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

What we see, is that when for the planets and moons their respective (N*cp) products are higher, then the planets and moons temperatures CRITERIA (Tsat /Te.correct) deflect towards the higher values.

Introduction

  "Christos Vournas’ X post links to his blog,http://cristos-vournas.com, where his "Rotational Warming Phenomenon" theory, arguing that Earth’s higher temperature compared to Moon results from its faster rotation and higher surface heat capacity (N*cp), not from Warming from Atmosphere.

 Opponent's comment: 

" mainstream climate science relies on extensive data like ice core samples showing CO2’s role in rapid warming."

 Answer:

" Density 1562kg/m³(solid at 1 atm (100 kPa) and −78.5 °C (−109.3 °F)) "

Link: Carbon dioxide - Wikipedia

On Earth the CO2 is a condencing gas when it is in an extreme low temperatures (less than −78.5 °C (−109.3 °F)).

That much low temperatures may occur at Earth's polar regions and at high altitudes (Greenland, Antarctica, at some 3.000 m high glaciers) and, more intensively, when Earth is in planetary colder periods (Ice Ages).

The higher CO2 content in ice core samples is related to the extremely lower temperatures when the ice in samples was created. 

The mechanism of CO2 capture in ice - it is not the air captured in snow flakes and being suppressed in ice... what is used to think happens - and so it was mistakenly concluded the high CO2 content in ice cores is related to higher CO2 concentration in atmospheric air - and, because it is  (also mistakenly asserted) according to the Greenhouse Gases Warming narrative - it was said, it should have been a much warmer climate at the times when the higher CO2 content in the ice core samples was created... (wich is a great mistake).

The mechanism - when it is extremely cold, less than −78.5 °C (−109.3 °F), the CO2 gets solidified and it precipitates out of air and on the high elevated glaciers' surfaces, where it gets captured in snow and suppressed in ice.

And that explains the higher CO2 content in ice core samples.

Thus the higher CO2 content captured in ice core samples should be related to the colder Earth's climate at that times.

And the mistake after mistake  - it led to the assertion that at Holocene Optimum times (~11.000 years ago) Earth's climate was much warmer than now (optimum), but actually it was much colder.

Earth's climate doesn't get cooler since, but Earth climate gets warmer.

Earth is in a slow, orbitally forced natural warming pattern. 

And to be more precise, Earth experiences now the culmination phase of the present orbitally forced natural warming pattern. 

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

The higher CO2 content in ice core samples relates to colder periods

  "Christos Vournas argues that higher CO2 levels in ice core samples, often linked to warmer climates in mainstream science, actually indicate colder periods because CO2 solidifies and precipitates at extremely low temperatures (below −78.5°C) in polar regions during Ice Ages, getting trapped in ice.

  He challenges the greenhouse gas warming narrative, suggesting that the mechanism of CO2 capture in ice is not from trapped air in snowflakes but from CO2 freezing out of the atmosphere, a process he claims has been misinterpreted to support warmer climate assumptions during times like the Holocene Optimum (~11,000 years ago).

  Vournas asserts Earth is currently in a natural, orbitally forced warming phase, not cooling, contradicting mainstream views by proposing that high CO2 in ice cores correlates with colder climates, supported by CO2’s physical property of solidifying at low temperatures as noted on Wikipedia."

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

https://en.wikipedia.org/wiki/Dry_ice

At pressures below 5.13 atm and temperatures below −56.4 °C (216.8 K; −69.5 °F) (the triple point), CO₂ changes from a solid to a gas with no intervening liquid form, through a process called sublimation.^[a] The opposite process is called deposition, where CO₂  changes from the gas to solid phase (dry ice). At atmospheric pressure, sublimation/deposition occurs at 194.7 K

(−78.5 °C; −109.2 °F).^[2]

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

Sensible Heat /Latent Heat ratio

Opponent:

"Christos Vournas's claims in his X post are not aligned with mainstream climate science. His interpretation of CO2 in ice cores as indicating colder periods is incorrect, as CO2 is trapped as gas and correlates with warmer periods.

His view on current warming being due to orbital forcing, not human activity, is unsupported, given the rapid pace and magnitude of modern warming driven by greenhouse gases. These findings highlight the importance of aligning interpretations with established scientific data and consensus."

(Emphasis added)

Answer:

"given the rapid pace and magnitude of modern warming"

Yes, in last 100 years we observe a rapid pace of modern warming.

Let's explain:

Earth's surface is covered about ~ 70% with oceanic waters. Also vast areas on land have water in soils and in plants...

Water is mostly present in liquid phase, but also water exists on Earth's surface in solid phase (snow and ice).

We have the seasonal changes in temperatures, because of Earth's axial tilt (23,4°).

And Earth is in a slow orbitally forced warming trend.

