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

Discussion 

Confirming the Orderly Universe.

The new equation shows that the NASA satellite measurements are very precise. Also it helps to explain some inconsistencies that scientists had noticed, in planet's and moon's temperature behavior.

When a new planet at different solar system is discovered, scientists speculate whether it is habitable or not. They were counting only on the star's irradiation flux and on the distance from the star. Now it is possible to have a much more precise estimation of the planet's temperature, in cases when the planet's spin is already known.

The new equation brings order in the field of planets' temperatures measurements.

Revising the Understanding of Planet Properties.

The new equation provides some new information about the physical properties of planets that changes established understanding. The new equation can accurately predict a planet's mean surface temperature, without using any terms in the equation to account for atmospheric properties or for internal heat, and consequently that implies that the planet's mean surface temperature is not affected by the atmospheric composition or the internal heat. The new equation shows that there is no greenhouse effect on Titan (the Saturn's satellite, which has an atmosphere of 95% N₂ and 5% methane - a very strong greenhouse gas). The 5% methane gas is not enough to create a measurable greenhouse effect on Titan. This changes the established understanding that Titan, similarly to Earth, has a strong greenhouse effect.

And also there is the consequence that the gaseous planets Jupiter, Saturn, Uranus and Neptune do not have any inner source of energy as it is wrongly assumed.

Revising the Understanding of the Greenhouse Effect.

Hansen et. al., (1981) gave an early estimate for the magnitude of the greenhouse effect as 33°C. This 33°C estimate was obtained by using the simple blackbody Equation (2) to calculate the Earth's effective radiating temperature (255 K), then comparing that to the NASA mean measured temperature (288 K), and assuming that the difference (the excess temperature of 33°C = 288 - 255 ) was entirely caused by the greenhouse effect.[22]

"Using values for planet Earth (with albedoa~ 0.3 and solar flux So = 1367 watts per square meter), this equation calculates that Te ~ 255 K."[23]

Notice that this calculated temperature of 255 K is less than the NASA's measured mean temperature of Tsat ~ 288 K by a difference of 33°C, and that this difference has been attributed to the greenhouse effect: . . . According to[24]| Hansen et. al. (1981)] . . . "The excess, Ts - Te, is the greenhouse effect of gases and clouds, which cause the mean radiating level to be above the surface."

However, attributing all of this difference (33°C = 288 - 255 ) entirely to the greenhouse effect is tantamount to assuming that the blackbody Equation (2) is perfect and has no error due to making simplifying assumptions -- which is unlikely. This is demonstrated in Table 1, which shows significant differences (Ts - Te) even for planets and moons having no atmosphere. Hence, the difference (Ts - Te) can be caused entirely or partly by factors other than a greenhouse effect.

The improved equation for the planet's surface temperature (Eqn.3) includes some additional factors to mathematically represent the planet's actual conditions more appropriately than the simplifying blackbody assumptions.

Using the new equation, the Earth's mean surface temperature (with no atmosphere) is calculated to be 288°K, which closely matches the NASA measured mean temperature (with atmosphere) of 288°K, leaving no error term (formerly 33°C) to attribute to a postulated atmospheric "greenhouse" effect.

The trace gas CO2 does not make planet warmer.

Our planet Earth is in continuous atmospheric CO2 depletion pattern for many hundred thousands and many millions years now.

If we humans had not used wood and fossil fuels burning, planet Earth would have been in a much worse atmospheric CO2 depletion ecological problem.
Natural carbon cycle inevitably leads to the Earth system carbon depletion, by sequestering it in fossil fuels natural deposits.

It is a one way natural ecological process.
Numerous species have flourished and dissappeared in that process.
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Live still exists on planet Earth because of the presence of some atmospheric CO2 gas. Planet Earth is in urgent need for more atmospheric CO2, not less.
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Atmospheric CO2 content is so small it is called trace gas.
The trace gas CO2 does not make planet warmer.
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It is a too small in magnitude phenomenon

Thank you, for your very substancial and informative comment. You are absolutely right when saying:

"...theres a very simple reason why the hottest places on Earth are those with the least supposed greenhouse gases in the atmosphere. There are less greenhouse gases to block the Sun when it hits. So it hits the hardest.

