### The new estimate closely matches the estimate from satellite observations

**The Planet Mean Surface Temperature Equation**

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

**gives wonderful results**

**Tmean.earth = 287,74 K,**

** Tmean.moon = 223,35 K, **

**Tmean.mars = 213,21 K **

**Tmean.mercury = 325,83 K**

**Using the new equation, the new estimate closely matches the estimate surface temperatures from satellite observations:**

**Tsat.mean.mercury = 340 K**

**Tsat.mean.earth = 288 K**

**Tsat.mean.moon = 220 K**

**Tsat.mean.mars = 210 K**

** It is time to abandon the old**

** Te = [ (1-a) S /4σ ]¹∕ ⁴ incomplete equation.**

### I propose here an entirely new approach to the planetary temperatures calculation.

**The “Planet Surface Rotational Warming Phenomenon” does not predict temperature trends.**

** It states: **

**"Planets' mean surface temperatures relate (everything else equals) as their (N*cp) products' sixteenth root.**

**I propose here an entirely new approach to the planetary without-atmosphere mean surface temperatures calculation.**

**What we have till now is the satellite precisely measured planetary mean surface temperatures.**

**What I have discovered is the "Planet Surface Rotational Warming Phenomenon".**

**Based on that Phenomenon I have discovered the Planet Mean Surface Temperature Equation.**

**The Equation has the wonderful ability to theoretically calculate the solar system planets and moons mean surface temperatures. **

**The calculated results match almost precisely the satellite measured ones.**

**And the RESEARCH METHOD I use is the ENTIRE SOLAR SYSTEM planets surface temperatures COMPARISON !**

### There has to be a PROCESS.

**Somehow, someway a transformation has to be generated to affect the planet’s surface temperature.**

** You can’t just say RADIATIVE energy get converted into Heat. It’s more likely it stays Radiative energy. **

**There has to be a PROCESS**.

### Interesting, very interesting what we see here

**Let's study the table of data:**

**Planet..Tsat.mean..Rotations..Tmin..Tmax**

**.............measured.....per day...................**

** Mercury..340 K.......1/176...100 K...700 K**

** Earth.......288 K..........1..........................**

** Moon......220 Κ.......1/29,5...100 K...390 K**

** Mars......210 K.......0,9747...130 K...308 K**

**-**

**Earth and Moon are at the same distance from the Sun **** R = 1 AU. **

**Earth and Mars have almost the same axial spin ****N = 1rotation /day. **

**Moon and Mars have almost the same satellite measured average temperatures 220 K and 210 K. **

**Mercury and Moon have the same minimum temperature 100 K. **

**Mars' minimum temperature is 130 K, which is much higher than for the closer to the Sun Mercury's and Moon's minimum temperature 100 K.**

** The planet's effective temperature old Te = [ (1-a) S /4σ ]¹∕ ⁴ incomplete equation gives very confusing results.**

** And the faster rotating Earth and Mars appear to be relatively warmer planets.**

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

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

**We have moved further from the incomplete effective temperature equation**

**Te = [ (1-a) S / 4 σ ]¹∕ ⁴**

**(which is in common use right now, but actually it is an incomplete planet Te equation and that is why it gives us very confusing results)**

**a - is the planet's surface average albedo**

**S - is the solar flux, W/m²**

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

**We have discovered the Planet Without-Atmosphere Mean Surface Temperature Equation**

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

**The Planet Without-Atmosphere Mean Surface Temperature Equation is also based on the radiative equilibrium and on the Stefan-Boltzmann Law.**

** The Equation is being completed by adding to the incomplete Te equation the new parameters Φ, N, cp and the constant β.**

**Φ - is the dimensionless Solar Irradiation accepting factor**

**N - rotations /day, is the planet’s axial spin**

**cp – cal /gr*oC, is the planet's surface specific heat**

**β = 150 days*gr*oC/rotation*cal – is the Rotating Planet Surface Solar Irradiation iNTERACTING-Emitting Universal Law constant.**

