The New equation

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

is based both, on precise radiative “energy in” estimation and on the “Planet Rotational Warming Phenomenon“.

The discovery has explained the origin of the formerly observed the planets' average surface temperatures comparison discrepancies.

The Planet Surface Rotational Warming Phenomenon states:

Planets' mean surface temperatures relate (everything else equals) as their (N*cp) products' sixteenth root.

Let's demonstrate the Planet Surface Rotational Warming Phenomenon on the:

Earth's /Moon's example

Earth is on average warmer 68°C than Moon.

It is not only because of the Earth having 29,53 times faster rotational spin.

Earth has a five (5) times higher average surface specific heat (for Earth cp.earth = 1 cal/gr*oC, it is because Earth has a vast ocean; and for Moon cp.moon = 0,19cal/gr*oC – its soil is a dry regolith).

Earth is warmer than Moon not because of Earth's very thin atmosphere trace greenhouse gasses content. Earth is warmer because its surface has 155,42 times higher the (N*cp)  product than Moon’s surface.

Earth(N*cp) /Moon(N*cp) = (29,53/1)*(1/0,19) = 155,42

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If Moon had Earth's albedo (a=0,306), Moon's mean surface temperature would have been 210K.

As we know, Earth's mean surface temperature is 288K. Earth is warmer because its surface has 155,42 times higher the (N*cp) product than Moon’s surface.

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Let's compare the Earth's and Moon's mean surface temperatures:

Tmean.earth /Tmean.moon = 288K /210K = 1,3714

and the Earth's and Moon's (N*cp) products sixteenth root:

[ Earth(N*cp) /Moon(N*cp) ]^1/16 = (155,42)^1/16 = 1,3709

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The results (1,3714) and (1,3709) are almost identical! 

It is a demonstration of the Planet Surface Rotational Warming Phenomenon:

Planets' mean surface temperatures relate (everything else equals) as their (N*cp) products' sixteenth root.

In this site the rightness of the Rotational Warming Phenomenon is many times demonstrated and, also, it has been theoretically explained by the physics first principles.

Somehow, someway a transformation has to be generated to affect the planet’s surface temperature.

You can’t just say RADIATIVE energy get converted into Heat. It’s more likely it stays Radiative energy.

There has to be a PROCESS.

At the very first look at the data table we distinguish the following:

Planet..Tsat.mean..Rotations..Tmin..Tmax

...........measured...per day......................

Mercury..340 K.....1/176....100 K...700 K

Earth.....288 K........1.............................

Moon....220 Κ.....1/29,5.....100 K...390 K

Mars.....210 K....0,9747.....130 K...308 K

The Earth's and Mars' by satellites temperatures measurements, in relation to the incident solar irradiation intensity, appear to be higher,

and it happens because of Earth's and Mars' faster rotation. 

I should say here that I believe in NASA satellites temperatures measurements. None of my discoveries would be possible without NASA satellites very precise planet temperatures measurements.

It is the "magic" of the planet's spin. When it is understood, it becomes science.

The closest to the sun planet Mercury receives 15,47 times stronger solar irradiation intensity than the planet Mars does.

However on the Mercury's dark side Tmin.mercury = 100 K, when on the Mars' dark side Tmin.mars = 130 K.

These are observations, these are the by satellite the planet surfaces temperatures measurements.

And they cannot be explained otherwise but by the planet Mars' 171,5 times faster rotation than planet Mercury's spin.

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Let's study the table of data above.

Interesting, very interesting what we see there

- Earth and Moon are at the same distance from the Sun

R = 1 AU.

Earth and Mars have almost the same axial spin

N = 1rotation /day.

Moon and Mars have almost the same satellite measured average temperatures

220 K and 210 K.

Mercury and Moon have the same minimum temperature

100 K.

Mars' minimum temperature is 130 K, which is much higher than for the closer to the Sun Mercury's and Moon's minimum temperature 100 K.

And the faster rotating Earth and Mars appear to be relatively warmer planets.

I’ll try here in few simple sentences explain the very essence of how the Planet Surface Rotational Warming Phenomenon occurs.

Lets consider two identical planets F and S at the same distance from the sun.

Let’s assume the planet F spins on its axis Faster, and the planet S spins on its axis Slower.

Both planets F and S get the same intensity solar flux on their sunlit hemispheres. Consequently both planets receive the same exactly amount of solar radiative energy.