... the hottest places on Earth cool the fastest. There are less greenhouse gases to block the radiation that leaves the Earth."

Today we had in Athens a sunny winter day. The cold and, therefore, very dry Northern winds blowing, and the sun shinning in the clear sky.

You know, it was unbearably hot in the sun, we used the shaded side in the street, just like we use to do in summer. But today it was even more necessary.

I think the sun on our bodies was at 1362 W/m2, and not less. There was not any Albedo a=0,3 there. The sun was definitelly burning.

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Well, I used to live in dessert. During the day it was unbearably hot. And during the night it was very cool.

The explanation they had was the very dry climate they had in there.

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Also, I have experienced in winter a sudden cloudy sky getting us warmer.

And, there are places in Greece, at seaside, when at summer there are times there is not any kind of air movement, and the moisture in the air is very much thick, and the sun from above is not so much burning, but the hot is deadly.

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All those are examples of the water vapor and of the clouds greenhouse warming effect.

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But, from that point, of some greenhouse warming effect at some places, at some times,

it is a too small in magnitude phenomenon, when compared with the alleged +33C atmospheric global greenhouse effect.

"As an approximation, the average flux will give the average temperature."

The approximation of Earth's

Te = 255K, when compared with the Earth's actual the average surface temperature

Tmean = 288K...

When 288K - 255K = 33°C, that approximation is what leads to mistaken conclusion the Earth's average surface atmospheric greenhouse effect is so much big +33°C!

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

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

The specular reflection is not included in albedo.

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

Thus, for Earth, the

Te =255K, when corrected, became Te.correct =210K.

The 288K - 210K = 78°C very big difference is, nevertheless gets "managed"by planet Earth's very powerful the Rotational Warming Phenomenon.

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The incoming solar EM energy averaging is a mistaken thought experiment - because the EM/surface interaction result is unique.

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

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

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

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

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

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For the Smooth Surface Planets and Moons their Strong Specular Reflection was Neglected.

Solar system planets and moons during their 4,5 bn years long live-time, and because of their very different the respective "personal"

conditions, at which the planets and moons had evolved - thus planets and moons have developed very different the planetary surface features.

Therefore, some planets and moons have developed the distinquishly smooth(for the incident solar EM energy the specular reflection to occur) the smooth planetian surfaces, whereas other planets and moons have developed the distinquishly rough surfaces (for capturing the incident solar EM energy).

The smooth surface planets and moons specular reflection should be necessarily considered in the planets' and moons' "Energy in" estimation, because the Planet Energy Income for the smooth surface planets and moons is very much overestimated.

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The more renewables we have, the harder it is to add

The more renewables we have, the harder it is to add.

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The key question is how to shield an electricity system with many renewables.

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A first answer is batteries, pumped storage which is a battery with water, hydropower, natural gas that will be part of the mix, coal that will be also part of the mix...

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And, international interconnections, and, a smarter system that the consumer can shift consumption from moments when there is not enough energy to moments when there is.

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Suggestion:

Have you "tuned" any parameters in derivation of these closely agreeing temperatures with the satellite measured ones?

And could the effect of an atmosphere be "hiding" in some of these parameters?

Answer:

These data, the calculated with a Planet Without-Atmosphere Surface MeanTemperature Equation and the measured by satellites are almost the same, very much alike.

They are almost identical, within limits, which makes us conclude that the Planet Without-Atmosphere Surface Mean Temperature Equation

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

can calculate a planet mean temperatures.

It is a situation that happens once in a lifetime in science. Although the evidences existed, were measured and remained isolated information so far.

It was not obvious one could combine the evidences in order to calculate the planet’s temperature.

A planet-without-atmosphere effective temperature equation

Te = [ (1-a) S / 4 σ ]¹∕ ⁴

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".

Those two parameters are not enough to calculate a planet effective temperature.

Planet is a celestial body with more major features when calculating planet effective temperature to consider.

The planet without-atmosphere effective temperature calculating formula has to include all the planet’s major properties and all the characteristic parameters.

3. The sidereal rotation period N rotations/day

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

5. The planet surface solar irradiation accepting factor Φ (the spherical surface’s primer quality).

For Mercury, Moon, Earth and Mars without atmosphere Φ = 0,47.