**........................................**

**The Planet Without-Atmosphere Mean Surface Temperature Equation is also based on the radiative equilibrium and on the Stefan-Boltzmann Law. **

**But the New Equation doesn't consider planet behaving as a blackbody, and the New Equation doesn't state planet having a uniform surface temperature.**

**Also - very important - the New Equation is based on Planet Surface Rotational Warming Phenomenon.**

### The first steps

**At the very first look at the data table we distinguish the following:**

**Planet..Tsat.mean..Rotations..Tmin..Tmax**

**...........measured...per day......................**

** Mercury..340 K.....1/176....100 K...700 K**

** Earth.....288 K........1.............................**

** Moon....220 Κ.....1/29,5.....100 K...390 K**

**Mars.....210 K....0,9747.....130 K...308 K**

**The Earth's and Mars' by satellites temperatures measurements, in relation to the incident solar irradiation intensity, appear to be higher,**

** and it happens because of Earth's and Mars' faster rotation. **

** I should say here that I believe in NASA satellites temperatures measurements. None of my discoveries would be possible without NASA satellites very precise planet temperatures measurements.**

**It is the "magic" of the planet's spin. When it is understood, it becomes science.**

** The closest to the sun planet Mercury receives 15,47 times stronger solar irradiation intensity than the planet Mars does.**

** However on the Mercury's dark side Tmin.mercury = 100 K, when on the Mars' dark side Tmin.mars = 130 K.**

** These are observations, these are the by satellite the planet surfaces temperatures measurements.**

** And they cannot be explained otherwise but by the planet Mars' 171,5 times faster rotation than planet Mercury's spin.**

### The Planet Surface Rotational Warming Phenomenon

**I’ll try here in few simple sentences explain the very essence of how the Planet Surface Rotational Warming Phenomenon occurs.**

** Lets consider two identical planets F and S at the same distance from the sun. **

**Let’s assume the planet F spins on its axis Faster, and the planet S spins on its axis Slower. **

**Both planets F and S get the same intensity solar flux on their sunlit hemispheres. Consequently both planets receive the same exactly amount of solar radiative energy. **

**The slower rotating planet’s S sunlit hemisphere surface gets warmed at higher temperatures than the faster rotating planet’s F sunlit hemisphere. **

**The surfaces emit at σT⁴ intensity – it is the Stefan-Boltzmann emission law. **

**Thus the planet S emits more intensively from the sunlit side than the planet F.**

** There is more energy left for the planet F to accumulate then.**

** That is what makes the faster rotating planet F on the average a warmer planet.**

** That is how the Planet Surface Rotational Warming Phenomenon occurs.**

**And it states:**

**Planets’ mean surface temperatures relate (everything else equals) according to their (N*cp) products’ sixteenth root.**