Every year there are colder periods (winters), and there are warmer periods (summers).

In winters the area of the sea-ice cover extends, and in summers the area of the sea-ice cover shrinks.

Also in winters the sea-ice gets thicker, and on summers the sea-ice gets thinner.

Earth is in a slow orbitally forced warming trend. Which means Earth's surface, year after year, continuously accumulates some excessive quantities of solar energy as heat.

Because Earth in its annual cycle around sun is currently subjected to a positive radiative energy balance.

Energy absorbed > Energy emitted

Every year in summers the sea-ice covered areas shrink a little more.

And every year in winters the sea-ice covered areas extend a little less.

The phenomenon is due to the heat accumulation process.

From Wikipedia:

Link: Water - Wikipedia

"Water is the only common substance to exist as a solid, liquid, and gas in normal terrestrial conditions.^[

States

The three common states of matter

Along with oxidane, water is one of the two official names for the chemical compound H₂O;^{[54 ]} it is also the liquid phase of H₂O.^[55]

The other two common states of matter of water are

the solid phase, ice, and the gaseous phase, water vapor or steam.

The addition or removal of heat can cause phase transitions: freezing (water to ice), melting (ice to water), vaporization (water to vapor), condensation (vapor to water), sublimation (ice to vapor) and deposition (vapor to ice).^[56] "

Sensible heat

To distinguish between the energy associated with the phase change (the latent heat) and the energy required for a temperature change, the concept of sensible heat was introduced.

The addition or removal of heat can cause phase transitions.

Here it is the key point:

Because of the cyclical seasonal changes, every year there are the Huge Phase Transitions Processes in Earth's system.

Enormous quantities of sea-ice get involved in melting in summers, and enormous quantities of sea-water get involved in freezing in winters.

Every year there is less and less sea-ice left.

Why is then the accelerated pace of warming?

Because what sea-ice has left is localized at much higher latitudes on the globe. Because there is not sea-ice at lower latitudes, as it was there a 100 years ago.

Thus, for the yearly portion of the excessive accumulated heat to effectively reach the remained sea-ice fields and to be consumed in ice melting as latent heat, without a significant along-side temperature rise becomes more and more difficult task.

We have the yearly accumulated excessive heat necessarily subjected to rise the Global temperature - more sensible heat in action - on the latent-heat-to-be expence.

The (Sensible Heat) /(Latent Heat) ratio (for a given radiative energy positive imbalance) is what determines the pace of the present-time planetary warming.

When the ratio is higher, planet experiences more rapid warming, than when it is lower.

At MWP (Medieval Warm Period) the ratio was higher, and at LIA (Little Ice Age) the ratio was lower.

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

The sensible heat to latent heat ratio (SH/LH)

The sensible heat to latent heat ratio (SH/LH) reflects how absorbed radiative energy is partitioned between directly warming the surface (sensible heat) and driving, evaporation, ice melting or sublimation (latent heat).

A higher SH/LH ratio means more energy goes to warming, accelerating temperature rise, while a lower ratio means more energy is used for evaporation and ice melting slowing warming.

During the Medieval Warm Period (MWP, ~950–1250 CE), conditions like reduced cloud cover or drier soils in some regions, or still colder sea-ice cover (still far lower from melting point) could have increased the SH/LH ratio, favoring sensible heat and faster warming.

In the Little Ice Age (LIA, ~1300–1850 CE),

increased cloudiness, wetter conditions, or a warmer sea-ice cover (closer to melting point) likely lowered the SH/LH ratio, diverting energy to latent heat and slowing warming.

Exact ratios depend on regional climate dynamics, vegetation, and moisture availability, but data is sparse for these periods.

Modern studies suggest global SH/LH varies (e.g., ~0.2–0.5 in arid regions, lower in wetter ones).

Without specific MWP or LIA measurements, we infer higher MWP ratios from proxy evidence of warmth and lower LIA ratios from cooler, wetter reconstructions.

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

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…

Completed DeepSearch

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Considering search tools

• 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.

Searching for https://t.co/DLRLWpOvjK

http://bit.ly/39HcCXs

t.co

http://bit.ly/2fsKxdC

t.co

World's Shortest URL Shortener - T.LY URL Shortener, Custom Domain & Short Link Management

t.ly

• The search for https://t.co/DLRLWpOvjKdidn't resolve the URL. It seems like the search engine can't handle shortened links directly, which is a bit tricky.

Browsing t.co for content of the page

• That browse tool didn't work out. It says there's no readable text, probably because the

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

See 5 more

• 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.

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

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

Faster rotation makes more heat get absorbed deep inside the lamb

Rotisserie - Wikipedia

"Rotisserie, also known as spit-roasting, is a style of roasting where meat is skewered on as pit – a long, solid rod used to hold food while it is being cooked over a fire in a fire place or over a campfire, or roasted in an oven. This method is generally used for cooking large joints of meat or entire animals, such as pigs or turkeys. The rotation cooks the meat evenly in its own juices and allows easy access for continuous basting."

