A planet does not emit at a SINGLE temperature


It was very much mistakenly asserted:


"If you take the average temperature of the earth, you can find the resulting blackbody spectrum."

Link to the image:


https://th.bing.com/th/id/R.24316dc9da7013286aa6719c65bac08c?rik=1BXisZ9xMlUCDA&pid=ImgRaw&r=0


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We have already demonstrated in the HOME PAGE and elswhere in this site that two planets with the same mean surface temperature (Tmean) may emit dramatically different amounts of INFRARED radiative energy.

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Please see the Moon-Mars comparison data, also see the planet Jupiter's satellites Io - Ganymede Tmean (110K & 110K).

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Therefore, the planet average surface temperature (Tmean) cannot reffer to any kind of the planet average surface the INFRARED radiative energy spectrum!

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I would like to focus here on the issue of the Infrared Spectrum Of The Earth.


A planet emits infrared radiation, when in a radiative energy equilibrium, a planet emits on a constant rate of


Energy out = Energy in


Also a planet has its average surface temperature (Tmean), for Earth it is estimated as Tmean.earth =288K


A planet does not emit at its average surface temperature (Tmean).

Therefore, a planet's average surface temperature (Tmean) cannot be associated with any kind of planet surface Infrared Emission Spectrum!


A planet does not emit at a single temperature


Jemit = σT⁴ W/m²


Earth does not emit


σ(Τmean.earth)⁴= σ*(288)⁴ W/m²


Consequently, the satellite measured infrared (frequency-by-frequency) for some local place the measured infrared emission curve cannot be compared with the planet average surface temperature the alleged (blackbody) emission curve, because there is not any such emission curve, since planet does not emit at its average surface temperature.


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They have confused the emission curves comparison with the emission comparison in the case of stars.


They neglect a very important difference stars and planets have!


Stars have a uniform surface temperature, whereas planets have average surface temperature...

And stars have their own inner infinite source of energy, when planets emit the radiative energy falling and interacting upon their surface.


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Below we demonstrate (some two of the many paradigms in internet) of the unfortunate earth's infrared emission curves comparisons with the earth's alleged blackbody 288K infrared emission curve.


In those unfortunate comparisons the gaps (the missing radiative energy) is attributed to the greenhouse gases radiative energy absorption bands.


What we notice here is that there is not any such absorption take place, because we are not justified to compare those curves!

Actually, there is not any measured emission from earth's surface on those frequencies which is then being absorbed...


Atmospheric gases cannot absorb, what is not emitted by the Earth's surface!


Link 1:"Simulated emission spectrum of the Earth's atmosphere in the zenith..."


Link 2:  "The Infrared Spectrum Of The Earth - Origin of Life - Fossil Hunters"


"The Infrared Spectrum Of The Earth

Last Updated on Sun, 11 Dec 2022| Origin of Life

Figure 13.4 shows the infrared emission spectrum of the Earth, as seen from space. This is not the spectrum obtained by the Galileo spacecraft but a much more detailed one obtained by the Nimbus-4 satellite in the 1970s. This particular spectrum was acquired in daytime above the western Pacific Ocean, and has been chosen because it resembles the sort of spectrum that would be obtained from a cloud-free Earth from a great distance, when the light from the whole planet would enter the spectrometer. The vertical scale shows the power emitted from the Earth at each wavelength (note that the wavelength scale is logarithmic - see Section 11.2).

There are several smooth curves, each labelled with a temperature. These correspond to emission from a surface that is black at infrared wavelengths, and has temperatures equal to those shown. There is also a jagged curve displaying much detail. This is the infrared power emitted by the Earth. It is the detail in frequency in millions of megahertz frequency in millions of megahertz wavelength in micrometers."


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What we have discovered is the ROTATING PLANET SPHERICAL SURFACE SOLAR IRRADIATION INTERACTING-EMITTING UNIVERSAL LAW

The non-linearity of the S-B radiation law, when coupled with a strong latitudinal variation of the INTERACTED solar flux across the surface of a sphere, and with the planet rotational spin, and with the average surface specific heat, creates a mathematical condition for a correct calculation of the true global surface temperature from a spatially integrated infrared emission.


Jemit = 4πr²σΤmean⁴ /(β*N*cp)¹∕ ⁴ (W) 


Where:

Jemit (W) - is the INFRARED emission flux from the entire planet (the TOTAL)


r - is the planet radius


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


β = 150 days*gr*oC/rotation*cal - is the Solar Irradiated Planet INTERACTING-Emitting Universal Law constant – ( the Rotational Warming Factor constant ).


