# The Planet Mean Surface Temperature Equation: Tmean = [ Φ (1-a) S (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴

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### The Te = Tsat equality concept is an old, wrong and misleading conception

The entire Greenhouse Gasses Warming Theory on Earth's surface is based on a misfortunate coincidence.

Please look at the following Table:

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

Planet…Te.incompl…Tmean…Tsat.mean

Mercury….439,6 K…….325,83 K…..340 K

Earth………255 K………287,74 K…..288 K

Moon……..270,4 Κ…….223,35 Κ…..220 Κ

Mars……209,91 K……..213,21 K…..210 K

In first column there are planets effective temperatures calculated with the Te blackbody equation

Te = [ (1-a) So /4σ ]¹∕ ⁴

When studying the Table we see that for Mars the

Te.mars = 209,91 K

And the satellite mean surface temperature

Tsat.mars = 210 K

These two temperatures, the calculated Mars' effective temperature and the Mars' average surface temperature measured by satellites are identical.

The fact these two temperatures for a planet without atmosphere, like Mars, is considered to be equal, led the worldwide scientific community to a very wrong conclusions.

It led people to a very mistaken way of thinking. As you know, the blackbody emission equation is based on science, it is based on the Stefan-Boltzmann emission law:

Jemit = σT⁴

For a flat blackbody surface perpendicular to the sun's rays the emission temperature according to the Stefan-Boltzmann emission law should be:

Te = ( So /σ )¹∕ ⁴

in a 1981 paper by James Hansen et. al. , based on the energy balance for a planet, under simplifying assumptions that the planet conforms to blackbody conditions (required for applying the Stefan-Boltzmann equation to determine outgoing energy emitted).

So we have the planet's effective radiating temperature (Te) as calculated by this simple blackbody equation:

Te = [ (1-a) So /4σ ]¹∕ ⁴

The effective temperature Te for Mars is:

Te.mars = 209,91 K

And the satellite measured mean surface temperature for Mars is:

Tsat.mars = 210 K

Let's now separate these two very different terms:

The planet's effective temperature by definition is a uniform on the entire planet's surface temperature.

So the calculated Te.mars = 209,91 K is a uniform on the entire Mars' surface theoretically calculated temperature.

Te is a mathematical abstraction, it cannot be measured, and it does not exist on the real planet's surface. We know well planet Mars has not uniform surface temperature - NO planet has.

Planets are irradiated only on the one side and the other side remains in dark. Also planets are not irradiated uniformly on the day side because of the planet's spherical shape. There are not uniform temperatures for the planets surfaces.

The Mars' satellite measured mean surface temperature

Tsat.mars = 210 K

is an entirely different thing. Tsat.mars = 210 K is a result of multiple satellite measurements when averaged on the entire Mars' surface.

Tsat.mars = 210 K does not mean that Mars has a uniform temperature. It is a result of averaging multiple satellite measurements.

Thus Te.mars = 209,91 K

And the satellite mean surface temperature

Tsat.mars = 210 K

These two temperatures, the calculated Mars' effective temperature and the Mars' average surface temperature measured by satellites being identical should not lead to any scientific conclusions, except of just constituting the fact of their coincidence.

### A fooling ourselves mistaken concept

The planets blackbody equilibrium temperatures (Te planets effective temperatures) cannot be considered as planets without atmosphere average (mean) surface temperatures.

It is a fooling ourselves mistaken concept.

And it is not proven by the observations.

For Mars Te.mars = 210 K

and Tsat.mean.mars = 210 K

these two temperatures - the theoretical mathematical abstraction's value of Te.mars to be equal to the satellite measured Tsat.mean.mars is a coincident.

This planets Te and Tsat temperatures equality is never observed again in the entire (measured) solar system.

Instead of accepting this fundamental observation as an undeniable fact, we are fooling ourselves trying to explain the observed differences between the every planet calculated Te and the satellite measured Tsat.mean.planet.

Thus for Earth we have the greenhouse warming effect theories.

For some planets (Jupiter, Saturn, Neptune) we have the huge inner sources of heat theories.

For some other cases we have the tidal warming theories (Jupiter's and Saturn's satellites).

Every planet-case we are looking for an excuse-explanation to keep fooling ourselves with the Te = Tmean equality for planets without atmosphere.

But the truth is there is not any measurable greenhouse warming effect on the Earth's surface.

The Earth's atmosphere is very thin and it is very transparent both ways - in and out.

And as for carbon dioxide - there are only traces of CO2 in Earth's atmosphere. Only traces... even children cannot be fooled about it.

Why keeping fooling ourselves then?

### Planet effective temperature Te and Planet average surface temperature Tsat.mean are completely different physics terms

Planet effective temperature Te is the planet surface uniform temperature in Kelvin when assuming planet emits the incident on the sunlit side solar flux's energy uniformly distributed on the entire planet's surface (the sunlit and the dark).

Therefore when we are referring to the planet effective temperature Te we have in consideration a uniform temperature at which the entire planet surface emits the same amount of the incident on the planet energy as the planet does with its actual temperatures distribution on its entire surface.

So the planet effective temperature is calculated by the equation:

Te = [ (1-a) S /4σ ]¹∕ ⁴

where

a - is the planet's surface average albedo (dimensionless)

S - is the solar flux (W/m²)

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

What we do here is that we average on the entire planet's surface the total energy of incoming solar flux, and then, using the Stefan-Boltzmann emission law, calculate the planet's surface effective temperature Te.

Te is a theoretical uniform temperature which does not exist and cannot be measured on the real planet's surface, because planet's surface cannot have a uniform temperature.

On the other hand, Tsat.mean is an average planet surface temperature in Kelvin.

Tsat.mean is a satellite measured planet average surface temperature.

To have Tsat.mean satellite performs countless measurements on countless planet surface spots.

Then computers produce the planet average surface temperature Tsat.mean.

Tsat.mean is not a planet uniform temperature, so it cannot be compared with the theoretical mathematical abstraction planet surface effective temperature Te.

Planet effective temperature Te and planet average mean surface temperature Tsat.mean both are planet solar flux and planet albedo dependent values.

The difference is that Te is ONLY planet solar flux and planet albedo dependent value.

As for Tsat.mean it is NOT ONLY planet solar flux and planet albedo dependent value.

Tsat.mean is also a planet rotational spin N and planet surface specific heat cp dependent value.

That is why we observe for the slow rotating Mercury and Moon the Tsat.mean satellite measured average surface temperatures being LOWER than the Mercury's and Moon's Te effective temperatures.

For the faster rotating planets and moons in the solar system we observe Tsat.mean temperatures being MUCH HIGHER than the uniform theoretical effective temperatures.

And that is why Earth's satellite measured average surface temperature Tmean = 288 K, when Earth's effective temperature Te = 255 K.

And that is why the difference 288 Κ - 255 Κ = Δ33°C does not exist in the real world.

Conclusion:

There is not a Δ33°C greenhouse warming effect on the Earth's surface.

Let's not fool ourselves anymore.