(Emphasis added)

I used helping my good friend - the great specialist - when he was spit-roasting a whole lamb (11 kilos).

When starting, before switching on the rotating device, he always asked me to help rotating the spit as fast as I could manually, because, as he said, he wanted the lamb to get well-warmed-through-in.

"I need more heat gets in..." were his exact words.

When I questioned why the need for faster rotation, he shrugged and pointed with his finger - it makes more heat to penetrate in - his answer.

And he was right, because he knew by experience, the fast rotation was the reason for more heat to get deep inside the lamb.

No need to say - my friend always cooked the lambs evenly through (not even at slightest raw inside, and not even at slightest burnt outside - as one would expect), I think it was many generations experience speaking - to cook a whole animal through, you have to rotate the spit as fast as you can.

-

The experience also says - the slow rotation of spit results the lamb being evenly burned to the almost black crust outside, and still remaining almost a raw meat inside.

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

Planets and Moons (the satellite measured) average surface temperatures comparison

Links:

Earth/Moon 288/220K

Earth/Mars 288K/210K

Earth/Europa 288K/102K

Io/Enceladus 110K/75K

Jupiter/Saturn/Neptune 165K /134K /72K

The Rotational Warming Phenomenon is right, because it has been many times demonstrated and, also, it has been theoretically explained by the physics first principles.

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

Planets and moons are not blackbodies

Planets and moons, when their average surface temperatures compared with their respective theoretical Effective Temperatures, they are compared with the black-body Temperatures, but planets and moons are not blackbodies.

The (S-B) theoretical effective  temperature of a planet (Te) is derived by assuming that planet has a hypothetical black-body uniform temperature outgoing infrared emission from the  entire planet surface - to balance the incoming solar radiation, which for calculation convinience is considered not as incident on solar lit  hemisphere, but as a perpendicular to the planet cross-sectional disk:

the incoming solar flux on disk                       πr² * S (W)

lessened by albedo   (1 -a)                             πr² * (1 - a)S  (W)  

and emitted from the entire surface       4πr² * σTe⁴  (W)

when equalizing both parts            πr²(1 - a)S = 4πr²σTe⁴

and  solving for Te                         Te = [ (1 - a)S /4σ ]¹∕ ⁴  (K)

and the Te.correct              Te.correct =  [ Φ(1 - a)S /4σ ]¹∕ ⁴  (K)             

where:

r - is the radius of a planet

a - the average albedo 

S - the flux of solar radiation (W/m²)

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

Φ - the solar irradiation accepting factor

The Total planetary

( energy in = energy out)  balance estimation

total not reflected   =     total IR emitted

       πr²(1 - a)S  (W)    =       4πr²σTe⁴  (W)

has two physical flaws

1).

Solar flux is considered not as incident on solar lit hemisphere, but as a perpendicular to the planet cross-sectional disk.

When the average surface Albedo measured the specular reflection was considered insignificant and therefore for smooth surface planets and moons the strong specular constituent was ignored.

This results for the smooth surface planets and moons (Mercury, Earth, Moon, Mars, Europa, Ganymede) the total not reflected portion overestimated, which led   to higher Te values.

Thus the need for Te to be corrected as Te.correct:

The Total planetary

( energy in = energy out) CORRECTED balance estimation

total not reflected = total IR emitted

πr²*Φ*(1 - a)S (W) = 4πr²σ (Te.correct)⁴ (W)

and solving for the Te.correct:

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

2).

And, the total not reflected portion is not entirely absorbed as heat in inner layers.

That is why Te and Te.correct cannot be considered as a mathematical constraint to planets and moons average temperature values.

  "Why it is cannot? The not entirely absorbed part - it means the opposite you claim for, it means that it strengthens the position of the Te and Te.correct as being a mathematical constraint to the average surface temperature value."

Yes, it strengthens the position - it is what mathematics says.

The theoretical entirely absorbing incident energy and evenly distributed emission should have higher the Te or the Te.correct, than the partly absorbing and strongly differenciated actual planets and moons average surface temperatures..

But the observations say otherwise: When checking among the planets and moons in solar system, only for the very slow rotating Mercury and Moon the average measured Tsat is lower than the Te or the Te.correct.

The partly absorbing and strongly differenciated actual planets and moons average surface temperatures... they have, almost all of them, they have higher the measured average surface temperatures Tsat, than their respective theoretically calculated Te or Te.correct.

Therefore, the fact that the planets and moons absorbing ability is not absolute, the fact that it is a dependent on rotational rate (N) and on average surface specific heat (cp), - dependent on (N*cp) product - along with them having higher the measured average surface temperatures Tsat -

 - it is a strengthening argument in favor to the point that theoretical Te and Te.correct are not applicable to the planets and moons average surface temperatures comparison as a theoretical mathematical constraint.

