Planet Surface Rotational Warming Phenomenon
Earth receives 29% less SW EM energy from sun than Moon per sq. meter. It is almost a one third less!
With the two thirds of SW EM energy Moon receives, Earth appears to be a much warmer on average surface temperature than Moon planet.
Question:
How it happens Earth receiving only the two thirds of SW EM energy Moon does, for Earth to be a much warmer than Moon planet?
Because no one disputes Earth has 29% less SW EM available energy per sq. meter to interact with than Moon has.
What we observe here is that for 29% less available energy per sq. meter Earth is, nevertheless, a much warmer planet!
Answer:
Earth's surface is on average much warmer than Moon's because of planet Earth's 29,5 times shorter diurnal cycle, which is a result of Earth's faster rate of rotation. Also, planet Earth is covered with water, and water has 5 times higher specific heat than the regolith covered lunar surface has.
It is the Planet Surface Rotational Warming Phenomenon we observe here. It states that planets' mean surface temperatures (everything else equals) relate
as their (N*cp) products' sixteenth root.
Mars and Moon the satellite measured mean surface temperatures comparison: 210 K and 220 K are very close
Very interesting !
Mars and Moon satellite measured mean surface temperatures comparison: 210 K and 220 K
Let's see what we have here:
Planet or........Tsat.mean
moon.............measured
Mercury...........340 K
Earth...............288 K
Moon...............220 Κ
Mars................210 K
Let’s compare then:
Moon:
Tsat.moon = 220K
Moon’s albedo is amoon = 0,11
What is left to absorb is (1 – amoon) = (1- 0,11) = 0,89
Mars:
Tsat.mars = 210 K
Mars’ albedo is amars = 0,25
What is left to absorb is (1 – amars) = (1 – 0,25) = 0,75
Mars /Moon satellite measured temperatures comparison:
Tsat.mars /Tsat.moon = 210 K /220 K = 0,9545
Mars /Moon what is left to absorb (which relates in ¼ powers) comparison, or in other words the Mars /Moon albedo determined solar irradiation absorption ability:
( 0,75 /0,89 )¹∕ ⁴ = ( 0,8427 )¹∕ ⁴ = 0,9581
Conclusions:
1. Mars /Moon satellite measured temperatures comparison ( 0,9545 ) is almost identical with the Mars /Moon albedo determined solar irradiation absorption ability ( 0,9581 )
2. If Mars and Moon had the same exactly albedo, their satellite measured mean surface temperatures would have been exactly the same.
And this is very interesting !
Mars rotates N = 0,9747 rotation /day
Moon rotates N= 1 /29,5 rotation day
Mars solar flux S = 586 W/m²
Moon S = 1361 W/m²
Mars is at 1,53 AU distance from the sun,
Moon is at 1 AU from the sun.
That is why Mars receives much weaker (586 W/m²) vs (1361 W/m² ) than Moon solar flux.
Nevertheless, Mars' surface develops almost the same average surface temperature ( 210 K ) as the Moon ( 220 K ).
Both Mars and Moon do not have atmosphere.
It is the Solar Irradiated Planet Surface ROTATIONAL Warming Phenomenon which does the job.
We observe here the solar irradiated Planet surface ROTATIONAL WARMING phenomenon!
Mars is at 1,524 AU distance from the sun and the solar flux on the top is S = So*(1/R²) = So*(1/1,524²) = So*1/2,32 .
(1/R²) = (1/1,524²) = 1/2,32
As a result the solar flux on the Mars' top is 2,32 times weaker than that on the Moon.
But, Mars rotates much faster, than Moon.
Mars performs 1 rotation every 24,622 hours, or 0,9747 rot /day
Moon performs 1 rotation every 29,531 earth days.
So, Mars rotates 29,531 *0,9747 = 28,783 times faster than Moon.
Interesting, Mars is irradiated 2,32 times weaker, but Mars rotates 28,783 times faster.
Let’s calculate:
The rotation difference's fourth root is
(28,783)¹∕ ⁴ = 2,3162
And the irradiating /rotating comparison
2,32 /2,3162 = 1,001625
It differs only 0,1625%
It is almost equal!
It is obvious - the Mars’ 28,783 times faster rotation equates the Moon’s 2,32 times higher solar irradiation. That is why Mars has almost the same satellite measured mean surface temperature as Moon.
Tmean.mars = 210 K
Tmean.moon = 220 K
What we observe here is the solar irradiated Planet surface ROTATIONAL WARMING phenomenon!
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Two planets with the same mean surface temperature can emit dramatically different amounts of energy
Moon's average surface temperature is Tmoon = 220 K
Mars' average temperature is Tmars = 210 K
Moon's Albedo 0,11
Mars' Albedo 0,25
It can be demonstrated that for the same Albedo Mars and Moon would have had the same average surface temperature.