N - rotation /per day, is planet’s rotational spin with reference to the sun in earthen days. Earth's day equals 24 hours= 1 earthen day.


cp - cal/gr*oC- is the planet average surface specific heat


Planet Energy Budget 


When planet surface is in radiative equilibrium,  planet energy balance should be met: Energy In  = Energy Out


Jnot.reflected = Jemit

πr²Φ(1-a)S  (W) - is on the entire planet surface the not reflected portion (the TOTAL not reflected) of the incident on planet surface solar flux


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


a - is the planet average surface Albedo (Bond)


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


πr²Φ(1-a)S = 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 interacting with planet surface the solar SW radiative energy on the same very instant does the following:  1). Gets partly SW reflected (diffusely and specularly).  2). Gets partly transformed into the LW  radiative emission - the IR emission energy.  3).  Gets partly transformed into HEAT, which is accumulated in the inner layers.

When interacting with planet surface the solar SW radiative energy on the same very instant does the following: 1). Gets partly SW reflected (diffusely and specularly). 2). Gets partly transformed into the LW radiative emission - the IR emission energy. 3). Gets partly transformed into HEAT, which is accumulated in the inner layers.

In short...

The Rotating Planet Spherical Surface Solar Irradiation Interacting-Emitting Universal Law

Here it is the ENTIRE planet surface IR emittance Universal Law

Jemit = 4πr²σΤmean⁴ /(β*N*cp)¹∕ ⁴ (W)

The solar irradiated rotating sphere (planet) does not emit as a uniform temperature sphere. A planet does not emit in accordance to the classical Stefan-Boltzmann emission law.

4πr²σΤmean⁴ (W) No, planet does not emit at the single temperature Tmean.

Yes, the solar irradiated rotating sphere (planet) emits as a rotating planet in accordance with both, the classical Stefan-Boltzmann emission law and the Newly discovered Planet Surface Rotational Warming Phenomenon.

4πr²σΤmean⁴ /(β*N*cp)¹∕ ⁴ (W)

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Let's continue...

Planet Energy Budget:

Jnot.reflected = Jemit

πr²Φ(1-a)S= 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) 

Rotating Planet Spherical Surface Solar Irradiation Interacting-Emitting Universal Law

Planet Energy Budget:

The Amount of Solar energy for further INTERACTION on a Hemisphere with radius "r", after some of the incident energy  instantly reflected is:

Jnot.reflected = πr²Φ(1-a)S      (W) 

What we have now is the following:

Jsw.incoming - Jsw.reflected = Jsw.not.reflected

Φ = (1 - 0,53) = 0,47

Φ = 0,47

Φ is the planet's spherical surface solar irradiation accepting factor.

Jsw.reflected = (0,53 + Φ*a) * Jsw.incoming

And

Jsw.not.reflected = Φ* (1-a) * Jsw.incoming

Where

(0,53 + Φ*a) + Φ* (1-a) = 0,53 + Φ*a + Φ - Φ*a =

= 0,53 + Φ = 0,53 + 0,47 = 1

The solar irradiation reflection, when integrated over a planet sunlit hemisphere is:

Jsw.reflected = (0,53 + Φ*a) * Jsw.incoming

Jsw.reflected = (0,53 + Φ*a) *S *π r²

For a planet with albedo a = 0

we shall have

Jsw.reflected = (0,53 + Φ*0) *S *π r² =

= Jsw.reflected = 0,53 *S *π r²

The fraction left for hemisphere to INTERACT WITH is:

Φ = 1 - 0,53 = 0,47

and

Jnot.reflected = Φ (1 - a ) S π r²

The factor Φ = 0,47 "translates" the "not reflected" of a disk into the "not reflected" of a hemisphere with the same radius. When covering a disk with a hemisphere of the same radius the hemisphere's surface area is 2π r². The incident Solar energy on the hemisphere's area is the same as on disk:

Jdirect = π r² S

The "not reflected" Solar energy by the hemisphere's area of 2π r² is:

Jnot.reflected = 0,47*( 1 - a) π r² S

It happens because a hemisphere of the same radius "r" "not reflects" only the 0,47 part of the directly incident on the disk of the same radius Solar irradiation.

In spite of hemisphere having twice the area of the disk, it "not reflects" only the 0,47 part of the directly incident on the disk Solar irradiation.

Jnot.reflected = Φ (1 - a ) S π r² , where Φ = 0,47 for smooth without atmosphere planets.

and

Φ = 1 for gaseous planets, as Jupiter, Saturn, Neptune, Uranus, Venus, Titan. Gaseous planets do not have a surface to reflect radiation. The solar irradiation is captured in the thousands of kilometers gaseous abyss. The gaseous planets have only the albedo "a".

And Φ = 1 for heavy cratered planets, as Calisto and Rhea ( not smooth surface planets, without atmosphere ). The heavy cratered planets have the ability to capture the incoming light in their multiple craters and canyons. The heavy cratered planets have only the albedo "a".