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

The Dynamic of planet or moon Rotational Warming

When rotating faster - to be exact - when having a higher (N*cp) product - planets or moons develop (everything else equals) a higher average surface temperature T (K).

Let's see the Dynamic of the process:

Assuming planet has an equilibrium radiative energy balance

(Energy in)1 = (Energy out)1

And planet has (N1*cp1) product and average surface temperature T1 (K).

When suddenly - a thought experiment - planet starts having a higher (N*cp) product, let's say

(N2*cp2) > (N1*cp1)

and, as a result, planet starts absorbing more solar energy as heat,

and the average surface temperature starts rising

At first there wouldn't be an equilibrium radiative energy balance, so:

(Energy in)2 > (Energy out)1 + a very little more out

Because it would have taken time, for the additional heat absorption to rise the planetary temperature to the level when what energy is additionally absorbed to be equally IR emitted out.

And - when in time - the New equilibrium radiative energy balance would be inevitably established, then it will be the

(Energy in )2 = (Energy out)2

And then the average temperature rise will stop, and the finally established the respective New average surface temperature T2 (K) will be in accordance with the new  (N2*cp2) product.

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

When an equilibrium radiative energy balance 

(Energy in) = (Energy out)

is reached, then the average surface temperature stops rising, because it has already reached its Maximum Possible level.

-

An analogical phenomenon we witness here on Earth.

The month of the year with an equilibrium radiative energy balance

(Energy in) = (Energy out)

in summer on Northern Hemisphere is the August, because at that time the land is already warm enough to entirely emitting out the solar energy which gets absorbed.

Also it is the August the hottest month of the Year.

-

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

Planets and moons do not absorb the entire not reflected portion of the incident solar SW flux, because they are material objects with their surfaces having physical features, which have limited abilities to absorb heat when interacting with electromagnetic (EM) energy.

Planets and moons do not absorb solar EM energy per ce.

The EM energy has to be transformed into heat first, then the heat has to manage making its way into surface inner layers. A part of energy doesn't make it in, because surface is not capable to conduct it in entirely, so a part of energy is instantly IR emitted - it is just 'pushed' away.

Only a fraction of the not reflected solar energy may succeed to get absorbed as heat.

-

Planets and moons do not intensively emit IR EM energy, as one would expect from black-bodies of the similar temperatures, because planets and moons are material objects with their surfaces having physical features, which have limited abilities to emit at their terrestrial temperatures.

Also, planets and moons do not appear having on their surface an abundance of heat - what they do is to balance the absorbed with the outgoing energy.

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

This new study reveals a factor (N*cp) that has been unknown, but plays a key role in the average surface temperature.

Where:

N - the spin (rotations/day)

cp - the average surface specific heat (cal/gr*oC)

To conduct this study, we first studied planets and moons without atmosphere, with various rotational rates, various surface specific heat, and various surface Albedo, which allowed us to analyze the presence and function of (N*cp) factor in planetary average surface temperatures formation.

The average temperature, in its turn, is not a temperature (per ce), the average temperature is not a formal temperature, but it is a comparison term between the various warming conditions.

Par example, we say Earth's average surface temperature

~ 15°C (288K) is a sustainable for life on the planet.

The measured Solar Flux at Eath's and Moon's distance from the sun 1 AU (150.000.000 km) is known as

Flux =  1.361 W/m².

But there could be numerous planets and moons in Universe with average surface temperature ~ 15°C (288K), which planets and moons would be completely hostile!

We shall explain:  Our Moon's, at Earth's distance from the sun 1 AU (150.000.000 km) the average surface temperature is ~ - 53°C (220K).

If Moon was closer to the sun, it could have (at some closer distance), it could developed average surface temperature ~ 15°C (288K), but Moon would have been (temperature-wise), Moon would have been way more hostile, than it is now.

Our calculation results to the necessary Solar Flux on Moon's surface then to be

Flux = 4.000 W/m²

For the Planets Temperatures Comparison THE INITIAL PREMISE.

(About the Initial Premise see further below)

For two completely identical planets (or moons), which may differ only in size, their respective average surface temperatures (T1) and (T2) in Kelvin, relate as the fourth root of their respective fluxes (Flux1) and (Flux2) in W/m²:

T1 /T2 = ( Flux1 /Flux2 ) ¹∕ ⁴

We shall apply the formula to the same Moon, to compare the solar fluxes at actual 220K and at hypothetical 288K.

220K /288K = ( 1.361 W/m² /Flux.X ) ¹∕ ⁴

( 220K /288K ) ⁴ = 1.361 W/m² /Flux.X 

Flux.X = 1.361 W/m² /0,3405

Flux.X = 3.997 W/m² = 4.000 W/m²

For comparison, on Venus the solar flux is 2.600 W/m².