The solar flux on Moon is So= 1361W/m²
The solar flux on Mars is S= 586W/m²
It is obvious, that for the same average surface temperature, the emitted amounts of energy from Moon are dramatically higher than the emitted amounts of energy from Mars.
The Planet Corrected Effective Temperature
The Planet Corrected Effective Temperature.
Moon's Te = 270 K is a mistakenly calculated Moon's theoretical uniform surface temperature by the old equation.
The Te.moon = 270 K is a mistaken number, it is a wrongly calculated result (270 K) which leads to very mistaken conclusions.
Te - planet effective temperature
Te = [ (1-a) S /4σ ]¹∕ ⁴
This outdated equation considers Moon as a disk, and also it considers Moon not having specular reflection. But Moon is a sphere, and Moon reflects both ways - diffusely and specularly.
Te.correct - the planet corrected effective temperature
Te.correct = [ Φ (1-a) S /4σ ]¹∕ ⁴
Φ - is the solar irradiation accepting factor (it is the planet surface spherical shape, and planet surface roughess coefficient)
Φ = 0,47 - for smooth surface planets without atmosphere
Φ = 1 - for heavy cratered without atmosphere planets
Φ = 1 - for gases planets
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Thus we have the corrected effective temperature for Earth Te.correct.earth = 210 K, instead of the mistaken Te.earth = 255 K
For Moon we have Te.correct.moon = 224 K, instead of the mistaken Te.moon = 270 K
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Also, notice that:
Te.correct = [ Φ (1-a) S /4σ ]¹∕ ⁴
Tmean = [ Φ (1-a) So (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴
Or
Tmean = Te.correct * [ (β*N*cp)¹∕ ⁴ ]¹∕ ⁴
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https://www.cristos-vournas.com/446375350
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Table 1. Comparison of Predicted vs. Measured Temperature for All Planets
Table 1. Comparison of Predicted vs. Measured Temperature for All Planets
..............Distance.. Flux... Factor. Bond... rot /day. surface... cal /gr.oC....warming .......°K ..........°K ...........°K ........°K ................( AU ).. ( W/m² ) ...Φ ....Albedo ..N Spin ......Type......... Cp .........(β*N*cp)¹∕ ⁴.....Te ....Te.correct....Tsv .....Tsat
Mercury 0,387 ...9082,7 ..0,47 ..0.068 ..0,00568 ...basalt......0,20 ......0,64250 .........(439,6) ....364,0 ... 325,83 ...340
Venus ....0,723 ...2601,3 ....1 .....0,77 .....60/243 ...gases ......0,19 .......1,6287 ..........226,6 ....255,98 ......- ........737
Earth ......1,0 ......1361 ....0,47 ...0,306 .......1,0 .......ocean ........1 .........3,4996 .........(254) .......211 .......287,74 ...288.
Moon ......1,0 ......1361 ....0,47 ...0,11 .....0,0339 ...regolith ....0,19 ......0,99141 .......(270,4) .....224 .....223,35 ....220
Mars .....1,524 .....586,4 ..0,47 ...0,25 .....0,9747 ......rock .......0,18 ......2,26495 .......(209,8) .....174 .....213,11 ....210
Ceres.... 2,77...... 177,38... 1...... 0,09..... 2,645........ rock.......... 1.........4,463........... 162,9 ......162,9.... 236.......... -
Jupiter .. 5,20 ......50,37 .....1 .....0,503 ....2,417....... gases .........- ..............- .............102 .........102 ........- ..........165 at 1 bar level
Io ..........5,20 ......50,37 ......1 .....0,63 .....0,5559 .....rock .......0,145 ......1,8647 .........95,16 .....95,16 ....111,55 .....110
Europa ..5,20 .....50,37 ....0,47 ..0,63 .....0,2816 ......rock ...........1 ........2,5494 ........(95,16) ....78,83 ....99,56 .......102
Ganymede 5,20 ..50,37 ...0,47 ..0,43 .....0,1398 ......rock ..........1 ........2,1398 ......(107,08) ....88,59 ....107,14 .....110
Calisto ......5,20 ..50,37 .....1 .....0,22 .....0,0599 ......rock ..........1 .........1,7313 .....114,66 .....114,66 ...131,52 ...134 ±11
Saturn ......9,58 ..14,84 .....1..... 0,342 ....2,273 ......gases ........ - .............. - ........... 81 ............ 81 .......... - .......... 134 at 1 bar level
Enceladus 9,58 ..14,84 .....1 .....0,85 ......0,7299 .....rock ...........1 ........3,2347 .......55,97 .......55,97 ....75,06 .......75
Tethys ......9,58 ..14,84.....1 .....0,70 ......0,52971 ....rock ..........1 ........2,9856 .......66,55 .......66,55 ....87,48 .......86 ± 1
Titan .........9,58 ..14,84 ....1 ....0,22 ......0,06289 ...gases ....0,498 ......1,47223 .....84,52 .......84,52 ....93,10 .......93,7
Uranus ....19,22 ...3,687 ..1 ....0,30 .......1,389 .......gases ...... - ............... - ........58 MM * .......... - ............ - ....... 76 at 1 bar level
Neptune .30,33 ...1,48 .....1 ...0,29 .......1,493 .......gases ......... - ............. - .......... 46,4 ............46,4 ......... - ...... 72 at 1 bar level
Triton .....30,33 ... 1,48 ..0,47 ..0,76 .....0,1702 ...... rock ......0,4116 .....1,800 .......35,4 ........29,29 .....33,92 .......38
Pluto ......39,48 ...0,874 .....1 ...0,50 .....0,1565 .......rock .......0,248 .......1,553 .......37 ...........37 ..........41,6 .........44
Charon ...39,48 ...0,874 .....1 ...0,2 ......0,1565 ........rock ..........1 ..........2,2014 ....41,90 .......41,90 .....51,04 .......53
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It is not a reasonably good approximation to assign the planet average surface temperature to the whole surface to estimate how much it radiates.
