Consequently, the planet mean surface temperature Tmean is based on Stefan-Boltzmann emission law,
and on precise estimation by planet surface the total amount of emitted energy
and on the different for each planet the energy emission distribution (the temperatures distribution) over surface area - resulting in the very POWERFUL
the Planet Surface Rotational Warming Phenomenon.
( ...on the way the energy emission is distributed over the entire planetary surface – the Planet Surface Rotational Warming Phenomenon. )
Earth's /Moon's example
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.
Earth and Moon are at the same distance from the sun. But Moon receives 28% more solar energy than Earth, because Moon's average surface Albedo is significantly lower (Moon’s Albedo a =0,11 vs Earth’s Albedo a =0,306).
Yet Earth is on average warmer 68°C than Moon.
The average surface temperature difference of 68°C can be explained only by the Planet Surface Rotational Warming Phenomenon.
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.
Earth is on average warmer than Moon not only because of the Earth having 29,53 times faster rotational spin.
Earth also 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.
Tmean.mars = 213,21 K is only by 1,53% higher than that measured by satellites
Tsat.mean.mars = 210 K !
We have calculated The Planet Mean Surface Temperatures by the use of the New Equation:
Tmean = [ Φ (1-a) S (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴
for all the twenty (20) major planets and moons in solar system. The results are very close to the satellite measurements.
The detailed Mean Surface Temperatures calculations for each and every planet and moon in solar system, by the use of the New Equation, are posted in the next pages of this site.
Φ - is the dimensionless Solar Irradiation accepting factor - very important.
It is a realizing that a sphere's surface "absorbs" the incident solar irradiation not as a disk of the same diameter, but accordingly to its spherical shape.
For a smooth spherical surface
Φ = 0,47
Φ factor explanation
The Φ - solar irradiation accepting factor - how it "works".
It is not a planet specular reflection coefficient itself. There is a need to focus on the Φ factor explanation. Φ factor emerges from the realization that a sphere reflects differently than a flat surface perpendicular to the Solar rays.
Φ – is the dimensionless Solar Irradiation accepting factor.
"Φ" is an important factor in the Planet Mean Surface Temperature Equation:
It is very important the understanding what is really going on with by planets the solar irradiation reflection. There is the specular reflection and there is the diffuse reflection. The planet's surface Albedo "a" accounts only for the planet's surface diffuse reflection.
The importance of the Solar Irradiation Accepting Factor Φ.
For smooth surface planets (like Earth) the Φ =0,47
So = 1362 W/m² - is the solar flux on the TOA (the top of atmosphere). It is also called the Solar Constant.
a = 0,306 - is the Earth's average surface Albedo.
Thus the incident on Earth solar energy not reflected from the planetary cross-section disk is:
This not reflected energy doesn’t get distributed over the hemisphere or over the sphere.
The not reflected portion of 444 W/m² is INTERACTING with planet’s surface matter on the very instant of incidence.
In short, the Φ -Factor is not the planet specular reflection portion itself. The Φ -Factor is the Solar Irradiation Accepting Factor (in other words, Φ is the planet surface spherical shape and planet surface roughness coefficient).
How to formally prove Φ -Factor's correctness in the
Ein = Eout formula.
- Answer: The Energy in:
Ein = (1-a)S W/m²
used in the blackbody planet effective temperature Te is an empirical assertion, which is not based on any theoretical research, not to say, its correctness has not been demonstrated, quite the opposite…
– The Energy in:
Ein = Φ(1-a)S W/m²
is based on measurements (the Drag Coefficient for smooth spheres in a parallel fluid flow Cd = 0,47), and it is demonstrated to be the correct one.
The Φ -Factor's importance is explained in every detail in next pages in this site.
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.
Planets and moons do everything differently.
Βy DEFINITION, the planet theoretical effective radiative temperature’s formula doesn’t consider planet rotating. The formula is for planet with uniform surface temperature, and it is for planet with uniform surface irradiance.
Te = [ (1-a) S /4σ ]¹∕ ⁴
The Te cannot be some kind of a theoretical limitation for planets and moons without-atmosphere the mean surface temperatures not to exceed their theoretical Te calculated temperature.
Planets and moons do not have uniform surface temperature; and they do not have uniform surface irradiance either. And planets and moons do ROTATE.
Consequently, the Te = [ (1-a) S /4σ ]¹∕ ⁴ is not capable to describe the real planets’ and moons’ the mean surface temperatures.
Planet mean surface temperature cannot be associated with any kind of BB profile spectrum.
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 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 cannot be associated with any kind of BB profile spectrum.
Two planets with the same mean surface temperature may emit dramatically different amounts of IR outgoing EM energy.
