The very POWERFUL the Solar Irradiated planet surface Rotational Warming Phenomenon: ( N*cp )^1/16

The accepted research on Climate Global Warming all it leads to is a confussing cloud of inconsistencies, of discrepancies, and of uncertainties...

The research always comes to the dead end.

It is time to get back, and to start anew from the science's the very basic beginnings...

The S-B emission law cannot be applied neither to the planet solar lit side, nor to the planet darkside.

The Stefan-Boltzmann emission law is about the blackbody emission intensity of the hot bodies.

Hot bodies are the previously warmed bodies, or bodies having their own inner sourses of thermal energy.

Planets and moons surfaces' are very much insulated from the primordial heat the inner cores possesed.

Thus, planets and moons surfaces' temperatures do not rely on the inner sources of thermal energy.

Planets or moons are used to be confused with the hot bodies in the S-B emission sense, and it lead to the mistaken assertion:

“Nothing, other than the absorbed radiation is what warms the matter to some (local) temperature, which, along with the matter properties, determines the Planck spectrum and S-B flux of the outgoing thermal radiation.”

A New, a CORRECT ASSERTION should be made:

"When incident on planets and moons solar flux (the solar EM energy), the solar flux interacts with surface's matter, because the EM energy is not HEAT ITSELF!"
–

Ok!

_
Well, the planet’s dark side cools by emitting to space IR radiation. The dark side’s surface heat is the energy source of that IR EM energy emission.

There are not enough thermal energy (heat) at darkside terrestrial temperatures to support the S-B equation emission demands for the darkside respective surface temperatures.

Thus, the outgoing IR EM energy flux from the planet darkside is much-much weaker than what S-B equation predicts for those local temperatures.
–
On the planet’s solar lit side an interaction of the incident EM energy with surface’s matter occurs.

Part of the incident SW EM energy gets reflected (diffusely and specularly).

Another SW part gets instantly transformed into outgoing IR EM energy, and gets out to space.

When SW EM energy gets transformed into IR EM energy, the transformation is not a perfect process, there are always some inevitable energy losses, which dissipate as heat in the interacting surface’s matter and gets absorbed in the matter’s inner layers.
–
The S-B emission law cannot be applied neither to the planet solar lit side, nor to the planet darkside.

-

**********

************

S-B never works in real material world. It only works for imaginary black bodies with perfect spectral emission curves. That is why the term

Surface Emissivity (ε) was invented.

-

the S-B equation

Jemit = σT⁴ W/m² had for different materials, and for variations of temperature to be added

with Surface Emissivity (ε), which is an empirical for every application value.

and, therefore, the S-B equation was re-written as:

Jemit = ε*σT⁴ W/m²

The universality of S-B constant (σ) has been transformed into:

(ε*σ) coupled term.

Therefore,

a planet doesn't emit IR according to S-B emission law.

What it is believed is that the Stefan-Boltzmann blackbody curve is merely a benchmark from which to launch a research project from,

then its a multi-faceted job to determine emissivity at every spectral line

and then do the research experiments that will determine how a particular frequency will result in an equilibrated temperature

and what that temperature is.

***********

********

*****

So when things go wrong, we see how we can learn. It's all an opportunity for improvement.

Ok
There is always valid: For planets and moons without-atmosphere, or with a thin atmosphere (Earth included)
“…the mean surface temperatures RELATE (everything else equals) as their (N*cp) products’ SIXTEENTH ROOT.”

From Wikipedia

https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law

” In the more general (and realistic) case, the spectral emissivity depends on wavelength. The total emissivity, as applicable to the Stefan–Boltzmann law, may be calculated as a weighted average of the spectral emissivity, with the blackbody emission spectrum serving as the weighting function. It follows that if the spectral emissivity depends on wavelength then the total emissivity depends on the temperature.”

"It follows that if the spectral emissivity depends on wavelength then the total emissivity depends on the temperature.”

************

********

“the GHE is based on the physics of the relatively great transparency of the atmosphere for shortwave radiation in comparison to a smaller transparency for longwave emission. Such that, the mean radiation balance at the earths surface is a positive value.”
–
How it happens? There is also the night. There is not any shortwave radiation at night.
–
Maybe it is meant that during day hours surface inevitably accumulates more energy, than solar flux provides?