Earth is considered without atmosphere because Earth’s atmosphere is very thin and it does not affect Earth’s Effective Temperature.

Altogether these parameters are combined in a Planet Without-Atmosphere Surface Mean Temperature Equation:

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

The Planet Without-Atmosphere Surface Mean Temperature Equation produces very reasonable results:

Tmean.earth = 288,36 K, calculated with the Complete Formula, which is identical with the

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

Tmean.moon = 221,74 K, calculated with the Complete Formula, which is almost the same with the

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

A Planet Without-Atmosphere Surface Mean Temperature Equation gives us a planet mean temperature values very close to the satellite measured planet mean temperatures.

Suggestion:

Is there a difference for Earth having an ocean either than just beeing a dry rocky planet?

Answer:

Yes there is a big difference. Earth’s Surface Mean Temperature Equation Tmean.earth:

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

Τmean.earth = [ 0,47(1-0,30)1.362 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(1-0,30)1.362 W/m²(150*1*1)¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =

Tmean.earth = 288,36 Κ

Moon’s Surface Mean Temperature Equation Tmean.moon:

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

Tmean.moon = { 0,47 (1-0,136) 1.362 W/m² [150* (1/29,5)*0,19]¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ }¹∕ ⁴ =

Tmean.moon = 221,74 Κ

cp.earth = 1 cal/gr*oC

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

The cp.earth is 5,263 times higher.

If Earth was not a Planet ocean, but a pure rocky planet, then:

Tmean.rocky.earth = 288,36 Κ * [(0,19)¹∕ ⁴ ]¹∕ ⁴ =

Tmean.rocky.earth = 288,36 Κ * 0,9014 = 259,93 K

If the Earth was a rocky planet the Tmean.earth would be

Te.rocky.earth = 259,93 = 260 K

Suggestion:

Isn't the Equation an adjustment on the already satellites measured planet mean temperatures?

Answer:

A Planet Without-Atmosphere Effective Temperature Calculating Equation, the Te equation, which is based on the radiative equilibrium and on the Stefan-Boltzmann Law, and which is in common use right now:

Te = [ (1-a) S / 4 σ ]¹∕ ⁴

is actually an incomplete Te equation and that is why it gives us very confusing results.

Comparison of results the planet Te calculated by the Incomplete Equation, the planet Te calculated by the Surface Mean Temperature Equation, and the planet Tsat.mean measured by satellites:

Planet or Te.incomplete Tmean Tsat.mean

moon equation equation measured

Mercury 437,30 K 323,11 K 340 K

Earth 255 K 288,36 K 288 K

Moon 271 K 221,74 K 220 K

Mars 209,91 K 213,59 K 210 K

The Planet Without-Atmosphere Surface Mean Temperature Equation:

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

is not a product of adjustments.

A Planet Without-Atmosphere Surface Mean Temperature Equation:

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

is based on a newly discovered Rotating Planet Surface Solar Irradiation Absorbing-Emitting Universal Law.

The planet average Jabs = Jemit, per m² planet surface:

Jabs = Jemit

Φ*S*(1-a) /4 = σTmean⁴ /(β*N*cp)¹∕ ⁴ (W/m²)

Solving for Tmean we obtain the surface mean temperature:

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

Jemit = σΤmean⁴/(β*N*cp)¹∕ ⁴ (W/m²)

It is obvious now that the planet without-atmosphere effective temperature incomplete formula:

Te = [ (1-a) S / 4 σ ]¹∕ ⁴

should not be in use anymore.

The satellites measured Planet Mean Temperatures we should relay on.

Suggestion:

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

For a very high N, will you get a very hot planet?"

Answer:

For the final Tmean result N (rotations/day) value is operated twice in fourth root .

Example: Let's say N = 100.000.000

[ ( 100.000.000 )¹∕ ⁴ ]¹∕ ⁴ = ( 100 )¹∕ ⁴ = 3,1623

And for N = 1000.000.000 it is 3,6525

But for N = 10 it is 1,1548

If Earth were rotating 10 times as fast, Earth's mean surface temperature would be:

288 K * 1,1548 = 332,58 K

"The simplest assumption possible"

Here it is a very interesting article, which is based on the mistaken assumption that the Stefan-Boltzmann emission Law can be applied for the estimation of the irradiated surface's temperature.