Earthrise, taken in 1968 Dec 24 by William Anders, an astronaut on board Apollo 8
Moon and Earth - so close to each other - and so much different...
We may conclude that for a faster rotating planet there is the phenomenon of its warmer surface...
The Planet Surface Rotational Warming Phenomenon
I’ll try here in few simple sentences explain the very essence of how the Planet Surface Rotational Warming Phenomenon occurs.
A planet surface doesn't absorb solar energy first, gets warmed and only then emits IR EM energy.
No, a planet surface emits IR EM energy at the very instant solar flux hits the matter.
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’ (without atmosphere, or with a thin atmosphere) the mean surface temperatures relate (everything else equals) according to their (N*cp) products’ sixteenth root.
1). The faster rotating planet has a less differentiated surface temperatures distribution. Thus, for the same amount of solar energy transformed into HEAT and accumulated in inner layers, the faster rotating planet has a higher average surface temperature.
2). The not reflected portion of the incident SW EM energy is NOT ENTIRELY transformed into HEAT.
3). In addition, the faster rotating planet is able to transform into HEAT and accumulate in inner layers LARGER amounts of the incident on surface solar energy, than a slow rotating planet.
Rotational Warming Phenomenon states about the (N*cp) products' sixteenth root, not only the planetary rotational spin (N) is involved, but also the planet average surface SPECIFIC HEAT (cp)!
the Incomplete Equation of the Planet Blackbody Effective Temperature
Te = [ (1-a) S / 4 σ ]¹∕ ⁴ K
should be abandoned, because it is very much wrong!
The false "RADIATIVE equilibrium" CONCEPT
Also, I should note that the average solar flux is a pure mathematical abstraction.
Solar flux does not average over the planet surface in the real world.
When we "imagine" solar flux averaging on the entire planet surface it is like having (the false RADIATIVE equilibrium CONCEPT), it is like having the actual planet being enclosed in an imaginary sphere, which sphere is emitting towards the planet surface a constant flux of 240 W/m^2.
But it is not what happens in the real world!
Planet is not a uniformly heated body.
Planet is a solar irradiated from one side spherical object.
The irradiated side is not uniformly irradiated.
The planet’s opposite side is in total darkness.
Thus, a planet is not a blackbody!
I use the Stefan-Boltzmann emission law in the right way.
The planet black body formula averages solar flux over the entire planet area in form of HEAT.
The New equation doesn’t average solar flux over the entire planet area in form of HEAT. For the New equation the outgoing EM is a result of the incident on the planet surface solar energy INTERACTION process with the matter.
Black body by definition transforms its calorimetric HEAT into its absolute temperature T fourth power EM emission intensity.
On the other hand, planet doesn’t emit EM energy supplied by a calorimetric source. The planet’s surface temperature is INDUCED by the incident on the planet solar EM flux.
Only a small portion of the incident solar EM energy is transformed into HEAT. The vast majority of the incident solar energy is IR emitted at the same very moment of incidence and interaction with matter.
This EM energy induces the planet surface temperature without being accumulated in the inner layers.
It is entirely different physics when compared with the “quiet” blackbody calorimetric HEAT black body emission phenomenon.
Earth “absorbs” 28% less solar energy than Moon (Albedo Earth a =0,306; Albedo Moon a =0,11).
The measured Earth’s average surface temperature Tearth=288K. The measured Moon’s average surface temperature Tmoon=220K.
Mars orbits sun at R = 1,524 AU.
(1/R²) = (1/1,524²) = 1/2,32 Mars has 2,32 times less solar irradiation intensity than Earth has
So the solar flux at Mars’ orbit is 2,32 times weaker than on Moon too.
The measured Mars’ average surface temperature Tmars=210K.
Which is close to the measured Moon’s average surface temperature Tmoon=220K.
Mars' Albedo a =0,250; Moon's Albedo a =0,11.
It can be shown, that for the same Albedo Mars and Moon would have the same average surface temperature.
Let's see now:
Tearth =288K (for Earth having 28% less than Moon solar energy "absorbed")
Tmars =210K (for Mars having 2,32 times less than Moon solar energy "absorbed")
These obvious discrepancies can be explained only by the Earth's and by the Mars' much faster than Moon's rotational spins.
These obvious discrepancies can be explained only by the Planet Surface Rotational Warming Phenomenon.
The Graph Ratio of Planet Measured Temperature to Corrected Blackbody Temperature (Tsat /Te.correct), as a linear function of the
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.
The Solar Radiation Input.
Every spot on planet surface experiences its peak hot and cold temperature. The less are those differences, the higher is the average surface temperature for the same not reflected portion of the incident solar flux.
The (N*cp)^1/16 is the way the planet average surface temperature “responds” to that.
