The Planet Surface Rotational Warming Phenomenon

Earth is warmer than Moon, because Earth rotates faster.

It is so simple, it should be taught in schools by now.

The method we use is the "Planets and moons surface temperatures comparison".

Earth is a planet, so Earth is subjected to the same universal laws as every planet and moon in solar system.

Let's introduce to the very POWERFUL the Solar Irradiated planet surface Rotational Warming Phenomenon ( N*cp )^1/16.

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' and moons' (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.

When Wiki entries refute claims you kept making for years, you need to reflect on your process.

Either that sixteenth root thing holds, or it does not.

Of course it holds, and here's why:

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!

Also the five (5) times difference in the average surface specific heat between Earth's and Moon's surfaces (water vs regolith), plays a very important role too.

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

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But shouldn't be there an equation which is capable to theoretically calculate every planet's and moon's without atmosphere, or with a thin atmosphere, (Earth included), shouldn't be there an equation which calculates the planet average (mean) surface temperature?

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What we need is an equation, when substituting a planet's the characteristic data, to theoretically calculate the planet average surface temperature (Tmean).

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Albedo

“Albedo (/ælˈbiːdoʊ/; from Latin albedo ‘whiteness’) is the fraction of sunlight that is diffusely reflected by a body. It is measured on a scale from 0 (corresponding to a black body that absorbs all incident radiation) to 1 (corresponding to a body that reflects all incident radiation).”
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“is the fraction of sunlight that is diffusely reflected by a body.”

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

The planet specular reflection was neglected

Smooth spherical shape objects have not only the solar light diffuse reflection, but also they have the solar light a strong mirroring reflection constituence, where there is the phenomenon of specular reflection involved.

Specular reflection is very well demonstrated when we "catch" solar light with a mirror.

The reflection of solar light by the mirror is blinding. It is so much strong, it is almost like looking at the sun with a naked eye.

When out in the street, turn your back to the sun. The illuminated asphalt is seen as a solar light diffuse reflection.

But when we turn towards the sun, when looking at asphalt, we need to narrow our eyes, because the reflection is much more intense.

It is happening so, because of the solar illuminated asphalt reflecting the combination of diffuse and specular reflected solar light.

When looking at the sea, we watch the open water areas the solar specular reflection.

Also, when we look from some elevation to the plain areas, we observe there solar specular reflection too.

But when we are looking at the Moon, we see the solar illuminated Moon in diffuse reflection only.

It happens so, because of the Moon's spherical shape, and the specular reflected from Moon's surface solar light, which is a directional light, cannot be seen from Earth's distance.

The specular reflected light from Moon does not go towards Earth's direction.

The same with spacecrafts, orbiting planets and moons. 

The spacecrafts sensors do not "see" the specular reflection, because it goes the different directions, and doesn't fall on the spacecrafts. 

And it was the planet surface Lambertian reflectance considerations (or diffusely reflecting surface) the cause to wrongly estimate the planet specular reflection as a negligible value.

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

When, for planets and moons with smooth surface, the specular reflection was neglected, it resulted to the very much mistakenly for the planet radiative "energy in" estimation.

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.

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.

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It is all explained further on below.

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Very well...

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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).

Those two terms,

the average surface temperature (Tsat),

and

the uniform surface temperature (Te)

are different physics terms.

Therefore, they cannot be straight-forwardly compared...

However, (Tsat) and (Te) depend heavily on the same two physical properties, namely:

S - the same solar flux (W/m²)

a - the same satellite measured average Albedo

Thus we are absolutely right when we compare for the different planets and moons the (Tsat/Te) ratio.

Below we can see:

The Graph Ratio of Planet Measured Temperature to  Blackbody (effective) Temperature (Tsat /Te), as a  function of the

Rotational Warming Factor = (β*N*cp)^1/16

In the above graph we can observe those two major scientific truths:

1). We can see the existing relation between the (Tsat/Te) ratio, and the Rotational Warming Phenomenon -

(the Warming factor (β*N*cp)^1/16 ).

2). The smooth surface planets and moons (the red dots) are streched in the lower line, under the heavy cratered planets and moons (the green dots), which are streched in the upper line.

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Yes, inevitably, there should be an equation theoretically calculating the planet average (mean) surface temperature.

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All planets and moons are subjected to the same universal physics laws.
And, also, for planets and moons, all the most significant  features happens to be the same.

1). Planets and moons are spherical shape selestial bodies.
2). They are solar irradiated objects.

3). Planets and moons rotate (having diurnal cycle).

4). And, all of them are irradiated from the same source of energy - our SUN.

Thus, planets and moons in solar system are subjected to the same EM (electromagnetic) radiative SPECTRUM.

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So, there should inevitably exist such an equation!
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And, we shall, further on, explain everything about that equation :

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

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Correcting the Effective temperature (Te) formula:

Te = [(1-a) S /4σ ]^1/4 (K) (2)

We insert the

Φ - the solar irradiation accepting factor

Φ =0,47  for smooth surface planets and moons

Φ =1  for heavy cratered (rough surface) planets and moons

 Te.correct = [Φ(1-a) S /4σ ]^1/4 (K) (3)

Te.correct, for the smooth surface planets and moons, has a much lower, than Te, numerical values.