Link:

https://www.pas.va/content/dam/casinapioiv/pas/pdf-volumi/acta/acta-22-pdf-papers/acta22-ramanathan.pdf

Here it is the interested us abstract:

"The thickening of the blanket has added 3 Wm-2 to the IR energy t othe planet. In response, the planet will warm and radiate this energy to restore the energy balance between the net solar energy flowing in and theinfrared energy flowing out.

We will begin this discussion by making the

simplest assumption possible, which is that the surface and the atmosphere behave like Max Planck’s black body, in which case it will radiate energy to space as a black body, which is given by σT⁴, where σ is a fundamental constant derived by Max Planck and T⁴ denotes the fourth power of temperature T.

Based on this law, the surface and the atmosphere will radiate 3.3 Wm-2 per 1°C of warming. In other words, the planet can get rid of 3.3 Wm-2 for every degree warming.

So to get rid of the 3 Wm-2 energy trapped by manmade greenhouse gases, the planet will warm by (3/3.3=) 0.9°C.

16_RAMANATHAN (cmyk)_PP_230-241.QXD_Layout 1 15/12/15 10:27 Pagina 235

236 Complexity and Analogy in Science: Theoretical, Methodological and Epistemological Aspects

V. RAMANATHAN"

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"simplest assumption possible, which is that the surface and the atmosphere behave like Max Planck’s black body, in which case it will radiate energy

to space as a black body"

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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.

The blackbody surface properties

A blackbody planet surface is meant as a classical blackbody surface approaching.

Here are the blackbody's properties:

1. Blackbody does not reflect the incident on its surface radiation. Blackbody absorbs the entire incident on its surface radiation.

2. Stefan-Boltzmann blackbody emission law is:

Je = σ*Τe⁴

Notice:

Te is the blackbody's temperature (surface) at every given moment.

When the blackbody is not irradiated, the classical blackbody gradually cools down, gradually emitting away its accumulated energy.

The classical blackbody concept assumes blackbody's surface being warmed by some other than incoming irradiation source of energy - see the Sun's paradigm.

Sun emits like a blackbody, but it emits its own inner energy source's energy. Sun is not considered as an irradiation receiver. And sun has a continuous stable temperature.

Therefore we have here two different blackbody theory concepts.

a. The blackbody with the stable surface temperature due to its infinitive inner source (sun, stars).

b. The blackbody with no inner energy source. This blackbody's emission temperature relays on the incoming outer irradiation only.

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Also in the classical blackbody definition it is said that the incident on the blackbody irradiation is totally absorbed, warms the blackbody and achieves an equilibrium emission temperature Te.

It is an assumption.

This assumption, therefore, led to the next assumption: the planet like a blackbody emitting behavior.

And, consequently, it resulted to the planet's Te incomplete formula, in which it is assumed that planet's surface is interacting with the incoming irradiation as by being in a uniform equilibrium temperature.

Consequently it was assumed that planet's surface had a constant equilibrium temperature (which was only the incident solar irradiation dependent value) and the only thing the planet's surface did was to emit in infrared spectrum out to space the entire absorbed solar energy.

3. When irradiated, the blackbody's surface has emission temperature according to the Stefan-Boltzmann Law:

Te = (Total incident W /Total area m² *σ)¹∕ ⁴ K

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

Notice:

This emission temperature is only the incoming irradiation energy depended value.

Consequently, when the incoming irradiation on the blackbody's surface stops, at that very moment the blackbody's emission temperature disappears. It happens because no blackbody's surface accumulates energy.

4. Blackbody interacts with the entire incident on the blackbody's surface radiation.

5. Blackbody's emission temperature depends only on the quantity of the incident radiative energy per unit area.

6. Blackbody is considered only as blackbody's surface physical properties. Blackbody is only a surface without "body".

7. Blackbody does not consist from any kind of a matter.Blackbody has not a mass. Thus blackbody has not a specific heat.

Blackbody's cp = 0.