**...............................................................................................................**

### There is no need in an experiment with a rotating sphere in a vacuum exposed to sunlight…

**The planet temperature varies with planet rotation. It is an observation.**

** There is no need in an experiment with a rotating sphere in a vacuum exposed to sunlight…**

** Here is the clear relation example:**

** Mars is irradiated 2,32 times weaker than Moon, but Mars rotates 28,783 times faster. **

**And… for the same albedo, Mars and Moon would have the same satellite measured mean temperatures.**

** For Moon Tmean = 220K; Moon’s Albedo a=0,11**

** For Mars Tmean= 210K; Mars’ Albedo a=0,25**

** Let’s do a simple calculation:**

** The rotation difference’s fourth root is**

** (28,783)¹∕ ⁴ = 2,3162 **

**Now, please compare these two numbers:**

** 2,32 and 2,3162**

** They are very-very much close, they are almost identical!**

** That is why no experiment is needed. **

**We have the "Planet Surface Rotational Warming Phenomenon" observed.**

### And it becomes very cold on the Moon at night

**Moon gets baked hard during its 14,75 earth days long lunar day.**

**And Moon also emits from its very hot daytime surface hard.**

**What else the very hot surface does but to emit hard, according to the Stefan-Boltzmann emission Law.**

**The very hot surface emits in fourth power of its very high absolute temperature.**

**Jemit ~ T⁴**

**A warm object in space loses heat via emission. The hotter is the object, the faster it loses heat. **

**So there is not much energy left to emit during the 14,75 earth days long lunar night.**

**And it becomes very cold on the Moon at night.**

**It is in our Earth's immediate neighborhood happens.**

**Φ - is the dimensionless Solar Irradiation accepting factor - very important.**

**It is a realizing that a sphere's surface absorbs the incident solar irradiation not as a disk of the same diameter, but accordingly to its spherical shape.**

** For a smooth spherical surface **

** Φ = 0,47**

### 1. Earth's Without-Atmosphere Mean Surface Temperature Calculation: Tmean.earth

**R = 1 AU, is the Earth's distance from the sun in astronomical units**

** Earth’s albedo: a earth = 0,306**

** Earth is a smooth rocky planet, Earth’s surface solar irradiation accepting factor Φ earth = 0,47**

** β = 150 days*gr*oC/rotation*cal – is the Rotating Planet Surface Solar Irradiation INTERACTING-Emitting Universal Law constant**

** N = 1 rotation /per day, is Earth’s sidereal rotation spin**

** cp.earth = 1 cal/gr*oC, it is because Earth has a vast ocean. Generally speaking almost the whole Earth’s surface is wet.**

** We can call Earth a Planet Ocean.**

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

**So = 1.361 W/m² (So is the Solar constant)**

** Earth’s Without-Atmosphere Mean Surface Temperature Equation Tmean.earth is:**

** Tmean.earth = [ Φ (1-a) So (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴ **

**Τmean.earth = [ 0,47(1-0,306)1.361 W/m²(150 days*gr*oC/rotation*cal *1rotations/day*1 cal/gr*oC)¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =**

** Τmean.earth = [ 0,47(1-0,306)1.361 W/m²(150*1*1)¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =**

** Τmean.earth = ( 6.854.905.906,50 )¹∕ ⁴ =**

** Tmean.earth = 287,74 Κ **

**And we compare it with the **

**Tsat.mean.earth = 288 K, measured by satellites.**

** These two temperatures, the calculated one, and the measured by satellites are almost identical.**

### We ended up to the following remarkable results

**Comparison of results the planet's Te calculated by the Incomplete Equation: **

**Te = [ (1-a) S / 4 σ ]¹∕ ⁴**

** the planet's mean surface temperature Tmean calculated by the Planet's Without-Atmosphere Mean Surface Temperature Equation: **

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

**and the planet's Tsat.mean measured by satellites:**

**To be honest with you, at the beginning, I got by surprise myself with these results. You see, I was searching for a mathematical approach…**

**We have collected the results now:**

** Te.incompl Tmean Tsat.mean**

** Mercury 439,6 K 325,83 K 340 Κ**

** Earth 255 K 287,74 K 288 K**

** Moon 270,4 Κ 223,35 Κ 220 Κ**

** Mars 209,91 K 213,21 K 210 K**

**the calculated with Planet's Without-Atmosphere Mean Surface Temperature Equation and the measured by satellites are almost the same, very much alike.**

**It is a situation that happens once in a lifetime in science.**

**Te = [ (1-a) S / 4 σ ]¹∕ ⁴**

**is incomplete because it is based only on two parameters:**

**1. On the average solar flux S W/m² on the top of a planet’s atmosphere and**

**2. The planet’s average albedo a.**

**The planet's without-atmosphere mean surface temperature equation has to include all the planet surface major properties and all the characteristic parameters.**

**3. The planet's axial spin N rotations/day.**

**4. The thermal property of the surface (the specific heat cp).**

**5. The planet surface solar irradiation accepting factor Φ ( the spherical surface’s primer solar irradiation absorbing property).**