And, in the below "Corrected Graph", we see an obvious LINEAR function,

between the (Tsat/Te.correct) ratio, and the Rotational Warming Phenomenon -

(the Warming factor (β*N*cp)^1/16 ).

Tsat = ~ Te.correct*(β*N*cp)^1/16

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

Rotational Warming Factor = (β*N*cp)^1/16

It is time to look elsewhere and retool.

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...

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.

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

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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 “small portion” that gets converted to heat and absorbed in the inner layers.

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

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The Planet Surface Rotational Warming Phenomenon is a UNIVERSAL PHENOMENON.

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

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Here it is a very well known scientific observation:

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

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The alleged  GREENHOUSE GLOBAL WARMING is a common deflection of the facts (which some  buy into ) which is a reflection of some people's inability to examine the full scope of the issues. 

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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).

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.

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

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NASA has precisely measured the solar system planets and moons the rotational spins.

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

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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, with their respective average surface reflectivity (Albedo), and, also, in accordance with their respective rotational spins, and with their respective surface chemical compositions and surface roughness features.

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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)

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

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

4. The rotational spin ("N" rotations/day)

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

Yes, the same universal laws, but applied to different input parameters.
So the same universal physical laws, but not the same behavior for different celestial bodies.

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

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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!

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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.

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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!

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.

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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).
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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.

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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.

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A planet surface in radiative equilibrium with the sun has NOT any resemblance with the radiative equilibrium in the cavity with a small hole.
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The planet average surface temperature (Tmean) is not a blackbody’s temperature.
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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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It was used saying:

“NET incoming solar (what will be absorbed by the surface, incoming minus reflected away).”
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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).

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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.
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The result is that only a small portion is accumulated as heat and gets IR emitted later at night, or at different times.
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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 small part is converted to 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. "
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Also it was very much wrongly concluded:

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

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Clearly there is something wrong

By accepting the 255K as an approximation, you accept the 255K or -18°Cto 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. It is not possible to use the Stefan-Boltzmann emission law.

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Nevertheless, they, the generally accepted physics, have derived (from the planetary average surface emission of 240 W/m²), they have derived the 255K or -18°Cas the Earth’s without-atmosphere uniform surface temperature.
They call it the Earth’s effective temperature

(Te =255K).

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Yes, it is a rather crude approximation. It rather much depends on the assumption of albedo. If you use the current average albedo of (about) 0.3, you get the 255 K, if you use the albedo of the moon ~0.1 (rock, no water), you get about 274 K.

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But Solar flux cannot be averaged over the entire planet surface as a kind of a "heat flux", because the radiative EM energy, when interacting with matter, does not input its respective energy in the surface.
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Only a small portion of the not reflected incident Solar flux’s energy gets transformed into heat and absorbed in inner layers.

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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."

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

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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.

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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.

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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 small portion of the incident solar energy a planet surface absorbs in inner layers.
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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, 

Tuniform = Tmean(maximum)

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

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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.

But, 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.

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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 (2)

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 (2)

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).

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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.

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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   

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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).
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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.

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: 

December 7, 2023

Again!

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' and moons' (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!

Also the five (5) times difference in the average surface specific heat between Earth's and Moon's surfaces (water vs regolith), plays a very important role too.

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 206,7K.

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 /206,7K = 1,3933

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 (1,3933) 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.

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

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.

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

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.

Thus, we have demonstrated that the planet mean surface temperature (Tmean) is amplified by the Planet Surface Rotational Warming Phenomenon.

Next, we formulated the Planet Mean Surface Temperature NEW Equation:

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

Where:

Φ- is the Planet Surface Solar Irradiation Accepting Factor (the planet spherical shape and the planet surface roughness coefficient).

The Φ -Factor is what made it possible the precise estimation of the NOT REFLECTED portion of solar flux.

In the appended pages we have thoroughly analyzed and explained the Φ -Factor's origine, the Φ -Factor's importance, and the Φ - Factor's variants.

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.

-

*****

In the current work, we use these exact two concepts, the Planet Surface Rotational Warming Phenomenon and the Solar Irradiation Accepting Factor (Φ).

We discuss the difference between the Hansen's formula on the one hand, and the New Equation's on the other hand, and test the hypotheses that Planet Mean Surface Temperature (Tmean) can be Theoretically calculated by mathematical methods.

After having addressed this core point, we performed the calculations based on the available data to see how they fit.

And, 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 then we proceed comparing with the planet's average surface temperatures, the actual 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..........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 Control Volume Approach

For energy transfer problems, the control volume approach involves studying the flow of energy across the boundaries of the control volume. This is done by considering the energy flux, at each boundary of the control volume. By applying the conservation of energy to the control volume, we can then derive an energy balance equation, which relates the rate of change of internal energy within the control volume to the net rate of energy transfer across its boundaries.
–
***
It is exactly what we do when deriving to the planet mean surface temperature NEW EQUATION (Tmean).
–
What we do in present research is to consider the planets’ surfaces energy transition boundaries in their entirety for every planetary surface.
–
A planet surface interacts with incident solar flux as a whole (IN TOTAL), and not in average surface, as it is very much wrongly asserted by the current scientific consensus.
–
While interacting a planet responds to the incoming solar energy AS A WHOLE, planet responds to the incoming solar energy with all its major characteristic features, or, in other words, planet responds with the entire “set” of the planetary surface qualities.
–
–

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,

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

πr²Φ*S*(1-a) (W)

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. )

-

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 be 210,8K, therefore it would be almost 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).