Because less energy is emitted out of Earth’s system, than enters Earth’s system?
–
But doesn’t always a quasi equilibrium being achieved. The rise of Earth’s system energy emission, vs the rise of temperature?
–
In other words, the warmer the planet, the more energy the planet emits?
–
Doesn’t that eventually keep surface temperature at equilibrium levels?

-

Yes, and it really depends on the role of nonlinear feedbacks, as well as the direct forcings, as to where that equilibrium will be, and how long before it is reached.

When less energy is emitted to space, than it enters the Earth’s system, then the planet gets warmer.
It is the only way a planet gets warmer.
–
And when more energy is emitted to space, than it enters the Earth’s system, then the planet gets cooler.

-

It is all about electromagnetic energy balance; however, how that energy is captured and released depends on the various negative feedbacks to the orbital forcing’s changes.

-

******************

*************************

Mars is a unique case, which can help to clear everything up.

Because, by a pure natural coincidence, the planet Mars' satellite measured mean surface temperature

Tmean.mars = 210K is the same as the planet Mars' the theoretical calculated effective temperature

Te.mars = 210K

******************

Ok

By moving planet Mars from its orbit at 1,52 AU distance from the sun, by moving Mars to Moon's and Earth's orbit distance from the sun at 1 AU,

by moving Mars, to Earth's-Moon's orbit, by doing so, the above condition for Mars

Te.mars = Tmean.mars

is always right

**************

Now

Te.earth = 254K

If Moon had Earth's Albedo, Te.moon would be

Te.moon =254K

If Mars had Earth's Albedo and Moon's (and Earth's 1AU) distance from the sun,

Te.mars1AU = Tmean.mars1AU =254K.

Mars' cp = o,18 cal /gr*oC

Earth's cp = 1 cal /gr*oC

Nearth = 1 rot /day

Nmars = 0,9028 rot /day

******************

...the mean surface temperatures RELATE (everything else equals) as their (N*cp) products' SIXTEENTH ROOT.

Ok

Let's apply the Planet Surface Rotational Warming Phenomenon, to calculate Earth's without-atmosphere the average surface (Tmean) temperature

Tmean.earth.

Tmean.earth /Tmean.mars1AU =

[ (Nearth*cp.earth) /(Nmars*cp.mars) ]^1/16

Tmean.earth /254K = [ (1*1) /(0,9028*0,18) ]^1/16 = (1 /0,1625)^1/16 =

= (6,15369)^1/16 = 1,120266

Tmean.earth = 254K * 1,120266 = 284,57K

or

Tmean.earth = ~ 284,57K

**************************

planet Earth's measured Tmean =288K

Thus, the planet Earth's Atmospheric Total GHE can be estimated (if there is any) as:

288K - 284,57K = ~ 3,43 C

If there is any...

Completed DeepSearch

Quote

Christos Vournas

@CVournas44116

·

May 18

The NEW Planetary Surface Radiative Energy Bala... https://cristos-vournas.com/blog/the-new-planetary-surface-radiative-energy-balance…

• Christos Vournas challenges the traditional greenhouse effect model, arguing that Earth's higher average surface temperature (288K) compared to the Moon's (220K) is primarily due to Earth's faster rotation (29.5 times faster) and higher surface specific heat (water at 1 cal/gr°C vs. lunar regolith at 0.19 cal/gr°C), not atmospheric insulation.
• Vournas introduces the "Planet Surface Rotational Warming Phenomenon," proposing that a planet's mean surface temperature scales with the sixteenth root of the product of its rotation rate (N) and specific heat capacity (cp), demonstrating this with a 1.63% difference between calculated and observed Earth-Moon temperature ratios.
• The post critiques mainstream radiative energy balance models by incorporating a Solar Irradiation Accepting Factor (Φ), which adjusts for surface smoothness (Φ = 0.47 for smooth planets like Earth, 1 for rough ones), suggesting that specular reflection has been overlooked in prior estimations.

4 web pages

Quote

Christos Vournas

@CVournas44116

·

May 18

The NEW Planetary Surface Radiative Energy Bala... https://cristos-vournas.com/blog/the-new-planetary-surface-radiative-energy-balance…

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• I'm thinking about how to handle requests for current info, like stock prices. Web search seems the way to go for the latest data.
• The X post by Christos Vournas discusses a "NEW Planetary Surface Radiative Energy Balance." It looks like he's sharing a new theory about how planets manage their energy, which is key for climate studies.