Everything else the same, the lunar Albedo, the lunar average surface specific heat (cp), and the lunar rate of rotation (N) - all of them the same, except for the solar flux.

But when the solar flux on our Moon would be

Flux = 4.000 W/m², the Moon's average surface temperature will be as our Earth's ~ 15°C (288K).

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

the Stefan-Boltzmann emission law.

Stefan–Boltzmann law - Wikipedia

When a surface emits EM energy, its intensity is related to fourth power of the surface's absolute temperature:

M = σT⁴ (W/m²)

where:

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

So the alleged black-body Earth temperature, the Earth's average surface tempetature (288K) is expexted to emit 

M = 5,67*10⁻⁸ W/m²K⁴ * (288K)⁴ = 390 W/m²

And Solar Flux on Earth's distance = 1.361 W/m².

-

-

And

the alleged black-body Moon temperature, when at  Earth's average surface tempetature (288K) is also expected to emit

M = 5,67*10⁻⁸ W/m²K⁴ * (288K)⁴ = 390 W/m²

But Solar Flux = 4.000 W/m².

We have demonstrated that the average surface temperature cannot be considered as planets or moons emitting temperature.

Planets and moons are not black-bodies.

The average surface temperature is not a temperature per ce.

The average surface temperature is an abstraction.

We have demonstrated further on below, - planets and moons with the SAME AVERAGE TEMPERATURE, may emit very different amounts IR energy.

Also, planets and moons with very DIFFERENT AVERAGE TEMPERATURES, may emit the same amounts IR energy.

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

Therefore - every planet or moon has an average surface temperature...

An unprecedented coincidence !!!

It is what the planet surface temperatures comparison method reveals

.

Let’s see:

Our Moon’s effective temperature

Te = 270,4 K
and our Moon’s average surface temperature Tsat = 220 K
Moon’s average Albedo a = 0,11
and Solar Flux = 1361 W/m²
****

Mars’ effective temperature Te = 210 K
Mars’ average surface temperature

Tsat = 210 K
Mars’ average Albedo a = 0,250
and Solar Flux = 586,4 W/m²

Thus for Mars Tsat = 210K = Te = 210K.

It is a unique coincidence.

We shall come to that again further on...

****

Next, Mars has a very much rare atmosphere – when compared even to Earth’s – Mars is almost airless.

It can be demonstrated, because for the same as our Moon’s Albedo
a = 0,11 Mars would have the same as Moon the average surface temperature

Tsat = 220 K.

Thus, for Mars when with Moon’s Albedo

a = 0,11 it would be

Tsat = 220K = Te = 220K.

But Mars has 1361 W/m² / 586,4 W/m² = 2,32 times lesser solar flux incident on the surface, when compared to Moon.

So, why – at first approach – our Moon doesn’t have the average surface temperature Tsat = Te = 270,4 K =  ?

And why the Moon’s actual Tsat = 220 K is lower than Moon’s effective temperature

Te = 270,4 K, why it is lower by the very large difference of 50,4°C ???

Link:

https://simple.wikipedia.org/wiki/Moon

Surface  temp.   min    mean    max

equator             100K    220 K

85°N^[3]                         70 K    130 K    230 K

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

Of course, we already know the why.

It is all explained in every possible detail further on.

But let's disclose a thing or two in advance.

Mars has 2,32 times lesser solar flux incident on its surface, when compared to Moon. Because Mars orbits further from the sun at 1,53 AU, whereas Moon orbits sun

(along with Earth) at 1 AU (150.000.000 km).

Mars' average surface specific heat

(ferrum oxides cp = 0,18 cal/gr*oC) is almost the same as for Moon's regolith

(cp = 0,19 cal/gr*oC).

So the major differences the Mars' and Moon's surfaces have are only that

Mars has 2,32 times lesser solar flux incident on its surface, when compared to Moon. But Mars rotates (with reference to the sun) 28,696 times faster, than Moon:

N.mars = 0,9728 rotations/day

N.moon = 0,0339 rotations/day

Thus:

0,9728 / 0,0339 = 28,696 times faster, than Moon.

When from the (28,696) taken the fourth root =

= (28,696)¹∕ ⁴ = 2,314

The 2,314 results very close to the 2,32 number, which is how much Mars' surface is lesser solar irradiated than Moon.

So in the case of Moon and Mars average surface temperatures comparison - the Mars' faster rotation compensates for the on the Moon's surface the stronger solar irradiation.

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

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

***********

Next issue is about Moon's Te = 270,4 K

and Mars' Te = 210 K

We had to correct them, because our Moon and planet Mars belong to smooth surface planets and moons.