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).

-

2. The planet average surface Albedo "a".

-

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

-

All those three major parameters are combined in the Radiative

"Energy In" Equation:

Energy In = Φ*(1-a)*S (W/m²)

-

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

-

****

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 hypotheses 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.

-

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.

-

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.

-

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.)

-

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

-

****

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.

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

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.

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

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 !

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

Now we can explain why the planet Mars’ average surface temperature Tsat.mean = 210K is the same as Mars’ theoretically calculated effective temperature Te = 210K

In the New Tmean equation in the case of Mars the

(β*N*cp)¹∕ ⁴

and

Φ

eliminate each other, because in the case of Mars, by a pure coincidence

Φ = ~ 1 /(β*N*cp)¹∕ ⁴

or

0,47 = ~ 1 /(150*0,9728*0,18)¹∕ ⁴ = 0,441138

( 0,47 /0,44 )¹∕ ⁴ = (1,0682)¹∕ ⁴ = 1,0166 

so there is only a

1,66 % difference in the final result of Te =210K and Tsat.mean =210K 

Thus we have here a clear confirmation of the rightness of Φ =0,47 for the smooth surface planets and moons.

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

In the New Tmean equation in the case of Mars the

(β*N*cp)¹∕ ⁴
and
Φ
eliminate each other, because in the case of Mars, by a pure coincidence
Φ = ~ 1 /(β*N*cp)¹∕ ⁴

********************
It is not a circular resoning. It is an observation, which proves right the initial insight, which assumes the similarity of the
Φ =0,47 for smooth surface planets and moons without-atmosphere, (or with a thin atmosphere, Earth included), assumes the similarity with the
Drag Coefficient =0,47 for smooth spheres in the parallel flow fluids.

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

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 theoretically calculated results for all  the twenty (20) major planets and moons in solar system being very much precisely close to the measurements performed by satellites is a sufficient and necessary condition, which states for the rightness of the Planet Surface Rotational Warming Phenomenon.

Also we have estimated the:

accurate values for (average) albedo, cp, β, Φ, S, with minor uncertainties for each.

thus there is no need for propagation of the uncertainties for the total equation, as a formal scientific research method requires.

because our calculations come so close to the measured for Earth, I think is not at all luck but the result of a thorough analysis.

*****

******

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.

******

*****

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

-

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?

-

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?

*****

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

Europa's Albedo a =0,62
–
Why there is so much difference?

-

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.
-
***

We demonstrate here that the Lambertian reflectance concept has very mistakenly influenced the planet radiative "energy in" estimation.

Lambertian reflectance - Wikipedia

"Lambertian reflectance is the property that defines an ideal "matte" or diffusely reflecting surface. The apparent brightness of a Lambertian surface to an observer is the same regardless of the observer's angle of view.^[1]More precisely, the reflected radiant intensity obeys Lambert's cosine law, which makes the reflected radiance the same in all directions. Lambertian reflectance is named after Johann Heinrich Lambert, who introduced the concept of perfect diffusion in his 1760 book Photometria.

Examples[edit]

Unfinished wood exhibits roughly Lambertian reflectance, but wood finished with a glossy coat of polyurethane does not, since the glossy coating creates specular highlights. Though not all rough surfaces are Lambertian, this is often a good approximation, and is frequently used when the characteristics of the surface are unknown.^[2]

Spectralon is a material which is designed to exhibit an almost perfect Lambertian reflectance.^{[1] "}

*****

And it was the planet surface Lambertian reflectance considerations (or diffusely reflecting surface) the cause to wrongly estimate the planet specular reflection as a negligible value.

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.

******

Let's introduce to the Φ -Factor 

It is very important!

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?

–

****

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.

-

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.

-

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

****

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.

-

*****

Opponent:

"We need some logical explanations of Φ (hydrodynamic drag coefficient of a sphere is not an adequate explanation), why earth [and other celestial bodies] are smooth (they are not with respect to the wavelength of the interacting EMR)."
–

Answer:

When spheres in parallel fluid flow, the spheres’ surface gets in interaction with the fluid’s atoms and molecules, which also are very small, not small as a photon is, but very small too.

-

Those spheres in the fluid’s flow, no matter how well polished they are, on the atomic and molecular level they interact with fluid, their surfaces also are not smooth.
–
The surface is smooth or not, it has to do with the dimensions of the objects.
A planet as a whole can be a smooth surface planet, or it can not be a smooth surface planet.
Some planets and moons are considered smooth surface, and others are considered not.

-

******

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).

****

Earth also has glint.

****

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...

-

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.

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

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.

The TSI (Total Solar Irradiance) is related to the amount of energy reaching a flat earth disc area at one solar unit.

The Solar Irradiation Accepting Factor "Φ" makes a difference, out by possibly as much as 53 percent and hence all figures for amount of energy in, amount of visible light reflected, amount of IR energy emitted are very much different too.

-

and that means nearly everything we considered till now about the earth’s surface energy budget needs to be thrown out.

Nearly everything we had considered about on the earth’s surface energy budget needs to be thrown out.

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

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).

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

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

Ein = Eout formula.

- Answer: The Energy in:

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.

Link:

https://www.cristos-vournas.com/445559911

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 subthread 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.

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

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.

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

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.