8. Blackbody has surface dimensions. So blackbody has the radiated area and blackbody has the emitting area.

9. The entire blackbody's surface area is the blackbody's emitting area.

10. The blackbody's surface has an infinitive conductivity.

11. All the incident on the blackbody's surface radiative energy is instantly and evenly distributed upon the entire blackbody's surface.

12. The radiative energy incident on the blackbody's surface the same very instant the blackbody's surface emits this energy away.

13.A blackbody doesn’t have a rate of warming, or a rate of cooling.
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A blackbody has only a steady temperature, at which temperature the blackbody emits EM energy.
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But what happens there on the rotating real planet's surface?

The rotating real planet's surface, when it turns to the sunlit side, is an already warm at some temperature, from the previous day, planet's surface.

Thus we, when assuming the planet's surface behaving as a blackbody, face the combination of two different initial blackbody surfaces.

a. The one with an inner energy source.

And

b. The one warmed by an outer irradiation.

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Planet is not a blackbody.

Planet reflects the (1-Φ + Φ*a)S part of the incident on the planet's surface solar irradiation "S".

Here "a" is the planet's average albedo and "Φ" is the planet's solar irradiation accepting factor.

For smooth planet without thick atmosphere, Earth included,

Φ=0,47

There is NO violation of the 1st law

To be honest with you I had at the beginning a serious dilemma:

Extra energy due to spin alone contravenes the first law.

It took me many sleepless nights to figure out what exactly happens here.

There is not any extra energy involved. There is not any additional energy "produced" by planet's faster spinning.

The energy from solar flux in, equals the energy reflected and emitted by the planet's surface out to space.

To explain the phenomenon of a planet being warmer when spinning faster one should refer to the Stefan-Boltzmann Law non-linearity.

I have a paradigm of how it happens here:

The faster a planet rotates ( n2 > n1 ) the higher is the planet’s average (mean) temperature T↑ mean

T min↑↑ →T↑mean ← T↓ max

when n2 > n1

( it happens because T min ↑ grows faster than T↓ max goes down )

It happens in accordance to the Stefan-Boltzmann Law.

Let’s explain: Assuming a planet rotates faster and Tmax1 - Tmax2 = 1 oC.

Then, according to the Stefan-Boltzmann Law:

Tmin2 - Tmin1 > 1oC

Consequently

Tmean2 > Tmean1

Assuming n2 > n1 the solar irradiated hemisphere average temperature T1 - T2 = 1oC

Then the dark hemisphere average temperature

T2 - T1 > 1oC

Consequently the total average

Tmean2 > Tmean1

So we shall have: when n2 > n1

T min ↑ → T↑ mean ← T↓ max

The faster a planet rotates ( n2 > n1 ) the higher is the planet’s average (mean) temperature T↑ mean.

When a planet rotates slowly the solar irradiated hemisphere warms at higher temperature. Consequently a warmer surface emits

Jemitt.₁= σΤ₁⁴

When a planet rotates faster the solar irradiated hemisphere warms at lower temperature.

Consequently a colder surface emits

Jemit.₂= σΤ₂⁴ , and

Jemit.₁> Jemit.₂

In both cases, slow or fast, the rotating planet interacts with the same amount of energy:

Jabs = Φ (1-a) So (1/R²)

The difference of

Jemit.₁- Jemit.₂

is what keeps the faster rotating planets warmer, everything else equals.

Now we should focus on what happens at the planet's dark side. As it was said "The change would be the difference between dawn and dusk temperatures, which would be smaller with a faster rotation period".

At dusk a faster rotating planet will have a higher local temperature.

At dawn a faster rotating planet would have a higher local temperature.

The new day for the faster rotating planet starts with a warmer surface.

At the culmination hours in the midday the slow rotating planet surface warms much higher and emits much more energy out to space

Jemit.₁= σΤ₁⁴ compared with

Jemit.₂= σΤ₂⁴ .

Τ₁> Τ₂

and due to the Stefan-Boltzmann Law non-linearity we have

Τ₁⁴ >>> Τ₂⁴

so we have Jemit.₁>>> Jemit.₂

Thank you for your Patience.

Where The Additional Solar Energy Comes From

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

Here it is what happens:

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

(SW) reflection,

(LW) emission and

(HEAT) absorption.