The slower rotating planet’s S sunlit hemisphere surface gets warmed at higher temperatures than the faster rotating planet’s F sunlit hemisphere.

The surfaces emit at σT⁴ intensity – it is the Stefan-Boltzmann emission law.

Thus the planet S emits more intensively from the sunlit side than the planet F.

There is more energy left for the planet F to accumulate then.

That is what makes the faster rotating planet F on the average a warmer planet.

That is how the Planet Surface Rotational Warming Phenomenon occurs.

And it states:

Planets’ mean surface temperatures relate (everything else equals) according to their (N*cp) products’ sixteenth root.

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The planet temperature varies with planet rotation. It is an observation.

There is no need in an experiment with a rotating sphere in a vacuum exposed to sunlight…

Here is the clear relation example:

Let's illustrate on the planet's effective temperature old equation

Te = [ (1-a) S /4σ ]¹∕ ⁴ (K)

Mars is irradiated 2,32 times weaker than Moon, but Mars rotates 28,783 times faster.

And… for the same albedo, Mars and Moon would have the same satellite measured mean temperatures.

For Moon Tmean = 220K; Moon’s Albedo a=0,11

For Mars Tmean= 210K; Mars’ Albedo a=0,25

Let’s do a simple calculation:

The rotation difference’s fourth root is

(28,783)¹∕ ⁴ = 2,3162

Now, please compare these two numbers:

2,32 and 2,3162

They are very-very much close, they are almost identical!

That is why no experiment is needed.

In this example we have demonstrated that the Mars' solar irradiation intensity deficit being 2,32 times less is compensated by Mars' 28,783 times higher rotational spin's fourth root

(28,783)¹∕ ⁴ = 2,3162

We have here the "Planet Surface Rotational Warming Phenomenon" observed.

We shall continue in the next pages.

Moon gets baked hard during its 14,75 earth days long lunar day.

And Moon also  emits from its very hot daytime surface hard.

What else the very hot surface does but to emit hard, according to the Stefan-Boltzmann emission Law.

The very hot surface emits in fourth power of its very high absolute temperature.

Jemit ~ T⁴

A warm object in space loses heat via emission. The hotter is the object, the faster it loses heat. 

So there is not much energy left to emit during the 14,75 earth days long lunar night.

And it becomes very cold on the Moon at night.

It is in our Earth's immediate neighborhood happens.

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The Planet Mean Surface Temperature New Equation.

It is time to abandon Te = [ (1-a) S /4σ ]¹∕ ⁴ (K) the old incomplete equation. You have to wonder how some people can so consistently get it all so wrong.

Te = [ (1-a) S /4σ ]¹∕ ⁴ (K) is a mathematical abstraction, it is not planet 1LOT energy balance analysis related equation.

Here it is the planet 1LOT energy balance analysis related equation:

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

R = 1 AU, is the Earth's distance from the sun in astronomical units

Earth’s albedo: aearth = 0,306

Earth is a smooth rocky planet, Earth’s surface solar irradiation accepting factor Φearth = 0,47

β = 150 days*gr*oC/rotation*cal – is the Rotating Planet Surface Solar Irradiation INTERACTING-Emitting Universal Law constant

N = 1 rotation /per day, is Earth’s sidereal rotation spin

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.

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

So = 1.361 W/m² (So is the Solar constant)

Earth’s Without-Atmosphere Mean Surface Temperature Equation Tmean.earth is:

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

Τmean.earth = [ 0,47(1-0,306)1.361 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(1-0,306)1.361 W/m²(150*1*1)¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =

Τmean.earth = ( 6.854.905.906,50 )¹∕ ⁴ =

Tmean.earth = 287,74 Κ

And we compare it with the

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

These two temperatures, the calculated one, and the measured by satellites are almost identical.

The planet Earth's and the planet Mars' faster rotation creates the necessary level of the "solar irradiation - planet surface" interaction phenomenon...

which results in the day-time much lower surface temperatures and, consequently, in much lower day-time surface infrared radiation emissions

and which results in higher planet surface 24-hours average temperatures.

The planet Earth’s and the planet Mars’ faster rotation is what creates the necessary interaction for the incident on the planets' surfaces solar energy the much more efficient accumulation.

It is all in the details...