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

More Planets and Moons the satellite measured average surface temperatures comparison

Links:

Earth/Mars 288K/210K

Earth/Europa 288K/102K

Mars/Moon 210K/220K

Mercury/Moon 340K/220K

Mercury/Mars 340K/210K

Calisto/Io 134K/110K

Io/Enceladus 110K/75K

Jupiter/Saturn/Neptune 165K /134K /72K

Earth/Moon 288K/220K

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

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.

Link:

https://www.cristos-vournas.com/445559910

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. 

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.

-

Hansen compared the theorized planet UNIFORM surface temperature
(the Earth's EFFECTIVE temperature Te =255K) with the Satellite Measured Earth's average surface temperature Tmean =288K.
-
Those temperatures, the planet UNIFORM surface temperature, and the planet AVERAGE surface temperature are different Physics Terms.
-
By Hansen's idealized Formula, when considering a planet AVERAGE surface temperature, it cannot mathematically exceed the same planet idealized UNIFORM surface temperature.
-
Thus, Hansen resumed, the satellite measured Earth's AVERAGE surface temperature Tmean =288K,
is at least +33°C warmer than the theorized Earth's UNIFORM temperature 255K.
-
The +33°C had to be somehow explained. So it was attributed to the not existent (the very insignificant) the Earth's atmosphere Greenhouse Effect.
-
Also, it was asserted, the above very confusing and very mistaken conclusion (the Earth having at least +33°C Greenhouse Effect), it was asserted the above was in full accordance with the 1st Law of Thermodynamics (1LOT).
-

They ignored the INITIAL Fundamental Mistake, they had made.

The Stefan-Boltzmann emission law cannot be used wise-versa. One cannot determine a surface temperature by simply measuring the radiative flux's intensity falling upon it.

-
***
-

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 hopped for coming up to 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,

Link from Wikipedia:

the Planet Effective Temperature Te https://en.wikipedia.org/wiki/Planetary_equilibrium_temperature

Another Link:

Lecture 2: Effective temperature of the Earth https://edisciplinas.usp.br/pluginfile.php/4355860/mod_resource/content/1/temperatura%20efetiva%20da%20Terra%20-%20paoc.mit.edu.pdf

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!

==========

The false "RADIATIVE equilibrium" CONCEPT 

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 irradiated side is not uniformly irradiated.

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 hypotheses. Otherwise its not reliable.

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

Not even peer review?

Its unreliable!

Answer:

"There has to be a tested hypotheses. 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 demonstrated 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

Rotational Warming Factor = (β*N*cp)^1/16

For further details please visit page:

https://www.cristos-vournas.com/448752897

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…

That is why no experiment is needed.

We have here the "Planet Surface Rotational Warming Phenomenon" observed.

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)

Mars is irradiated 2,32 times weaker than Moon, but Mars rotates 28,783 times faster.

And… for the same albedo, Mars and Moon would have the same satellite measured mean temperatures.

For Moon Tmean = 220K; Moon’s Albedo a=0,11

For Mars Tmean= 210K; Mars’ Albedo a=0,25

Let’s do a simple calculation:

The rotation difference’s fourth root is

(28,783)¹∕ ⁴ = 2,3162

Now, please compare these two numbers:

2,32 and 2,3162

They are very-very much close, they are almost identical!

That is why no experiment is needed.

In this example we have demonstrated that the Mars' solar irradiation intensity deficit being 2,32 times less is compensated by Mars' 28,783 times higher rotational spin's fourth root

(28,783)¹∕ ⁴ = 2,3162

We have here the "Planet Surface Rotational Warming Phenomenon" observed.

*****

We shall continue in the next pages.

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

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

              Distance   Flux    Factor   Bond     rot /day   surface  cal /gr.°C  Warm.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          270,04    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         111,55     110

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

Ganymede5,20      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

The Solar Radiation Input.

And

———-

The Solar Radiation Input.

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 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 physics notion: solar radiation input.

It is important to differentiate between the “not reflected portion of the incident solar flux ” and the “solar radiation input.”

—

Well, the “not reflected portion of the incident solar flux” is not even ” with solar radiation input.

—

The “solar radiation input” is only a part of the “not reflected portion of the incident solar flux”, it is only a part of “Energy in”.

—–

The “solar radiation input” is only the energy accumulated in inner layers. It is not the entire “Energy in”.

Energy in = energy out

Energy in = πr²Φ*S*(1-a) (W) is the “not reflected portion of the incident solar flux”

Jemit = 4πr²σΤmean⁴ /(β*N*cp)¹∕ ⁴ (W) is the energy out

Planet Energy Budget:

Jnot.reflected = Jemit πr²Φ*S*(1-a) = 4πr²σTmean⁴ /(β*N*cp)¹∕ ⁴ (W)

Solving for Tmean we obtain the PLANET MEAN SURFACE TEMPERATURE EQUATION:

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

——–

When hitting matter the solar EM energy INDUCES surface skin layer’s temperature.

The higher this temperature, the more the instantly emitted IR EM radiative energy out, and the lesser the solar radiation input.

And

The lesser this temperature, the less the instantly emitted IR EM radiative energy out, and the more the solar radiation input.

———

When planet rotates faster it has for a constant

“Energy in = πr²Φ*S*(1-a) (W)” a larger solar energy input.