**Altogether these parameters are combined in the Planet's Without-Atmosphere Mean Surface Temperature Equation:**

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

### Earth is warmer because Earth rotates faster and because Earth’s surface is covered with water

**We had to answer these two questions:**

** 1. Why Earth’s atmosphere doesn’t affect the Global Warming? **

**It is proven now by the Planet's Mean Surface Temperature Equation calculations. There aren’t any atmospheric factors in the Equation. Nevertheless the Equation produces very reasonable results:**

** Tmean.earth = 287,74 K, **

**calculated by the Equation, which is the same as the**

** Tsat.mean.earth = 288 K,**

** measured by satellites.**

** Tmean.moon = 223,35 K, calculated by the Equation, which is almost identical with the**

** Tsat.mean.moon = 220 K, measured by satellites.**

** 2. What causes the Global Warming then?**

** The Global Warming is happening due to the orbital forcing.**

** And… what keeps Earth warm at Tmean.earth = 288 K, when Moon is at Tmean.moon = 220 K? Why Moon is on average 68 oC colder? It is very cold at night there and it is very hot during the day…**

** Earth is warmer because Earth rotates faster and because Earth’s surface is covered with water.**

** Does the Earth’s atmosphere act as a blanket that warms Earth’s surface?**

** No, it does not.**

### It is all in the details...

**The planet Earth's and the planet Mars' faster rotation creates the necessary level of the "solar irradiation - planet surface" interaction phenomenon...**

** which results in the day-time much lower surface temperatures and, consequently, in much lower day-time surface infrared radiation emissions**

**and which results in higher planet surface 24-hours average temperatures.**

**The planet Earth’s and the planet Mars’ faster rotation is what creates the necessary interaction for the incident on the planets' surfaces solar energy the much more efficient accumulation. **

**It is all in the details...**

### W/m² is NOT cal/m²...

**What the current scientific view does here is to confuse solar flux's W/m² with heat's cal. **

**W/m² is NOT cal/m²... **

**When we say for Planet Radiative Energy Budget **

**energy in = energy out**

** then what we refer to is the radiative energy.**

** Radiative energy is measured in W/m² unit. W/m² is radiative energy intensity measure, it is not an amount of heat added to planetary surface, as one might think.**

** The not reflected portion of the incident on the planet surface radiative energy does not get ENTIRELY absorbed AS HEAT . What radiative energy does is to INTERACT with the surface's matter. **

**The planet average surface specific heat cp and the planet rotational spin N are of the major factors in the "radiative energy - planet surface" INTERACTION PROCESS. **

**In planetary surface Radiative Equilibrium the entire incident solar radiative energy is re-radiated out.**

** 1). On the spot and on the very instant the partial SW Reflection (specular and diffuse) of the incident radiative flux.**

**2). On the spot and on the very instant IR emission of a transformed from SW into LW fraction of the not reflected portion. **

**3). On the very instant and on the spot the rest of the not reflected and not IR emitted solar radiative energy gets accumulated in form of heat in the surface's inner layers. The amount of heat accumulated in the surface's inner layers will later (at the night time hours), it will also be IR emitted as outgoing energy. **

**The amount of heat accumulated in the surface's inner layers is what varies for planet's variations of "the planet average surface specific heat cp and the planet rotational spin N" products. **

**When INTERACTING with planetary surface the energy is reflected, IR emitted and accumulated at the same time.**

** Only a fraction of EM energy is accumulated in form of HEAT for the later IR emission. **

**When at nighttime hours, surface does not interact with solar flux. At nighttime hours surface emits IR EM radiative energy as the Stefan-Boltzmann emission law requires.**

** Surface's spots emit at nighttime hours as previously warmed blackbody spots which they are then. **

**Conclusion:**

** There is not any violation of The first law of thermodynamics, when a faster rotating planet appears to be on average a warmer planet.**