The faster the rotation, the less time every spot is exposed to the solar flux’ EM radiative energy, the less the skin surface layer’s INDUCED temperature is.
The more atoms (higher surface cp) are getting exposed (INTERACTED) on the skin layer to the solar flux’ EM radiative energy, the less the skin surface layer’s INDUCED temperature is.
The Planet Surface Rotational Warming Phenomenon:
It is well known that when a planet rotates faster its daytime maximum temperature lessens and the night time minimum temperature rises. But there is something else very interesting happens.
When a planet rotates faster it is a warmer planet.
The physics notion: solar radiation input.
It is important to differentiate between the “not reflected portion of the incident solar flux ” and the “solar radiation input.”
Well, the “not reflected portion of the incident solar flux” is not even ” with solar radiation input.
The “solar radiation input” is only a part of the “not reflected portion of the incident solar flux”, it is only a part of “Energy in”.
The “solar radiation input” is only the energy accumulated in inner layers. It is not the entire “Energy in”.
Energy in = energy out
Energy in = πr²Φ*S*(1-a) (W) is the “not reflected portion of the incident solar flux”
Jemit = 4πr²σΤmean⁴ /(β*N*cp)¹∕ ⁴ (W) is the energy out
When hitting matter the solar EM energy INDUCES surface skin layer’s temperature.
The higher this temperature, the more the instantly emitted IR EM radiative energy out, and the lesser the solar radiation input.
The lesser this temperature, the less the instantly emitted IR EM radiative energy out, and the more the solar radiation input.
When planet rotates faster it has for a constant
“Energy in = πr²Φ*S*(1-a) (W)” a larger solar energy input.
The entire “Energy out” = Jemit = 4πr²σΤmean⁴ /(β*N*cp)¹∕ ⁴ (W) consists from both “the instantly emitted IR EM radiative energy out” plus the solar radiation input.
When rotating faster, planet surface has more “solar radiation input” to get rid of, thus the Tmean gets “balanced” at higher level.
So, the higher the (N*cp)¹∕ ⁴ is, the higher should be the Tmean⁴.
That is why it is so powerful the Planet Surface Rotational Warming Phenomenon.
“The amount of solar radiation received does not change because a planet spins faster. It has to radiate away what it receives.”
It is a basic principle! The difference is that, when interacting with matter, the “not reflected portion of solar flux” is not getting inside the skin layer in its entirety. A very considerable part of it gets IR emitted on the very instant the solar EM energy hits the surface. This part of energy goes immediately out, it INDUCES the surface temperature on the instant of incidence, and that temperature is the temperature of that spot at that particular instant.
And, there is another part, the “SOLAR RADIATION INPUT” which is on that instant is accumulated in the inner layer. And this part is radiated away later…
Planet always radiates away what it receives. Planet with a higher (N*cp) product has this second part, the “SOLAR RADIATION INPUT” larger, and the on the instant of incidence IR emitted amount of solar EM energy is smaller, because a planet with a higher (N*cp) product INDUCES a lower on the spot of incidence the skin layer’s temperature.
We shall call from now on as “the “SOLAR RADIATION INPUT” the amount of energy the Solar Flux – Planet Surface INTERACTION process manages to PUT IN the planet inner layer.
The First 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.
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.
The planet mean surface temperature New equation is written for planets and moons WITHOUT atmosphere. The results of calculations are remarkably exact!
When applied to Earth (Without Atmosphere) the New equation calculates Earth's mean surface temperature as 287,74K, which is very much close to the satellite measured 288K.
It happens so because Earth's atmosphere is very thin and, therefore, doesn't have any essential greenhouse effect on the Earth's average surface temperature.
We have to answer these two questions:
1. Why Earth’s atmosphere doesn’t affect the Global Warming?
It is proven now by the Planet's Mean Surface Temperature Equation calculations. There aren’t any atmospheric factors in the Equation. Nevertheless the Equation produces very reasonable results:
Tmean.earth = 287,74 K,
calculated by the Equation, which is the same as the
Tsat.mean.earth = 288 K,
measured by satellites.
Tmean.moon = 223,35 K, calculated by the Equation, which is almost identical with the
Tsat.mean.moon = 220 K, measured by satellites.
2. What causes the Global Warming then?
The Global Warming is happening due to the orbital forcing.
And… what keeps Earth warm at Tmean.earth = 288 K, when Moon is at Tmean.moon = 220 K? Why Moon is on average 68 oC colder? It is very cold at night there and it is very hot during the day…
Earth is warmer because Earth rotates faster and because Earth’s surface is covered with water.
Does the Earth’s atmosphere act as a blanket that warms Earth’s surface?
No, it does not.
It is all in the details...
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.