—

The entire

“Energy out” = Jemit = 4πr²σΤmean⁴ /(β*N*cp)¹∕ ⁴ (W) consists from both “the instantly emitted IR EM radiative energy out” plus the solar radiation input.

———-

When rotating faster, planet surface has more “solar radiation input” to get rid of, thus the Tmean gets “balanced” at higher level.

So, the higher the (N*cp)¹∕ ⁴ is, the higher should be the Tmean⁴.

That is why it is so powerful the Planet Surface Rotational Warming Phenomenon.

———-

------

“The amount of solar radiation received does not change because a planet spins faster. It has to radiate away what it receives.”

It is a basic principle! The difference is that, when interacting with matter, the “not reflected portion of solar flux” is not getting inside the skin layer in its entirety.

A very considerable part of it gets IR emitted on the very instant the solar EM energy hits the surface.

This part of energy goes immediately out, it INDUCES the surface temperature on the instant of incidence, and that temperature is the temperature of that spot at that particular instant.

———-

And, there is another part, the “SOLAR RADIATION INPUT” which is on that instant is accumulated in the inner layer. And this part is radiated away later…

———-

Planet always radiates away what it receives.

Planet with a higher (N*cp) product has this second part, the “SOLAR RADIATION INPUT” larger, and the on the instant of incidence IR emitted amount of solar EM energy is smaller, because a planet with a higher (N*cp) product INDUCES a lower on the spot of incidence the skin layer’s temperature.

———-

We shall call from now on as “the “SOLAR RADIATION INPUT” the amount of energy the Solar Flux – Planet Surface INTERACTION process manages to PUT IN the planet inner layer.

********

-

What GREENHOUSE EFFECT?

The actual greenhouse (agricultural, with transparent to solar rays glass windows, or with transparent to solar rays membrane...) gets warmed because the solar SW EM energy comes thru and warms the inside walls and the inside floor.

The emitted by the walls and the floor IR EM energy is only absorbed or reflected back from the glass windows or the membrane, because they are not transparent to the IR EM energy. The phenomenon causes the rise in temperature of the inside of the greenhouse's walls and floor.

The phenomenon is called greenhouse effect.

-

Now, when a greenhouse is hermetically closed, it resemblances the case of the indoors air. The indoors air is in thermal equilibrium with the surrounding walls, and, therefore, the indoors thermometer indicates the same exactly temperature for the inside of the walls and for the inclosed air.

-

If we let an outside cold air indoors (into a room, or into a greenhouse) the air temperature will remain cold for a while, untill it is adjusted to the inside temperature.

-

The air inside of a greenhoouse, or inside of a room, gets warmed by conduction from the inside of walls.

The lnside air is not getting warmed by EM radiation, because, as it is known, air is for the most of its content is transparent to both, SW and IR EM energy.

-

The same, the greenhouse effect phenomenon, the same is taking place in the case of planets, which planets have some amounts of greenhouse gasses in their atmospheric content.

-

Greenhouse gasses in atmosphere are transparent to the incoming SW EM energy, but the greenhouse gasses are capable to reflect back to the planet surface some amount of emitted by the surface IR EM energy.

-

As a result, the temperature of the planet surface gets higher, than it would otherwise be in the absense of those greenhouse gasses.

-

-

Earth's atmosphere is very thin. The greenhouse gasses content in Earth's atmosphere are considered as trace gasses.

-

So, we have in Earth's already thin atmosphere some trace greenhouse gasses...

-

-

It was those very obvious circumstances that lead us to the only conclusion - there cannot be +33 oC greenhouse effect from Earth's atmosphere.

-

I estimate the Earth's atmosphere TOTAL GREENHOUSE EFFECT about some +0,4 oC, which is almost two orders of magnitude less than +33 oC.

-

“The Tmean equation gives a decent approximation for small range of rotation rates.”

Yes, that is what it does. The equation is limited in a small range of rotation rates.
–
Let’s see what we have:

We have an equation which theoretically calculates for all planets and moons (without-atmosphere, or with a thin atmosphere), the average surface temperatures (Tmean), and the equation's results are very much close to those measured by satellites.
–
Also we have the Rotational Warming Phenomenon, and all planets and moons, (including the gaseous giants Jupiter, Saturn, Uranus and Neptune), all of them are subjected to that Rotational Warming Phenomenon, which is demonstrated in the site, and which could be considered as a confirmed observation.
–
And, for all planets and moons, (without-atmosphere, or with a thin atmosphere), the theoretical effective temperatures (Te), when calculated, are always lower than the satellite measured mean surface temperatures (Tmean).
The only exception is the very slow rotating Mercury.
–
And there is the planet Mars with the satellite measured Tmean =210 K, the Mars having dramatically less than our Moon (because of the distance from the sun) having dramatically less solar irradiation, vs Moon’s the satellite measured Tmean =220 K.

The Mars' and Moon's Tmean proximity can only be explained by the  Mars’ very fast, compared to Moon rotational spin.

-

*******

It is the same model, but the settled science mistakenly uses – the comparison of the planets' without-atmosphere the theoretical uniform surface effective temperatures Te, (which is a mathematical abstraction), the settled science uses Te for the comparison with the actual satellite measured average surface temperatures Tmean, for every planet and moon, Earth included.

Scientists base their ideas on evidence. What they can observe, measure and test. They change their ideas to match what is observed. This is science in a nutshell. Follow the evidence!