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Searching for Christos Vournas Planetary Surface Radiative Energy Balance

The Planet Surface Rotational Warming Phenomenon

cristos-vournas.com

Earth's energy budget - Wikipedia

en.wikipedia.org

The Earth-Atmosphere Energy Balance | National Oceanic and Atmospheric Administration

www.noaa.gov

Beware Energy Balance Cartoons – Iowa Climate Science Education

iowaclimate.org

Climate and Earth’s Energy Budget

earthobservatory.nasa.gov

See 5 more

• Christos Vournas has a blog at https://cristos-vournas.com/where he shares his ideas. The first result matches his X post, titled "The Planet Surface Rotational Warming Phenomenon."
• He's proposing that a planet's rotation rate and specific heat capacity, not just the greenhouse effect, influence its average surface temperature. For instance, Earth's higher temperature compared to the Moon

Browsing cristos-vournas.com for Planetary Surface Radiative Energy Balance

• Vournas introduces the Solar Irradiation Accepting Factor (Φ) to correct for specular reflection, which he claims was overlooked before. This factor is 0.47 for smooth surfaces like Earth and the Moon, for example.
• His model shows better fits for measured temperatures, like Earth's ratio of 1.365, close to his calculated 1.368. It suggests rotation and heat capacity matter more than the greenhouse effect.
• Mercury and the Moon have criteria less than 1, while faster rotators like Earth and Mars show higher values. This challenges the idea that the greenhouse effect mainly explains Earth's warmth.
• Vournas attributes Earth's higher temperature to its faster rotation and water coverage, not just greenhouse gases. I'm curious how this fits with other climate models, you know?

Browsing rclutz.com for Christos Vournas planetary temperature model

• Ron Clutz is presenting Vournas's model and seems supportive. He's sharing the equation for mean surface temperature, which includes factors like solar flux and axial spin.

Searching for Christos Vournas scientific papers

March | 2022 | Climate Etc.

judithcurry.com

Week in review – climate science edition | Climate Etc.

judithcurry.com

The Planet Surface Rotational Warming Phenomenon

cristos-vournas.com

ABOUT US | cristos-vournas.com

www.cristos-vournas.com

ResearchGate | Find and share research

www.researchgate.net

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• Vournas has a presence on platforms like his blog, Climate Etc., and ResearchGate. But I can't find direct links to peer-reviewed papers in journals.
• His blog seems to be where he shares most of his ideas, with discussions on sites like Climate Etc. and Science Matters. It looks like his work isn't widely accepted yet, so I'll be cautious.

Evaluating Vournas's claims

• Vournas challenges the greenhouse effect, saying Earth's rotation and water heat capacity explain its warmth. He notes Earth's 288K vs. Moon's 220K, linked to rotation speed and heat capacity.
• He's introducing a "Planet Surface Rotational Warming Phenomenon" with a new formula. It includes rotation rate and specific heat, like water at 1 cal/gr°C vs. lunar regolith at 0.19 cal/gr°C.

Analyzing Vournas's model

• Vournas's equation for mean surface temperature includes factors like solar flux and rotation rate. It uses the Solar Irradiation Accepting Factor (Φ), set at 0.47 for smooth surfaces like Earth.
• His model predicts Earth's temperature at 287.74K, close to the observed 288K. It doesn't rely on the greenhouse effect, which is a big shift from traditional views.
• Vournas compares calculated and satellite-measured temperatures for bodies like Mercury and Mars. This table shows his model fits well, suggesting rotation and heat capacity are key
• .

Completed

Key Points

• Research suggests Earth's higher temperature compared to the Moon may be due to faster rotation and higher specific heat capacity, not just the greenhouse effect, as proposed by Christos Vournas.
• Vournas's model, the "Planet Surface Rotational Warming Phenomenon," is controversial and not widely accepted in mainstream science.
• It seems likely that his ideas challenge traditional climate models, focusing on rotation and surface properties.