So Moon's corrected effective temperature

Te.correct = 224 K

and Mars' corrected effective temperature

Te.correct = 174 K.

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

Also view:

Apollo mission's multi-year lunar equatorial

temperatures

"in situ" measurements...

In-Situ Measurements of Lunar Heat Flow

Link:

19780005001.pdf

p. 287

"1. The upper 1 to 2 cm must have an ex
tremely low thermal conductivity, and
this conductivity must be temperature
dependent. The conductivity at the
mean surface temperature (216 K)
is approximately 1.5 X 10^-5W/cm-K,
which is in good agreement with
measurements on returned lunar fines.

2. At a depth of about 2 cm, the conduc
tivity must increase greatly to values
5 to 7 times greater than the surface value."

(Emphasis added)

-

And it was a Unique physical experiment, and it was a Unique physical observation.

"1. The upper 1 to 2 cm must have an ex
tremely low thermal conductivity, and
this conductivity must be temperature
dependent."

And it is because we observe the Solar Irradiation /surface interaction process.

Solar Radiative energy induces the lunar surface (regolith cp =0,19 cal.gr*oC) low specific heat regolith, also the insolation lasts ~ 14 days - solar energy induces the lunar surface temperatures to high levels.

Thus the hot regolith emits much more IR energy to outer space, than it is able to conduct and accumulate in inner layers.

And this is observed as "The upper 1 to 2 cm must have an extremely low thermal conductivity".

Also view there the Figure 3, Figure 4, Figure 5.

Link:

19780005001.pdf

p. 287

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

Two basic physics planetary AXIOMS

We shall start our narrative with two very simple, but nevertheless very important basic physics planetary AXIOMS.

1. The planet's equatorial mean surface temperature (Tmean.equatorial) is always higher than the entire planet's the global mean surface temperature (Tmean.global).

and

2. The faster a planet rotates, the bigger is the difference

Δt = Tmean.equatorial - Tmean.global

and, likewise, the slowera planet rotates, the smaller is the difference

Δt = Tmean.equatorial - Tmean.global.

-

*******

These two simple axioms led us to the following very important conclusions:

1. No matter how fast a planet rotates, planet surface never approaches a uniform surface temperature (Tmean.uniform).

and

2. For a very slow rotating planet the

Δt = Tmean.equatorial - Tmean.global

the difference "Δt" is very small, and for the entire planet surface, the global mean surface temperature (Tmean.global) is very close to the equatorial mean surface temperature value (Tmean.equatorial).

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

Moon's surface temperature

Volokin and ReLlez SpringerPlus 2014, 3:723 Page 10 of 21

Link: Moon's mean surface temperature

" Figure 5 Typical diurnal course of the Moon’s equatorial surface temperature according to Diviner radiometric measurements and simulations by the revised TWO model (based on data in Figure nine(a) of Vasavada et al. 2012). Also shown are the maximum (Tmax), minimum (Tmin) and mean (Tmean) temperature of the lunar Equator.

In agreement with Hölder’s inequality, Tmean = 213 K is about 57 K cooler than the Moon’s effective emission temperature (270.2 K) calculated from Eq. (3)."

(Emphasis added)

Lunar surface temperature observations from the Apollo 15 mission

Link: Lunar surface temperature.

Lunar surface temperature observations from the Apollo 15 mission. Red and yellow-green short horizontal bars on the left show the theoretical (red) and actual (yellow-green) lunar average temperatures.

Let's see how little the moon IR emits after dark.

At lunar sunset, the moon’s surface temperature shown

in Figure 1 is about -60°C (213 K). Over the next 20 hours, it dramatically drops. At that point the temperature is about -180°C (93 K).

From there it cools linearly (because of the at day-time accumulated heat by the conduction from inner layers gradual release) for the next 14 days, the surface cooling is extremely slow, because the emitting temperatures are very low.

And, at its coolest, the lunar surface is at about -191°C (82 K), and at that point it is emitting a tiniest 2,5 W/m² !!!

-

The after sunset dramatical drop in surface temperature testifies for the fact that during the intensivly solar lit hours lunar surface doesn't accumulate much of the incident solar energy as a heat in the surface inner layers.

Because surface cannot transform and accumulate so much electromagnetic energy, lunar surface cannot transform so much solar energy into heat.

The radiative solar energy to get accumulated in inner layers has to be conducted there in form of heat. But the radiative solar energy has to be transformed into heat first.

It is the so-called "narrow point" in the radiative solar energy accumulation process...

-

-

So we conclude, according to the graph, that our Moon's almost the entire IR emission outgoing electromagnetic energy actually occurs during the lunar day-time hours.

Even it happens the most intensively at the around lunar noon's hours.

At dark hours the lunar surface IR emission is very weak, it is so much insignificant that it can be neglected in the lunar surface radiative enegy balance, - so much weak it is.