-

We can’t talk, evidence based, about the impact of CO2 on the climate system of the Earth.

-

We have already established that Planet Surface Rotational Warming Phenomenon is what actually accounts for the full difference between Earth and Lunar mean global surface temperature.

The First Conclusions

Conclusions:

1). The planet mean surface temperature equation

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

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

Planet…....Tmean….Tsat.mean

Mercury.....325,83 K…..340 K

Earth……....287,74 K…..288 K

Moon……...223,35 Κ…..220 Κ

Mars………..213,21 K…..210 K

The 288 K – 255 K = 33 oC difference does not exist in the real world.

There are only traces of greenhouse gasses. The Earth’s atmosphere is very thin.

There is not any measurable Greenhouse Gasses Warming effect on the Earth’s surface.

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

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

Tmean.earth = 287,74K = 288 K.

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

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 as 287,74K, which is very much close to the satellite measured 288K.

It happens so because Earth's atmosphere is very thin and, therefore, doesn't have any essential greenhouse effect on the Earth's average surface temperature.

When it is acknowledged Earth’s atmosphere is very thin – it will become obvious, Earth doesn’t have any significant greenhouse warming effect.

-

***

Earth's atmosphere greenhouse effect is only some

+0,4 oC.
-
Earth's atmosphere greenhouse effect was very mistakenly estimated as being

+33 oC

which is very much wrong !
-
The +1,5 oC rise is due to orbital forcing, the additional CO2 cannot be considered as warming Earth's surface by +1,5 oC, because the entire atmosphere warms surface only by some

+0,4 oC !
-

*****

Thus, the current observed GLOBAL WARMING cannot be attributed to the fossil fuels burning.

-

*****

Earth's average surface temperature is 68°C higher than Moon's average surface temperature.
Also Earth, because of a higher than Moon Albedo, Earth receives 28% less solar radiative energy than Moon.
-
And yet, Earth's average surface temperature is 68°C higher than Moon's average surface temperature.
-
Since Earth and Moon are at the same distance from the sun, but Earth's average surface temperature is 68°C higher than Moon's average surface temperature... there is only one explanation left:

It is the planet surface ROTATIONAL WARMING PHENOMENON !
-

2). There is not any detectable (spacecraft measured) the solar system moons' (Io, Europa and etc.) tidal warming.

-

3). Gaseous Giants (Jupiter, Saturn, Uranus and Neptune) do not have any detectable (spacecraft measured) inner source of energy.

-

We have to answer these two questions:

1. Why Earth’s atmosphere doesn’t affect the Global Warming?

It is proven now by the Planet's Mean Surface Temperature Equation calculations. There aren’t any atmospheric factors in the Equation.

Nevertheless the Equation produces very reasonable results:

Tmean.earth = 287,74 K,

calculated by the Equation, which is the same as the

Tsat.mean.earth = 288 K,

measured by satellites.

Tmean.moon = 223,35 K, calculated by the Equation, which is almost identical with the

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

2. What causes the Global Warming then?

The Global Warming is happening due to the orbital forcing.

And… what keeps Earth warm at

Tmean.earth = 288 K,

when Moon is at

Tmean.moon = 220 K?

Why Moon is on average 68 oC colder? It is very cold at night there and it is very hot during the day…

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

Does the Earth’s atmosphere act as a blanket that warms Earth’s surface?

No, it does not.

And Moon also emits from its very hot daytime surface hard.

What else the very hot surface does but to emit hard, according to the Stefan-Boltzmann emission Law.

The very hot surface emits in fourth power of its very high absolute temperature.

Jemit ~ T⁴

A warm object in space loses heat via emission. The hotter is the object, the faster it loses heat.

Moon gets baked hard during its the 14,75 earth diurnal cycles long lunar day.

So there is not much energy left to emit during the 14,75 earth diurnal cycles long lunar night.

And it becomes very cold on the Moon at night. It is in our Earth's immediate neighborhood happens.

That has almost nothing to do with atmosphere, and everything to do with rotation speed.

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

The planet Earth's and the planet Mars' faster rotation creates the necessary level of the "solar irradiation - planet surface" interaction phenomenon...

which results in the day-time much lower surface temperatures and, consequently, in much lower day-time surface infrared radiation emissions

and which results in higher planet surface 24-hours average temperatures.

The planet Earth’s and the planet Mars’ faster rotation is what creates the necessary interaction for the incident on the planets' surfaces solar energy the much more efficient accumulation.

The best news science could give us is that we aren’t about to be destroyed by calamitous climate change, that there’s no need to panic, there’s still plenty of time to solve, to adapt, to reconcile ourselves to a different future, and to stop worrying.

Science is all about confirming theories.

-

See, science can be either confirming or denying conjectures, depending on the conjectures.

It is all in the details...