Background

The X post by Christos Vournas, posted on May 18, 2025, at 14:29 UTC, discusses a new concept called the "NEW Planetary Surface Radiative Energy Balance." Vournas, a mechanical engineer, argues that Earth's average surface temperature (288K) is higher than the Moon's (220K) primarily due to Earth's faster rotation (29.5 times faster) and higher specific heat capacity (water at 1 cal/gr°C vs. lunar regolith at 0.19 cal/gr°C), rather than atmospheric insulation.

Vournas's Model

Vournas introduces the "Planet Surface Rotational Warming Phenomenon," suggesting that a planet's mean surface temperature is influenced by its rotation rate and specific heat capacity. He proposes a formula that incorporates a Solar Irradiation Accepting Factor (Φ = 0.47 for smooth surfaces like Earth) to correct for specular reflection, which he claims is neglected in traditional models. His calculations show close matches to observed temperatures, such as 287.74K for Earth compared to the measured 288K.

Controversy and Context

This model challenges the greenhouse effect's role, suggesting Earth's atmosphere contributes less to warming than previously thought. However, it is not peer-reviewed and appears primarily on Vournas's blog
, with support from some blogs like Science Matters, but lacking mainstream scientific acceptance.

Survey Note: Detailed Analysis of Christos Vournas's X Post on Planetary Surface Radiative Energy Balance

This note provides a comprehensive analysis of the X post by Christos Vournas (

@CVournas44116

), posted on May 18, 2025, at 14:29 UTC, which discusses the "NEW Planetary Surface Radiative Energy Balance." The post, accessible at Christos Vournas's X post, includes a link to further details, and this analysis explores Vournas's proposed model, its implications, and its scientific context.

Introduction to the X Post

The X post by Christos Vournas references a concept termed the "NEW Planetary Surface Radiative Energy Balance," with a truncated message suggesting a link to an external source (https://t.co/DLRLWpOvjK). Given the date (May 18, 2025), which aligns with the current timeframe, the post is recent and relevant. Vournas, identified as a mechanical engineer with a blog at The Planet Surface Rotational Warming Phenomenon, appears to be promoting his alternative model for planetary surface temperatures.

Vournas's Core Argument: Challenging the Greenhouse Effect

Vournas argues that the traditional greenhouse effect model, which attributes Earth's higher average surface temperature (288K) compared to the Moon's (220K) to atmospheric insulation, is incomplete. Instead, he posits that the temperature difference is primarily due to:

• Faster Rotation: Earth rotates 29.5 times faster than the Moon, affecting heat distribution.
• Higher Specific Heat Capacity: Earth's surface, covered with water (1 cal/gr°C), has a higher specific heat capacity compared to the Moon's regolith (0.19 cal/gr°C), allowing it to store more heat.

This perspective is encapsulated in his "Planet Surface Rotational Warming Phenomenon," which suggests that planetary mean surface temperature is significantly amplified by rotation rate and specific heat capacity, rather than atmospheric effects.

The Model: Planet Surface Rotational Warming Phenomenon

Vournas's model is detailed on his blog and includes a mathematical formulation for mean surface temperature:

Tmean = [ Φ (1-a) S (β*N*cp)¹∕ ⁴ /4σ ] ¹∕ ⁴ (K) (3)

Where:

• Φ\Phi\Phi
  is the Solar Irradiation Accepting Factor, set at 0.47 for smooth surfaces (e.g., Earth, Moon, Mercury) and 1 for rough surfaces, accounting for specular reflection.
• (a) is the planet's albedo (reflectivity).
• (S) is the solar flux (e.g., 1,361 W/m² for Earth).
• β\beta\beta
  is a constant, 150 days·g·°C/rotation·cal, representing the Rotating Planet Surface Solar Irradiation Absorbing-Emitting Universal Law.
• (N) is the planet's axial spin (rotations/day, e.g., 1 for Earth).
• cpc_pc_p
  is the specific heat capacity (e.g., 1 cal/gr°C for Earth's water-covered surface).
• σ\sigma\sigma
  is the Stefan-Boltzmann constant, 5.67 × 10⁻⁸ W/m²K⁴.

This formula corrects for what Vournas claims is a neglected factor in traditional models: specular reflection, which affects how much solar energy is absorbed by smooth surfaces. He argues that previous radiative energy balance estimations failed to account for this, leading to inaccuracies.