Another thing that I should explain is that planet's albedo actually doesn't represent a primer reflection. It is a kind of a secondary reflection ( a homogenous dispersion of light also out into space ).

That light is visible and measurable and is called albedo.

The primer reflection from a spherical hemisphere cannot be seen from some distance from the planet. It can only be seen by an observer being on the planet's surface.

It is the blinding surface reflection right in the observer's eye.

That is why the albedo "a" and the factor "Φ" we consider as different values.

Both of them, the albedo "a" and the factor "Φ" cooperate in the Planet Rotating Surface Solar Irradiation Absorbing-Emitting Universal Law: 

Jsw.incoming - Jsw.reflected = Jsw.not.reflected

Jsw.not.reflected = Φ * (1-a) * Jsw.incoming

Total energy emitted to space from entire planet:

Jemit = A*σΤmean⁴ /(β*N*cp)¹∕ ⁴        (W)

Α - is the planet's surface (m²)

(β*N*cp)¹∕ ⁴ - dimensionless, is a Rotating Planet Surface Solar Irradiation Warming Factor

A = 4πr² (m²), where r – is the planet's radius

Jemit = 4πr²σTmean⁴ /(β*N*cp)¹∕ ⁴   (W)

global Jabs = global Jemit

πr²Φ(1-a)S = 4πr²σTmean⁴ /(β*N*cp)¹∕ ⁴

Or after eliminating πr²

Φ(1-a)S = 4σTmean⁴ /(β*N*cp)¹∕ ⁴

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) 

β = 150 days*gr*oC/rotation*cal – is a Rotating Planet Surface Solar Irradiation INTERACTING-Emitting Universal Law constant – ( the Rotational Warming Factor constant ).

N rotations/day, is the planet’s axial spin

cp – is the planet surface specific heat

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.

Here (β*N*cp)¹∕ ⁴ - is a dimensionless Rotating Planet Surface Solar Irradiation Warming Factor

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

Rotating Planet Spherical Surface Solar Irradiation Interacting-Emitting Universal Law:

  Jemit = 4πr²σΤmean⁴/(β*N*cp)¹∕ ⁴  (W)

The year-round averaged energy flux at the top of the Earth's atmosphere is Sο = 1.361 W/m².

With an albedo of a = 0,306 and a factor Φ = 0,47 we have Tmean.earth = 287,74 K or 15°C.

This temperature is confirmed by the satellites measured Tmean.earth = 288 K.

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When interacting with planet surface the solar SW radiative energy on the same very instant does the following:

1). Gets partly SW reflected (diffusely and specularly).

2). Gets partly transformed into the LW  radiative emission - the IR emission energy.

3).  Gets partly transformed into HEAT, which is accumulated in the inner layers.

 Jemit = 4πr²σΤmean⁴ /(β*N*cp)¹∕ ⁴ (W)

The Rotating Planet Surface Solar Irradiation Interacting-Emitting Universal Law is based on a simple thought.

It is based on the thought, that physical phenomenon which distracts the "black body" surfaces from the instant emitting the absorbed solar radiative energy back to space, warms the "black body" surfaces up.

In our case those distracting physical phenomena are the planet’s sidereal rotation, N rotations/day, and the planet’s surface specific heat, cp cal/gr oC.

http://www.cristos-vournas.com

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

Tmin→ T↑mean ← Tmax

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The S-B emission law cannot be applied neither to the planet solar lit side, nor to the planet darkside.


"Nothing, other than the absorbed radiation is what warms the matter to some (local) temperature, which, along with the matter properties, determines the Planck spectrum and S-B flux of the outgoing thermal radiation."
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Well, the planet's dark side cools by emitting to space IR radiation. The dark side's surface heat is the energy source of that IR EM energy emission.


There are not enough thermal energy (heat) at darkside terrestrial temperatures to support the S-B equation emission demands for the darkside respective surface temperatures.


Thus, the outgoing IR EM energy flux from the planet darkside is much-much weaker than what S-B equation predicts for those local temperatures.
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On the planet's solar lit side an interaction of the incident EM energy with surface's matter occurs.


Part of the incident SW EM energy gets reflected (diffusely and specularly).


Another SW part gets instantly transformed into outgoing IR EM energy, and gets out to space.


When SW EM energy gets transformed into IR EM energy, there are always some inevitable energy losses, which dissipate as heat in the interacting surface's matter and gets absorbed in the matter's inner layers.
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The S-B emission law cannot be applied neither to the planet solar lit side, nor to the planet darkside.


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Notice:


The Effective temperature (1) and (2) equations (Te and Te.correct) helped us to have formulated the Planet Mean Surface Temperature Theoretical Equation:


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


But the Planet Mean Surface Temperature Theoretical Equation is based on different than the Planet Blackbody Effective Temperature (Te and Te.correct) physics principles.