# The Planet Surface Rotational Warming Phenomenon

## The Planet Mean Surface Temperature Equation Tmean = [ Φ (1-a) S (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴

### 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!

### 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