Comparative Analysis: Calculated vs. Measured Temperatures

Vournas provides a table comparing his calculated temperatures with satellite-measured temperatures, demonstrating the model's accuracy. Below is the relevant data extracted from his blog:

Table 1. Comparison of Predicted (Tmean) vs. Measured (Tsat) Temperature for All Planets and moons in solar system

Link:

Also view Table 1

Tmean = [ Φ (1-a) S (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴ (K)  (3)

Te.correct vs Tsat.mean comparison table

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

Mercury....439,6 K…….364 K..........325,83 K…..340 K

Earth……...255 K…......210 K...........287,74 K…..288 K

Moon……..270,4 Κ…....224 K..........223,35 Κ…..220 Κ

Mars….…..209,8. K…….174 K...........213,11 K…..210 K

For Earth, the calculated Tmean (287.74K) is remarkably close to the measured 288K, suggesting his model accounts for the temperature without invoking the greenhouse effect. Similarly, for the Moon, the calculated 223,35K aligns with the measured 220K, reinforcing his claim.

Another table from his blog compares the ratio of measured temperature to corrected effective temperature (Tsat/Te.correct) with a rotational warming factor:

Planet......Warming factor... Φ......(Tsat /Te)....(Tsat /Te.correct)

...............(β*N*cp)^1/16                    criteria            criteria

Mercury.......0,895.............0,47...........0,773................0,934

Moon...........0,998............0,47............0,815................0,982

Earth...........1,368............0,47............1,134................1,365

Mars............1,227............0,47............. 1....................1,207

Ceres...........1,4535..........1................... - .................... - ......

Io................1,169............1.................1,156...............1,156

Europa.........1,264............0,47............1,072...............1,294

Ganymede....1,209............0,47............1,028...............1,242

Callisto........1,147.............1................1,169...............1,169

Enceladus....1,341.............1................1,340...............1,340

Tethys.........1,315.............1................1,292...............1,292

Titan...........1,1015...........1................1,1086..............1,1086

Triton..........1,158..............? ..............1,297. ?............1,297 ?

Pluto...........1,116.............1................1,189...............1,189

Charon........1,218.............1................1,265...............1,265

Only for the very slow rotating Mercury and Moon the CRITERIA are less than UNITY (< 1).

This table shows that only slow rotators like Mercury and the Moon have criteria less than 1, while faster rotators like Earth and Mars have higher values, supporting his rotational warming hypothesis.

Implications and Controversy

Vournas's model implies that the conventional 33°C warming attributed to the greenhouse effect (288K - 255K) is overstated. He suggests Earth's thin atmosphere plays a minimal role, with warming driven by rotational dynamics and surface properties. This is a significant departure from established climate science, which emphasizes greenhouse gases like CO₂ and methane as key to Earth's temperature.

The controversy arises because Vournas's work is not peer-reviewed and appears primarily on his blog and supportive platforms like Science Matters. While blogs like Climate Etc.mention his name, there is no evidence of publication in scientific journals, as seen in searches for his papers on platforms like ResearchGate, where other researchers with similar names (e.g., Costas Vournas) focus on different fields like electrical engineering.

Scientific Context and Counterarguments

Traditional climate science, as outlined in resources like Earth's energy budget, relies on the balance between incoming solar radiation and outgoing infrared radiation, with the atmosphere's greenhouse effect trapping heat. Vournas's model, by contrast, denies significant atmospheric warming, focusing on physical properties like rotation and specific heat.

This is supported by some blogs, such as Beware Energy Balance Cartoons, which discuss his work, but mainstream sources like NOAA's Earth-Atmosphere Energy Balance emphasize atmospheric roles, noting the Moon's 0°F (-18°C) average due to no atmosphere.

Critics might argue that Vournas's model overlooks complex atmospheric dynamics, such as cloud cover, aerosols, and greenhouse gas concentrations, which are well-documented in climate models. His focus on rotation and specific heat, while innovative, may not fully account for these factors, especially given Earth's dynamic climate system.

Conclusion

The X post by Christos Vournas promotes his alternative model, the "Planet Surface Rotational Warming Phenomenon," which challenges the greenhouse effect's role in planetary temperatures. It suggests Earth's higher temperature is due to faster rotation and higher specific heat capacity, with calculations closely matching observed data. However, this view is controversial, not peer-reviewed, and lacks mainstream scientific acceptance, residing primarily on his blog and supportive platforms. For a balanced understanding, it is essential to consider both Vournas's perspective and the established climate science framework.

