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

### Planet Mars black-body temperature (effective temperature) Te misfortunate coincidence

Planet Mars black-body temperature (effective temperature) Te misfortunate coincidence

We have calculated the Corrected Effective Temperature for Mars Te.correct.mars = 174 K

But let's see what happened when the Effective Temperature of Mars was not yet corrected. Te.mars = 209,8 K (https://nssdc.gsfc.nasa.gov/planetary/factsheet/marsfact.html)

Tsat. mean.mars = 210 K (https://en.wikipedia.org/wiki/Mars)

We have here planet Mars mean temperature measured by satellites:

Tsat.mean.mars = 210 K

We have the Mars black-body temperature

Te = 209,8 K

These temperatures the Tsat.mean.mars = 210 K and the black-body temperature Te.mars = 209,8 K are almost identical.

These two very important for planet Mars temperatures are almost identical, but it is a coincident.

It is a coincident, but with very important consequences.

Let's explain:

Tsat.mean.mars = 210 K measured by satellites is almost equal with Te.mars = 209,8 K

When measuring by satellites the Tsat.mean.mars = 210 K and calculating Mars black-body temperature Te.mars. = 209,8 K scientist were led to mistaken conclusions.

First they concluded that the planet's effective and planet's without-atmosphere mean temperatures should normally be equal, which is wrong.

Secondly they concluded that Earth without atmosphere should have an average surface temperature equal to the black-body temperature (effective temperature), Te.earth = 255 K (https://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html)

Then they compared the Te.earth = 255 K with the measured by satellites Tsat.mean.earth = 288 K (https://nssdc.gsfc.nasa.gov/planetary/factsheet/)

The difference of 288 K - 255 K = Δ33 oC was then attributed to the Earth’s atmosphere greenhouse warming effect.

Now we have the Mars Corrected Effective Temperature

Te.correct.mars = 174 K.

The fact that the Corrected Effective Temperature of Mars is Te.correct.mars = 174 K, which is not even close to the satellite measured Tsat.mean.mars = 210 K debunks the above syllogism that the planet the calculated black-body temperature Te (effective temperature) is equal to the planet without atmosphere mean surface temperature Tmean.

The above wrong syllogism happened because of the wrongly estimated Mars black-body temperature.

It was calculated assuming planet absorbing incoming solar energy as a disk. We know now that planet absorbs the incoming solar energy as a sphere, and not as a disk.

### Comparison of Te and Te.correct for planets Mars, Earth, Moon and Mercury

Φ = 0,47 is the for smooth without atmosphere planet surface solar irradiation accepting factor

Planet...Tsat.mean.....Te…..Te.correct

Mars …....210 K ....209,8 K …174 Κ

Earth.......288 K.......255..K......210 K

Moon.......220 K......270,4..K....224 K

Mercury....340 K......440 K......364 K

Let's explain:

For Mars

Tsat.mean.mars = 210 K measured by satellites is almost equal with

Te.mars = 209,8 K (black-body equation calculated)

So scientist were led to mistaken conclusions.

First they assumed that the planet's without-atmosphere effective and mean surface temperatures were equal, which is wrong.

Second, Earth's effective temperature was calculated as

Te.earth = 255 K

The measured by satellites

Tsat.mean.earth = 288 K.

The difference of Δ 33 oC was attributed to the Earth’s atmosphere greenhouse warming effect.

Now we have calculated Mars' effective temperature as

Te.correct = 174 K

So the assumption that planet without-atmosphere mean surface temperature

Tmean = Te is wrong.

Mars' Tsat.mean.mars = 210 K.

We can conclude now that Earth's

Te.earth = 255 K is not equal with the Earth's Tmean.earth.

The satellite measured Tsat.mean.earth = 288 K

and it is the Earth's actual average (mean) surface temperature.

Thus the difference of 288 K - 255 K = Δ33 oC does not exist.

Also we have calculated the Earth's Te.correct.earth = 210 K

which is much less than the previously calculated by the black-body equation

Te.earth = 255 K.

## .

### Te is a misleading mathematical abstraction, which, in addition, is wrongly estimated…

What I insist in is that planet without-atmosphere effective temperature Te is a wrong and misleading mathematical abstraction.

Also, I have shown, (this wrong and misleading mathematical abstraction) Te is, at the same time, wrongly estimated.

Thus we deal here with a misleading mathematical abstraction, which, in addition, is wrongly estimated…

As it is shown in the Table above:

Te.mars = 210 K, Te.correct.mars = 174 K

Te.earth = 255 K, Te.correct.earth = 210 K