Blackbody theory was developed initially by Kirchhoff for bodies in thermal equilibrium. It never has applied to bodies of different temperatures.

We are dealing with the long ago established blackbody EM ENERGY emission THEORY by applying it to the real rotating planets surfaces with the use of our very precise and very accurate approach.

Here’s the Wikipedia definition of a black body - “A black body or blackbody is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. … It is an ideal emitter: at every frequency, it emits as much or more thermal radiative energy as any other body at the same temperature.”

"It is an ideal emitter: at every frequency, it emits as much or more thermal radiative energy as any other body at the same temperature.”

Please, anyone, where in the definition of the blackbody is said that blackbody is warmed by the "incident electromagnetic radiation"? 

"A black body or blackbody is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence..."

"absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence..."

It is said so in the definition for the necessary reason to underline the notion that blackbody's emission is purely the blackbody's surface state temperature function, and should not be confused with any other source's incident radiation reflection. 

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In real objects, when deriving the Stefan-Boltzmann emission law J=σT⁴, the incident from surrounding environment the low temperature radiation falling upon the surface of hot filaments', which filaments were used in experiments for blackbody emission measurements, this environment originated low temperature incident radiation was simply omitted as negligible...

The ideal blackbody is a thermodynamic limiting case against which the performance of real radiating bodies can be compared.

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But to come to terms with this very important notion the real radiating bodies' radiative balance (energy in =energy out) should be very much correctly estimated. Thus we come again to the Φ -factor and to the Planet Surface Rotational Warming Phenomenon.

Why is the actual mean temperature of the moon so much lower than the effective temperature?

NASA lists the effective temperature of the moon at 270.6 kelvin. The mean temperature of the moon at the equator is 220 kelvin.

With no atmospheric effects, why is the surface temperature so much lower than the effective temperature predicts?

What factor is NOT part of the effective temperature formula that so dramatically affects the actual temperature of the moon?

I'll tell you what it is:

It is the Φ -the planet solar irradiation accepting factor. For smooth surface Moon Φ= 0,47.

Te.correct.moon = [ Φ (1-a) So /4σ ]¹∕ ⁴

Te.correct.moon = [ 0,47 (1-0,11) 1.362 W/m² /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =

Te.correct.moon = [ 0,47 (0,89) 1.362 W/m² /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =

Te.correct.moon = [ 2.510.168.871,25 ]¹∕ ⁴ =

Te.correct.moon = 223,83 Κ

This simple example clearly demonstrates the CORRECTNESS of the Φ -the planet solar irradiation accepting factor.

For smooth surface planets, like Moon, Φ= 0,47.

Conclusion:

From now on, for every smooth surface planet and moon, we should take in consideration instead of the planet blackbody effective temperature Te , the corrected VALUES of the planet blackbody effective temperature - the Te.corrected.

Table of results for Te and Te.corrected compared to Tsat and to Rotations/day for smooth surface planets and moons with Φ=0,47

Planet…….. Te.... Te.corrected…..Tsat…Rot/day

Mercury…..440 K…….364 K…...340 K…0,00568

Moon……….270 K…….224 K…...220 K.…0,0339

Earth………255 K…….210 K…...288 K..….1

Mars……….210 K…….174 K…..210 K..…0,9747

Europa…….95,2 K…...78,8 K….102 K...0,2816

Ganymede..107,1 K.....88,6 K…110 K….0,1398

Notice:

The number 0,47 for smooth surface in a parallel fluid flow is taken from the well measured and long ago known Drag Coefficient Data, where Cd =0,47 is for sphere. It is the portion of incident on sphere energy which should be resisted by sphere to remain in balance.

Conclusions:

The planet mean surface temperature equation

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

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

Planet…....Tmean….Tsat.mean

Mercury.....325,83 K…..340 K

Earth……....287,74 K…..288 K

Moon……...223,35 Κ…..220 Κ

Mars………..213,21 K…..210 K

The 288 K – 255 K = 33 oC difference does not exist in the real world.

There are only traces of greenhouse gasses. The Earth’s atmosphere is very thin.

There is not any measurable Greenhouse Gasses Warming effect on the Earth’s surface.

There is NO +33°C greenhouse enhancement on the Earth's mean surface temperature.

Both the calculated by equation and the satellite measured Earth's mean surface temperatures are almost identical: Tmean.earth = 287,74K = 288 K