Below we can see:

The Graph Ratio of Measured Planet Temperature to NOT CORRECTED Blackbody Temperature (Tsat /Te), as a linear function of the Rotational Warming Factor = (β*N*cp)^1/16

Here it is a necessary excurse approaching the topic about the smooth surface planets and moons strong specular reflection constituent, which is being mistakenly neglected in the radiative energy balance estimation.

The Bond albedo definition:

Link : Bond albedo - Wikipedia

"The Bond albedo (also called spheric albedo, planetary albedo, and bolometric albedo), named after the American astronomer George Phillips Bond (1825–1865), who originally proposed it, is the fraction of power in the total electromagnetic radiation incident on an astronomical body that is scattered back out into space.

Because the Bond albedo accounts for all of the light scattered from a body at all wavelengths and all phase angles, it is a necessary quantity for determining how much energy a body absorbs. This, in turn, is crucial for determining the equilibrium temperature of a body.

Because bodies in the outer Solar System are always observed at very low phase angles from the Earth, the only reliable data for measuring their Bond albedo comes from spacecraft."

(Emphasis added)

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

Albedo:

Link : Albedo - Wikipedia

"Albedo (/ælˈbiːdoʊ/al-BEE-doh; from Latin albedo  'whiteness') is the fraction of sunlight that is diffusely reflected by a body. It is measured on a scale from 0 (corresponding to a black body that absorbs all incident radiation) to 1 (corresponding to a body that reflects all incident radiation)."

(Emphasis added)

"Water reflects light very differently from typical terrestrial materials. The reflectivity of a water surface is calculated using the Fresnel equations.

At the scale of the wavelength of light even wavy water is always smooth so the light is reflected in a locally specular manner (not diffusely). The glint of light off water is a common place effect of this. At small angles of incident light, waviness results in reduced reflectivity because of the steepness of the reflectivity-vs.-incident-angle curve and a locally increased average incident angle.^[59]

Although the reflectivity of water is very low at low and medium angles of incident light, it becomes very high at high angles of incident light such as those that occur on the illuminated side of Earth near the terminator (early morning, late afternoon, and near the poles). However, as mentioned above, waviness causes an appreciable reduction. Because light specularly reflected from water does not usually reach the viewer, water is usually considered to have a very low albedo in spite of its high reflectivity at high angles of incident light."

(Emphasis added)

"The terminator is defined as the locus of points on a planet or moon where the line through the center of its parent star is tangent."

(Emphasis added)

The terminator is a circle with a diameter that is approximately the diameter of the planet or the moon.

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

Here it is the key point:

"Because light specularly reflected from water does not usually reach the viewer, water is usually considered to have a very low albedo <b>in spite of its high reflectivity at high angles of incident light</b>.”
(emphasis added)

Link:
https://en.wikipedia.org/wiki/Albedo

Here it is the key point:

"... in spite of its high reflectivity <b>at high angles of incident light</b>."

(early morning, late afternoon, and near the poles)

Sun shines on the Globe all the time.

At every given moment there is only one point on the Globe where the angle of incidence is zero.

And, at every given moment there are always the high angles of incident light on the Globe.

So, every given moment the most of the Globe's surface area is at high angles of incident light.
-
******************

When sun is at its ZENITH POINT the angle of incidence is equal to zero.

The angle of incidence is measured at the base of the normal to the surface at the point.

“The highest angles of incidence will only occur near the terminator…”

But the highest angles of incidence do not occur, because they are always present there – regardless of rotation, because there always is a solar illuminated Hemisphere.

The solar irradiation intensity starts weakening from the very first degree away from the zenith point. The further away from that point of zenith, the weaker the intensity.

The intensity starts lowering dramatically from the 45 degree and further. But the globe's area from the 45 degree and further starts dramatically grow.

The areas of globe with the higher angles of incidence (the highest reflectivity) are the vastly larger areas of the illuminated Hemisphere.

Consequently, the smooth surface planets and moons (Mercury, Earth, Moon, Mars, Europa, Ganymede) have a very strong specular reflection constituent!

Thus, when averaged over the entire illuminated Hemisphere, the solar irradiation accepting factor

Φ = 0.47

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

NASA Technical Memorandum

An Earth Albedo Model
A Mathematical
104596
Model for the Radiant
Energy Input to an Orbiting Spacecraft
Due to the Diffuse Reflectance
of Solar Radiation
From the Earth Below
Thomas W. Flatley and Wendy A. Moore

National Aeronautics and
Space Administration
Goddard Space Flight Center
Greenbelt, Maryland
1994

Link:

19940020024.pdf

Albedo

"With specular reflection (as commonly occurs with mirrored surfaces) some or all
of the incoming solar rays are reflected with the angle of reflection equal to the
angle of incidence. Since a spacecraft would receive very little energy from even
an entire Earth which was specularly reflecting this type of reflection is ignored here."