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The average surface temperature (Tmean) is not a reasonably good approximation. Because planets and moons emit the very most of the outgoing IR EM energy during the intensive solar lit hours.
When EM energy hits surface matter, the EM energy Interacts with surface matter. The SW incident gets reflected, and also it gets transformed instantly into re-emitted IR.
Only a small portion gets absorbed in the inner layers.
The absorbed portion is formidably larger for the less the surface temperature differentiated Earth.
But stil, in the inner layers the absorbed portion for Earth too, it is much-much smaller than the transformed instantly, during the intensive solar lit hours, the portion of the incident SW EM energy which instantly is re-emitted as IR EM outgoing energy.
The average surface temperature (Tmean) is not a reasonably good approximation. Because planets and moons emit the very most of the outgoing IR EM energy during the intensive solar lit hours.
The SW incident gets reflected, and also it gets transformed instantly into re-emitted IR. Only a small portion gets absorbed in the inner layers.
A planet does not emit at its average surface temperature (Tmean).
Therefore, a planet’s average surface temperature (Tmean) cannot be associated with any kind of planet surface Infrared Emission Spectrum.
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The specular reflection of Moon’s surface is ignored
Moon absorbs from averaged solar flux 1.370 W/m² minus albedo the 303 W/m², but, because of its temperature at 220 K, Moon ought to be transferring only around
5.67e-8*220⁴ = 133 W/m².
How the slow rotation and lack of ocean to retain heat disappear the rest of
303 W/m² - 133 W/m² = 170 W/m² ?
And here it is how:
Moon is a smooth surface celestial body.
Thus for Moon the Φ = 0,47
Let’s calculate:
Φ*(1 – a)*So = 0,47(1 – 0,11)*1.370 W/m²
=
= 0,47*0,89*1370 W/m² = 573,071 W/m²
When “averaging” by dividing by “4” we shall obtain:
573,071 W/m² /4 = 143,27 W/m²
this result (143,27 W/m²) is very close to the “Moon at 220 K ought to be transferring only around
5.67e-8*220^4 =133 W/m².”
Conclusion:
Moon’s surface has a strong specular reflection. The specular reflection of Moon’s surface is ignored in Moon’s
Energy in = Energy out
radiative energy balance estimation.
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I think, for all planets and moons, the lit side, while interacting with solar radiation, during the intensive solar lit hours, the lit side strongly emits IR radiation.
I think, the solar imput (in form of HEAT)) is relatively smaller, when compared with the day-time IR emitted EM energy.
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Solar input takes long time to warm land enough - it becomes warm at nights in late July and August.
Here in Athens, Greece it is May 22 now, it is quite hot during the days, it is about 27C, but as sun sets, the temperature quickly drops to 19C, which is quite cool.
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Here it is a strong example from our Moon's behavioral case.
It is well known that the dark side of the Moon, because it has a low heat capacity and has 29 times as long as the Earth to cool each night, cools to very low temperatures, and emits very little radiation.
While the lit side has low heat capacity and 29 times as long to heat up, and heats up to a very high temperature (~380 K), and emits very much more than the average temperature would, because of the T ⁴ factor in the emission.
It is an obviously inappropriate approximation assign its average temperature to its whole surface to estimate how much it radiates from the Moon.
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In the case of Moon we have the phenomenon demonstrated in a very impressive manner. But the same phenomenon happens all the same way, for all planets and moons.
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Because a planet does not emit at its average surface temperature (Tmean).
Therefore, a planet's average surface temperature (Tmean) cannot be associated with any kind of planet surface Infrared Emission Spectrum.
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