ENTIRELY transformed into HEAT.

3). In addition, the faster rotating planet is able to transform into HEAT and accumulate in inner layers LARGER amounts of the incident on surface solar energy, than a slow rotating planet.

Important Notice:

Rotational Warming Phenomenon states about the (N*cp) products' sixteenth root, not only the planetary rotational spin (N) is involved, but also the planet average surface SPECIFIC HEAT (cp)!

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

Every spot on planet surface experiences its peak hot and cold temperature. The less are those differences, the higher is the average surface temperature

for the same not reflected portion of the incident solar flux.

-

The (N*cp)^1\16 is the way the planet average surface temperature “responds” to that.

The faster the rotation, the less time every spot is exposed to the solar flux’ EM radiative energy, the less the skin surface layer’s INDUCED temperature is.

The more atoms (higher surface cp) are getting exposed (INTERACTED) on the skin layer to the solar flux’ EM radiative energy, the less the skin surface layer’s INDUCED temperature is.

### The Planet Mean Surface Temperature New equation

The planet mean surface temperature New equation is written for planets and moons WITHOUT atmosphere. The results of calculations are remarkably exact!

When applied to Earth (Without Atmosphere) the New equation calculates Earth’s mean surface temperature very much close to the 288K.

Earth is a planet, like any other planet we know in solar system. Neither Stefan, no Boltzmann said anything about planets being ideal blackbodies.

What I did in my research was to compare the satellite measured planetary temperatures for every known planet and moon in solar system, Earth included.

When I wrote the New equation, yes I was expecting something, but the results were successful beyond any expectations.

Here it is the planet 1LOT energy balance analysis related New equation:

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

The New equation is based both, on precise radiative

“energy in = Φ (1-a) S” estimation and

on the “Planet Rotational Warming Phenomenon“.

We are capable now for the THEORETICAL ESTIMATION of the planetary mean surface temperatures.

And, now, it should be considered proven - there is not any  Greenhouse Warming Effect on the Earth's surface temperature!

Also, the Incomplete Equation of the Planet Blackbody Effective Temperature

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

the Incomplete Equation of the Planet Blackbody Effective Temperature

Te = [ (1-a) S / 4 σ ]¹∕ ⁴ K

should be abandoned, because it is very much wrong!

==========

Also, I should note that the average solar flux is a pure mathematical abstraction.

Solar flux does not average over the planet surface in the real world.

When we "imagine" solar flux averaging on the entire planet surface it is like having (the false RADIATIVE equilibrium CONCEPT), it is like having the actual planet being enclosed in an imaginary sphere, which sphere is emitting towards the planet surface a constant flux of 240 W/m^2.

But it is not what happens in the real world!

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

Planet is not a uniformly heated body.

Planet is a solar irradiated from one side spherical object.

The planet’s opposite side is in total darkness.

Thus, a planet is not a blackbody!

……………..

I use the Stefan-Boltzmann emission law in the right way.

The planet black body formula averages solar flux over the entire planet area in form of HEAT.

The New equation doesn’t average solar flux over the entire planet area in form of HEAT. For the New equation the outgoing EM is a result of the incident on the planet surface solar energy INTERACTION process with the matter.

Black body by definition transforms its calorimetric HEAT into its absolute temperature T fourth power EM emission intensity.

On the other hand, planet doesn’t emit EM energy supplied by a calorimetric source. The planet’s surface temperature is INDUCED by the incident on the planet solar EM flux.

Only a small portion of the incident solar EM energy is transformed into HEAT. The vast majority of the incident solar energy is IR emitted at the same very moment of incidence and interaction with matter.

This EM energy induces the planet surface temperature without being accumulated in the inner layers.

It is entirely different physics when compared with the “quiet” blackbody calorimetric HEAT black body emission phenomenon.

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

Earth “absorbs” 28% less solar energy than Moon (Albedo Earth a =0,306; Albedo Moon a =0,11).

And yet

The measured Earth’s average surface temperature Tearth=288K. The measured Moon’s average surface temperature Tmoon=220K.

Mars orbits sun at R = 1,524 AU.

(1/R²) = (1/1,524²) = 1/2,32 Mars has 2,32 times less solar irradiation intensity than Earth has

So the solar flux at Mars’ orbit is 2,32 times weaker than on Moon too.

And yet

The measured Mars’ average surface temperature Tmars=210K.

Which is close to the measured Moon’s average surface temperature Tmoon=220K.

Mars' Albedo a =0,250; Moon's Albedo a =0,11.

It can be shown, that for the same Albedo Mars and Moon would have the same average surface temperature.

……………..

Let's see now:

Tmoon =220K

Tearth =288K (for Earth having 28% less than Moon solar energy "absorbed")

Tmars =210K (for Mars having 2,32 times less than Moon solar energy "absorbed")

These obvious discrepancies can be explained only by the Earth's and by the Mars' much faster than Moon's rotational spins.

These obvious discrepancies can be explained only by the Planet Surface Rotational Warming Phenomenon.

Opponent:

There has to be a tested hypothesis. Otherwise its not reliable.

No quality assurance? No replication? No checking? No testing?

Not even peer review?

Its unreliable!

"There has to be a tested hypothesis. Otherwise its not reliable.”

Or , as Richard Feynman said “It doesn’t matter how beautiful your theory is, it doesn’t matter how smart you are. If it doesn’t agree with experiment, it’s wrong.”
-
Well, the method we use in present research is "the planets surface the satellite measured temperatures comparison".
-
We do everything correctly. Haven't we demonstrate reproducible experiments?
-
When we do the same calculations on every planet and on every moon in solar system and the results are so very much close to those measured by satellites... those calculations are adequate to the very much convincing reproducible experiments!

The Graph Ratio of Planet Measured Temperature to Corrected Blackbody Temperature (Tsat /Te.correct), as a linear function of the

Warming Factor = (β*N*cp)^1/16

For further details please visit page:

The planet temperature varies with planet rotation. It is an observation.

There is no need in an experiment with a rotating sphere in a vacuum exposed to sunlight…

Here is the clear relation example:

Let's illustrate on the planet's effective temperature old equation

Te = [ (1-a) S /4σ ]¹∕ ⁴ (K)