(Emphasis added)

"This incoming solar flux is partially absorbed and partially reflected. The
amount of light reflected is proportional to the incident light by an albedo
constant, ALB, which depends on the Earth's surface characteristics.
(See Appendix II.) This model assumes that the albedo constant does not vary over the Earth's surface, neglecting the variation of diffuse reflectance with geographical features. a good estimate of the Earth's annual average albedo constant is 0.3."

(Emphasis added)

"Conclusions
This simplified albedo model was developed for use in spacecraft control system
simulations, specifically, for modeling Coarse Sun Sensors. It is based on
several approximations. Only diffuse reflectance is included; specular
reflectance is neglected. For an elliptical orbit, the unit vectors associated with
the incremental areas should change direction with altitude; instead, this
algorithm assumes a circular orbit. The albedo constant is set to the annual
global average for the entire Earth; Appendix II illustrates how the percentage of light reflected truly varies with geographical features. The Earth is considered a perfect sphere which does not rotate; it was unnecessary to model rotation since the albedo constant was not varied."

(Emphasis added)

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

Spacecrafts measure the average surface diffuse reflection. They do not measure Bond Albedo.

Spececrafts do not "see" the planet surface specular reflection, and therefore they do not measure specular reflection along with the diffuse reflection.

The smooth surface planets and moons (Mercury, Earth, Moon, Mars, Europa, Ganymede), they all have a very strong specular reflection constituent.

When the planetary surface is smooth, the measured by spacecrafts average surface Albedo (a), which is the diffuse reflection portion of the "scattered back out into space", and because it is only the diffuse reflection portion - then the measured Albedo (a) is way too small to correctly estimate "for all of the light scattered from a body at all wavelengths and all phase angles".

And by definition, the average surface Bond Albedo (a) "is crucial for determining the equilibrium temperature of a body."

So the planet Effective Temperature (Te), (equilibrium temperature) formula had to be corrected.

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

Here it is the formula of the Planetary Effective Temperature (Te):

Te = [(1 - a}S /4σ ]¹∕ ⁴ (K)

Where (a) - in the formula - is the satellite measured average surface diffuse reflection - "is the fraction of sunlight that is diffusely reflected by a body", whereas the Bond albedo is"the fraction of power in the total electromagnetic radiation incident on an astronomical body that is scattered back out into space".

Thus (a) - in the formula isn't the Bond albedo, but (a) - in the formula, is the satellite measured average surface diffuse reflection- we can call it diffuse albedo, or simple albedo, but we cannot call it Bond albedo, because it is not.

Satellites cannot measure planet average surface Bond albedo.

Nevertheless, we cannot ignorefor the smooth surface planets and moons their very strong specular reflection constituent, because otherwise we have a very much mistaken - for those planets and moons - the very much mistaken the planet surface radiative energy balance.

Likely, we are able to correct the mistaken radiative energy balance. We employ theSolar Irradiation Accepting Factor (Φ).

Φ = 0,47 for the smooth surface planets and moons,

Φ = 1 for the rough surface planets and moons (heavy cratered),

Φ = 1 for the opaque gasses planets or moons.

Both Temperatures, the not corrected (Te), and the corrected (Te.correct), are the Planetary Uniform Surface Temperature MATHEMATICAL ABSTRACTIONS,

but the (Te.correct) has the not reflected portion of the incident solar flux

(1 - a}S (W/m²)

now being corrected as

Φ(1 - a}S (W/m²)

And the formula of the Planetary Corrected Effective Temperature (Te. correct):

Te.correct = [Φ(1 - a}S /4σ ]¹∕ ⁴ (K)

The (Te.correct) is still the Planetary Uniform Surface Temperature MATHEMATICAL ABSTRACTION, but with the CORRECT the radiative energy balance estimation.

We explain about Φ -factor in every detail further on.

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

The Graph Ratio of Measured Planet Temperature to CORRECTED Blackbody Temperature (Tsat /Te.correct), as a Quasi-LINEAR function of the Rotational Warming Factor = (β*N*cp)^1/16

It had to be corrected for the smooth surface planets and moons (Mercury, Earth, Moon, Mars, Europa, Ganymede) their effective temperatures (Te) because of their surfaces having a strong specular reflection constituent.

When corrected the (Te) into (Te.correct) the Planet Surface ROTATIONAL WARMING PHENOMENON is demonstrated in GRAPH in its Full Magnificent Glory!

In the Graph the cause and effect move in the same direction.

The Graph Ratio of Measured Planet Temperature to Corrected Blackbody Temperature (Tsat /Te.correct), as a Quasi-LINEAR  function of the Rotational Warming Factor = (β*N*cp)^1/16