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

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

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

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

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

Φ*(1-a)*S (W/m²)

where

S - the solar flux (W/m²)

a - the satellite measured average Albedo

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

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

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

or

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

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

the amount of

(LW emitted)

or

[ 2). the (LW)] (W/m²)

varies because of the Rotational Warming Phenomenon.

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

the amount of

(LW emitted)

or

[ 2). the (LW)] (W/m²)

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

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

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

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

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

Notice:

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

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

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

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

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

Example:

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

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

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

3m x3m x6 = 9m^2 x6 = 54m²

54m² x240W/m² = 12.960 W or ~ 13 kW

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

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

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

Opponent:

"The Stefan-Boltzmann equation has been derived from first principles and is applicable to all temperatures”.

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Gordon Robertson explains:

Link: 

"What would those first principles be, especially when Stefan derived it before the relationship between EM and atoms had yet to be derived?

When Boltzmann added his fake science based on statitical mechanics, the same situation applied.

He was using statistical inference to analyze fake atoms, the electron and neutron still being unknown. In fact, the only known atomic part, the proton, was known for only one element, hydrogen.

The basis for claiming EM in W/m² by Boltzmann is obviously in error since it is based on the 1840 finding of the scientist Joule, who found an equivalence between heat and work.

Work is measured in HP with the joule being a European unit based on the horsepower.

Therefore claiming radiation (EM) in watts, particularly at the time S-B emerged, is plain wrong.

The reason it is wrong is this. Radiation was considered at the time as a means of transferring heat as heat rays. Therefore, it was believed that heat moved through space as a form of radiation.

It was also known from Faraday et al, that radiation was also associated with electric and magnetic fields, so there was considerable confusion about the meaning of radiation.

Stefan based his original Τ⁴ relationship on Tyndall’s experiment in which he heated a platinum filament electrically till it glowed different colours as the current was incrased.

That is the EM referenced in S-B, the colour temperature of a heated filament wire.

Since that took place in a Temperature range of about 500C to 1500C, how can anyone claim it applies outside that range?

Furthermore, how can anyone claim the radiation to be measured in watts, a measure of work, which has a heat equivalent, not equality?

Surely they are referring to heat dissipation at the radiating surface, not the radiation itself, which contains no heat and has a very different set of properties than heat?

They might be able to claim a heat equivalence, since the same radiation, when absorbed by a cooler body, can heat the body. However, the relationship is far from one to one.

Suppose we have a surface radiating EM. That radiation dissipates according to the inverse square law, so any cooler body absorbing that radiation will heat according to the distance it is located from the surface.

Where in S-B does it deal with that issue?"

October 4, 2024

Link:

https://en.wikipedia.org/wiki/Effective_temperature#:~:text=The%20effective%20temperature%20of%20the%20Sun%20(5778%20kelvins)%20is%20the

“Earth effective temperature
See also: StefanBoltzmann law Effective temperature of the Earth
Earth has an albedo of about 0.306 and a solar irradiance
(L / 4 π D2) of 1361 W m−2 at its mean orbital radius of 1.510^8 km. The calculation with ε=1 and remaining physical constants then gives an Earth effective temperature of 254 K (−19 C).[11]

The actual temperature of Earth’s surface is
an average 288 K (15 C) as of 2020.[12] The difference between the two values is called the greenhouse effect. The greenhouse effect results from materials in the atmosphere (greenhouse gases and clouds) absorbing thermal radiation and reducing emissions to space, i.e., reducing the planet’s emissivity of thermal radiation from its surface into space.

Substituting the surface temperature into the equation and solving for ε gives an effective emissivity of about 0.61 for a 288 K Earth. Furthermore, these values calculate an outgoing thermal radiation flux of 238 W m−2 (with ε=0.61 as viewed from space) versus a surface thermal radiation flux of 390 W m−2 (with ε≈1 at the surface). Both fluxes are near the confidence ranges reported by the IPCC.[13]:934”
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The “Earth effective temperature” compares the blakbody uniform surface temperature Te = 254K with the Earth’s average surface temperature 288 K.

“The difference between the two values is called the greenhouse effect.”

To be continued...