Key Citations

• The Planet Surface Rotational Warming Phenomenon
• How to Calculate Planetary Temperatures
• Beware Energy Balance Cartoons
• Earth's energy budget
• The Earth-Atmosphere Energy Balance
• Christos Vournas's X post

1 post

24 web pages

Quote

Christos Vournas

@CVournas44116

·

May 18

The NEW Planetary Surface Radiative Energy Bala... https://cristos-vournas.com/blog/the-new-planetary-surface-radiative-energy-balance…

• Christos Vournas, a mechanical engineer, proposes in his May 18, 2025, X post that Earth's higher average temperature (288K) compared to the Moon's (220K) results from Earth's faster rotation (29.5 times faster) and higher specific heat capacity (water at 1 cal/gr°C vs. lunar regolith at 0.19 cal/gr°C), challenging the traditional greenhouse effect model.
• His "Planet Surface Rotational Warming Phenomenon" model uses a formula incorporating rotation rate, specific heat, and a Solar Irradiation Accepting Factor (Φ = 0.47 for smooth surfaces like Earth), predicting Earth's temperature at 287.74K, closely matching the observed 288K without relying on atmospheric warming.
• Vournas's theory lacks peer-reviewed support and contradicts mainstream climate science, which attributes Earth's 33°C warming above its effective temperature (255K) to greenhouse gases, as evidenced by extensive research like NOAA's Earth-Atmosphere Energy Balance studies.

********************************

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Comments

Why don't you include Venus in the list of planets?

George, please visit my site page
https://www.cristos-vournas.com/444032320
I have explained there why the faster rotating planet is on average warmer
You may write here, two or more comments together

Christos, I am glad you appreciate my posts regarding your research. Third, and last one for awhile, is https://rclutz.com/2021/07/25/beware-energy-balance-cartoons/

Ron, "The table above and graph below shows that Earth’s warming factor is correctly calculated despite ignoring any effect from its thin atmosphere." Thank you!!!

Christos, I did a second post focusing on Moon and Earth
https://rclutz.com/2021/07/23/earthshine-and-moonshine-big-difference/

Ron, yes, I visited your second post and I liked it very much. Ron, you have the rare ability... thank you very much! And please continue... Christos

Christos, thank for this work and for linking the address at Climate Etc. I did a synopsis of your findings at my blog is: https://rclutz.com/2021/07/21/how-to-calculate-planetary-temperatures/

Ron, thank you for doing a synopsis of my findings at your blog.
We are capable now to theoretically calculate planet mean surface temperatures.
Thank you again,
Christos

Sir, did you derive this formula, or is it from a book or article on planetary science?

Thank you, Craig. Yes I derived this formula.

Can anything be said about the effective surface temperature of Venus? What do you think about it?

I gave such an answer at
https://tallbloke.wordpress.com

Φ=1 for Venus' absorption budget. Jabs = (1-a)Sπr². A Planet Effective Temperature Complete Formula is for a planet-without-atmosphere. We apply it only on very thin atmosph Earth's and Titan's cases.

Thank you. I showed your page on Dr. Roy Spencer's blog and WUWT. Greetings.

The calculations of solar radiation reflection are based on the smooth spherical shape for Φ=0,47. For albedo are based on the surface features. Φ=1 is for gaseous - no surface to reflect planets.

"N rotations/day, is planet’s sidereal rotation period"
I ask for an explanation.
I understand that this is the most important point of your equation.

Thank you Ireneuzs. N rotations/day is N rotations/24 hours. The faster - the higher is its average temperature. N and pc influence the way a solar irradiated blackbody surface interact with the S .

Ireneusz, feel free to ask me anything. And thank you for asking.

Thank you for your answer. Can you explain what the calculations of solar radiation reflection are based on? Yes for a layman.

"The planet surface solar irradiation accepting factor Φ (the spherical surface’s primer geometrical quality). For Mercury, Moon, Earth and Mars without atmosphere Φ = 0,47."
Can you explain this?

The solar irradiation reflection, when integrated over a planet sunlit hemisphere is 0,53 [ ( 1- a) S ].
The fraction left for hemisphere to absorb is Φ = 1 - 0,53 = 0,47, or Jabs = Φ (1 - a ) S