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 Global average surface atmospheric greenhouse effect +33°C PARADOX

I also tried to answer that question:

“If the Global average surface atmospheric greenhouse effect is +33°C, then what approximately is the atmospheric greenhouse effect at the different latitudes, like:

1). Kenya
2). Egypt
3). Greece
4). Czechia
5). Sweden
6). North Pole

Notice, the higher latitudes represent smaller areas on the Globe.”
-
But I couldn’t answer that question, because there is not such an answer.
-

***

******

If there is +33°C atmospheric global average surface greenhouse warming effect, it should be stronger at places with higher solar irradiance, because the core issue in atmospheric global average surface greenhouse warming effect is the surface LW emission atmospheric feedback.
–
If there is +33°C atmospheric global average surface greenhouse warming effect, it should be the strongest at equatorial zone, because at equatorial zone the solar irradiance is the strongest.
–
We face a paradox here:
We should have assumed, in the case of Planet Earth without-atmosphere, at Earth’s equatorial zone the far below zero °C the surface temperatures…

***

******

**********

The next very important topic we discuss in the current research, which is explained and analized in every detail in the appended pages is:

The actual reason of the observed Global Warming.

It is dedicated to Milankovitch cycle and it explains where Milankovitch was absolutely right, and what Milankovitch assumed wrong.

Earth is going thru a very slow and naturally caused warming trend!

-

Planet Earth is very slowly getting warmer. It is happening due to orbital forcing.

It has been calculated by Milankovitch.

-

The Milankovitch cycle shows for current time Earth being in a slow cooling trend.

-

Milankovitch simply assumed the glacial periods should be associated with North Hemisphere's cooler summers. Which what happens in our time.

-

Actually when North Hemisphere is in cool summers, the South Hemisphere is in very Hot Summers.

-

Earth's surface thermal energy reservoir are Earth's oceans. There are much more oceanic waters in Southern Hemisphere, compared to the North Hemisphere.

-

In our time Earth accumulates much heat in the Southern Oceans during those very hot summers. That is why Earth's Global temperature rises!

-

The Milankovitch cycle is being very precisely calculated. Only it has to be read reversed.

When we look at the Milankovitch cycle graph reversed, it becomes very much obvious, Earth is going thru a very slow and naturally caused warming trend!

-

-

What Earth's surface does, is to still emerging from an ice age!

The Original Milankovitch Cycle states:

"You get an interglacial when the Summer is warm enough to melt the snow that fell during the Winter.

You get a glacial period when there is not enough summer heat to melt the snow. Then each year the thickness of the snow increases until you have new ice sheets."

-

-

The Reversed Milankovitch Cycle states:

You get an interglacial when Winter on North Hemisphere occurs close to Earth's Perihelion. The Southern Hemisphere's vast oceanic waters are tilted towards the sun, when Earth is at its closest to the sun.

Thus, as it occurs in our era, during the North Hemisphere's warmer Winter, the very much hotter Southern Hemisphere's SUMMER oceanic waters are heavily accumulating, and that is why we observe the current Global Warming.

-

Earth in our era is in a very long term continuous warming period. This warming is caused by natural orbital forcing.
–
It is the continuation of the MWP (Medieval Warm Period). The LIA (Little Ice Age) was a phenomenical cold because of the intensive mitigation of sea ice. During the LIA period, Earth continued accumulating solar energy, Earth continued getting warmer.
–

******

Milankovitch Cycles and Glaciation (iu.edu)

https://geol105.sitehost.iu.edu/images/gaia_chapter_4/milankovitch.htm

*****

And from the current temperature data there is no question that we are firmly in a steady secular warming period.

*****

Every planet is subjected to its annual average surface temperature (the mean surface temperature) T (K).

The planet annual average surface temperature is a dependent on the planet's distance from sun value.

Of course it is dependent on the planet's radiative energy balance.

It is also dependent on the planet's rotational warming phenomenon.

And, in addition to all that above, the planet annual average surface temperature is a dependent on the annual planet surface temperature differentiation.

The less planet surface temperatures annually differentiated - the higher is the planet annual average surface temperature.

And the more planet surface temperatures annually differentiated - the lower is the planet annual average surface temperature.

 -

In our times Planet Earth is in an exceptional annual orbital pattern, which pattern (earth's orbit eccentricity, when Earth is at its closest to the sun during the North Hemisphere's winter, and it is very much close to the sun at the times of winter Solstices...)

What we witnessing in Northern Hemisphere is the summers being cooler and winters being warmer.

The opposite phenomenon, (the summers being hotter and the winters being colder) which actually takes place in Southern Hemisphere, is being smoothed by the Southern Hemisphere's vast oceanic waters areas.

As a result, at current times Earth's annual orbital pattern creates a slow lowering the Planet Earth's the annual average surface temperature differentiation.

This exact phenomenon is what creates the observed in our era the very slow (millennia’s long) continuous (gradual) Global Warming.

********

My greatest philosophy has been that to know any subject accurately, a scientist must look at the cause and effects in the simplest terms. That way, errors in assessments will not skew the predictions unnecessarily.

********

I was reffering to the Precession.

“The third and final of the Milankovitch Cycles is Earth’s precession. Precession is the Earth’s slow wobble as it spins on axis. This wobbling of the Earth on its axis can be likened to a top running down, and beginning to wobble back and forth on its axis. The precession of Earth wobbles from pointing at Polaris (North Star) to pointing at the star Vega. When this shift to the axis pointing at Vega occurs, Vega would then be considered the North Star. This top-like wobble, or precession, has a periodicity of 23,000 years.”

https://geol105.sitehost.iu.edu/images/gaia_chapter_4/milankovitch.htm

“Due to this wobble a climatically significant alteration must take place. When the axis is tilted towards Vega the positions of the Northern Hemisphere winter and summer solstices will coincide with the aphelion and perihelion, respectively. This means that the Northern Hemisphere will experience winter when the Earth is furthest from the Sun and summer when the Earth is closest to the Sun. This coincidence will result in greater seasonal contrasts. At present, the Earth is at perihelion very close to the winter solstice.”

