Planet's Without-Atmosphere Mean Surface Temperature New Equation: Tmean = [ Φ (1-a) S (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴ (K)

REFUTING Planet Blackbody Temperature (Planet Effective Temperature).

 

Proof of the Atmospheric Greenhouse Effect

Arthur P. Smith∗

American Physical Society, 1 Research Road, Ridge NY, 11961

A recently advanced argument against the atmospheric greenhouse effect is refuted.

A planet without an infrared absorbing atmosphere is mathematically constrained to have an average temperature less than or equal to the effective radiating temperature.

Observed parameters for Earth prove that without infrared absorption by the atmosphere, the average temperature of Earth’s surface would be at least 33 K lower than what is observed.

Link:

https://arxiv.org/pdf/0802.4324.pdf

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REFUTING Planet Blackbody Temperature (Planet Effective Temperature).

1. A Planet is solar irradiated from one side only. So, Planet cannot have uniform energy distribution.

2. Also, Planet's spherical shape doesn't permit uniform temperature distribution.

3. Not the entire not reflected portion of the incident on planet surface solar energy (solar flux) is accumulated in inner layers.

4. A planet doesn't rotate fast enough to even "approach" some uniform temperature distribution.

5. The "energy in" is wrongly estimated. The Φ - the solar irradiation accepting factor is completely ignored. 

6. There is always the average surface temperature (Tmean.equator) on a ROTATING planet's equator is being higher than the entire planet's Tmean. The faster a planet rotates, the higher is the difference:

Tmean.equator - Tmean.entire. 

7. And, two planets with the same average surface temperature (Tmean) may emit dramatically different amounts of IR  electromagnetic energy.

8. Due to a nonlinearity of the SB law and a non-uniform distribution of the incident solar radiation on the surface of a NON-ROTATING sphere, the equilibrium temperature (Te) computed from a spatially averaged radiation flux is always higher than the arithmetic average temperature (Tmean).

9. Except for the very slow ROTATING planet Mercury and the slow ROTATING Moon, every planet and moon without-atmosphere in solar system has the satellite MEASURED mean surface temperature (Tmean) being HIGHER than its the calculated theoretical blackbody temperature Te (effective temperature Te).

view page: "All planets' temperatures"

https://www.cristos-vournas.com/446393385

Thus, the actual planet mean surface temperatures are not "constrained" by the mathematical abstraction of planet blackbody temperature Te.

An excerpt from the above PDF article:

"A planet without an infrared absorbing atmosphere is mathematically constrained to have an average temperature less than or equal to the effective radiating temperature."

10. The Stefan-Boltzmann emission law doesn't "work" vice-versa.

The detailed analysis is given in page:

"T = ( J /σ )¹∕ ⁴ mistake"

view page:

https://www.cristos-vournas.com/451800938

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CONCLUSION:

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 (Tmean) 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 (Tmean) cannot be associated with any kind of BB profile spectrum.

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