********

Our planet Earth is in millennials long continuous orbital forced warming pattern.

-

When in warming pattern, a planet accumulates more solar energy than planet is capable to emit.

In planet's effort to emit that excessive solar energy so to establishing the radiative energy equilibrium, the planet average surface temperature rises.

-

When the planetary temperature becomes higher, then, according to the Stefan-Boltzmann emission law, the planet surface becomes capable of emitting IR (infrared radiation) more intensively.

Thus the mechanism of getting rid of energy does establish onto the planet surface, a close to radiative equilibrium (energy in =energy out) state.

-

The planet surface temperatures from Equator to Poles are very much differenciated.

Here it is when the nonlinearity of the Stefan-Boltzmann's emission law gets in action!

-

The Polar zone's temperature rises faster, than the equatorial, or the average planet surface mean.

It is the phenomenon of Polar Temperatures Amplification.

-

Due to the Stefan-Boltzmann emission law nonlinearity, the Polar areas (in order to get rid of the excessive incoming solar energy)...

The Polar areas surface temperatures rise faster - and it is observed in the melting of the ice sheet sea cover.

********

The orbital cycles forcings are slow. Only our Earth is now in a culmination phase of the current orbital warming curve.
–
Milankovitch cycle, read as it should be read – when it is read correctly, when it is read the inverse way, because currently when our planet is nearPerihelion (the closest to the sun point) at January 4,
At that exactly time Earth’s Southern Hemisphere is in Solstice, and the Earth’s Southern End of axis is tilted towards sun.
–
In our era we are witnessing an exceptional coincidence phenomenon – Earth is accumulating solar energy at its fastest way in millennials.

********

For more Pages please Click on the Box at the Top

Opponent

“Christos,
And you don’t include the effects of atmosphere and its composition (rather, dismissing it as “thin” when it is not), which has been the whole point of this never-ending discussion. I hope the discussion will help you reformulate your analysis and to justify the unjustified dismissals, but I fear not – it is rather circular to dismiss the effect that you are trying to prove doesn’t exist.”
–

Thank you for your comment.

“you don’t include the effects of atmosphere and its composition (rather, dismissing it as “thin” when it is not)”

Well, I do not dismiss the Earth’s Global Greenhouse Effect.
What I say is I don’t see it happening.
–
When eight years ago I started having my very serious reservations about the role of CO2 trace greeehouse gas content of ~400 ppm in Earth’s atmosphere I learned about an equation (the planet effective temperature equation) which theoretically estimated planet average surface temperature for every planet and moon without-atmosphere in solar system.

When the planet without-atmosphere New Tmean equation was formulated, I tried it on every planet and moon without-atmosphere in solar system, and, when realising the equation was very much precise, then I also checked the New Tmean equation in the case of Earth… to estimate what the on the Earth’s surface the whole atmosphere greenhouse effect would be.

And, the New Tmean equation for planets and moons without-atmosphere, which equation didn’t include the effects of atmosphere and its composition (why it had to, it was for planets and moons without-atmosphere, the exact way the effective temperature equation is), that New Tmean equation is able to theoretically calculate the Earth’s average surface temperature very precisely close to the measured by satellites.

It is then I added to the planets and moons without-atmosphere expression, I added the sentence : “(or with a thin atmosphere, Earth included)”.

Because I understood, that for EM (electro-magnetic) radiative energy an Earth’s kind of atmosphere should be considered thin, or transparent, to the solar energy interaction processes with planetary surface, as it is happen to be transparent for planets and moons without or with a thin planetary atmospheres.

If the New Tmean equation had theoretically calculated for Earth, par example, Tmean =275K, then the Earth’s entire atmosphere greenhouse effect would have been as:

288K – 275K =13C

But,
And the result was, that the equation calculated Earth’s without-atmosphere average surface temperature being as Tmean =287,74K

wich result is very much close to the measured by satellites the T = 288K.

The New Tmean equation does not include the effects of atmosphere and its composition…

And it is concluded then, that the equation does not have to include the effects of atmosphere and its composition, because their effect is very insignificant when the Earth’s mean surface temperature is being by the New Tmean equation theoretically calculated.
–
So, we should conclude, and we conclude with great confidence, there is no room left for the trace greenhouse gas CO2 to influence in any possible way the Earth’s average surface temperature.

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

Opponent:

“How do you (1) calculate the solar flux absorbed if it is not S(1-α)πr² ?”
–
I do not calculate the absorbed part, what I do is to correctly calculate the not reflected portion of the incident on planet the TOTAL solar energy:

πr²*Φ*(1 -a)*S by the use of the Φ -the solar irradiation accepting factor (the planet spherical shape and roughness coefficient).

Φ =0,47 for smooth surface planets and moons.
Φ =1 for heavy cratered planets and moons, and, also for gases planets and moons.

the not reflected portion of the incident on planet the TOTAL solar energy:

πr²*Φ*(1 -a)*S is the TOTAL solar energy which actually interacts with the planetary surface.

The same πr²*Φ*(1 -a)*S is the TOTAL IR emitted, because of energy in = energy out to met
–

Important NOTICE: