### A Planet Effective Temperature Complete Formula: Te = [ Φ (1-a) S (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴ (1)

**My name is Christos J. Vournas, M.Sc. mechanical engineer.**

I launched this site to have an opportunity to publish my scientific discoveries on the Climate Change.

I have been studying the Planet Earth’s Climate Change since November 2015; I have been studying it for four years now.

First I discovered the **Reversed Milankovitch Cycle.**

Then I found **the faster a planet rotates (n2>n1) the higher is the planet’s average (mean) temperature T↑mean:**

** Tmin↑→ T↑mean ← T↓max **

when** n2>n1 (it happens because Tmin↑ grows faster than T↓max goes down)**

The further studies led me to discover the **Rotating Planet Spherical Surface Solar Irradiation Absorbing-Emitting Universal Law** and the **Planet Effective Temperature Complete Formula.**

### The faster a planet rotates (n2>n1) the higher is the planet’s average temperature: Tmin↑→T↑mean←T↓max

**My name is Christos J. Vournas, M.Sc. mechanical engineer.**

I am 68 years old and I live in Athens Greece.

My e-mail address is: **vournas.christos@yahoo.com**

The date is October 11, 2019

All these discoveries are based on the **Stefan-Boltzmann Law.**

### Rotating Planet Spherical Surface Solar Irradiation Absorbing-Emitting Universal Law: Jabs=Φ*S*(1-a)/4= Jemit=σΤe⁴/(β*N*cp)¹∕ ⁴ (W/m²)

### A Rotating Planet Surface Solar Irradiation Absorbing-Emitting Universal Law

**Planet Energy Budget:**

Solar energy absorbed by a Hemisphere with radius "r" after reflection and dispersion:

** Jabs = Φ*πr²S (1-a)** (W)

Total energy emitted to space from a whole planet:

** Jemit = A*σΤe⁴ /(β*N*cp)¹∕ ⁴ ** (W)

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

**(1 - Φ)** - is the reflected fraction of the incident on the planet solar flux

**S ** - is a Solar Flux at the top of atmosphere (W/m²)

** Α** - is the total planet surface (m²)

**Te** - is a Planet Effective Temperature (K)

** (β*N*cp)¹∕ ⁴** - dimensionless, is a **Rotating Planet Surface Solar Irradiation Warming Ability**

** A = 4πr²** (m²), where **r** – is the planet's radius

** Jemit = 4πr²σTe⁴ /(β*N*cp)¹∕ ⁴ ** (W)

**global Jabs = global Jemit**

**Φ*πr²S (1-a) = 4πr²σTe⁴ /(β*N*cp)¹∕ ⁴**

Or after eliminating **πr²**

**Φ*S*(1-a) = 4σTe⁴ /(β*N*cp)¹∕ ⁴**

The planet average **Jabs = Jemit** per m² planet surface:

Jabs = Jemit

**Φ*S*(1-a) /4 = σTe⁴ /(β*N*cp)¹∕ ⁴ ** (W/m²)

Solving for **Te** we obtain the effective temperature:

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

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

** N rotations/day,** is planet’s sidereal rotation period

** cp** – is the planet surface specific heat

**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.

Here **(β*N*cp)¹∕ ⁴** - is a dimensionless **Rotating Planet Surface Solar Irradiation Warming Ability**

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

The year-round averaged energy flux at the top of the Earth's atmosphere is **Sο = 1.362 W/m².**

With an albedo of **a = 0,3** and a factor **Φ = 0,47** we have **Te = 288,36 K or 15°C. **

This temperature is confirmed by the satellites measured **Tmean.earth = 288 K.**

### A Planet Effective Temperature Complete Formula

The **Effective Temperature Complete Formula** has the wonderful ability to calculate **Planets Surface Effective Temperatures (mean temperatures)** getting almost the same results as the **measured by satellites planet mean temperatures.** This Complete Formula can be applied to all the without atmosphere planets and moons in a solar system.

### A Planet Effective Temperature Complete Formula: Te = [ Φ (1-a) S (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴ (1)

### We ended up to the following remarkable results:

Comparison of results the planet **Te** calculated **by the Incomplete Formula:**

Te = [ (1-a) S / 4 σ ]¹∕ ⁴

the planet **Te** calculated** by the Complete Formula:**

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

and the planet **Te (Tsat.mean) measured by satellites:**

**Planet or Te.incomplete **** Te.complete Te.satellites**

** moon formula formula measured**

**Mercury 437 K 346,11 K 340 K **

**Earth 255 K 288,36 K 288 K **

**Moon 271 Κ 221,74 Κ 220 Κ **

**Mars 211,52 K 215,23 K 210 K**

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…

### A Planet Universal Law Formula

As you know, to maintain **a Planet Universal Law Formula** one has to study all the planets' behavior. In that way only one may come to general conclusions. That is why I call our Earth as **a Planet Earth.** After all Earth is a Planet and as a Planet it behaves in accordance to the Universal Laws - as all Planets in the Universe do.

### Φ - is the dimensionless solar irradiation spherical surface accepting factor, Φ=0,47

### The 288 K - 255 K = 33°C difference does not exist

When I saw the Earth’s both measured by satellites and calculated with Formula temperatures being **288 K,** I felt extremely well and satisfied. It was a nice feeling. It was a discovery, it worked and it was promising sigh, and the **33°C difference** did not exist anymore.

The **Tsat.earth - Te.incompl = ****288 K - 255 K = 33°C** difference **does not exist.**

The first thing I had to do was to check the **Complete Formula** on some **other planets.** And it didn’t take me too long to realize that **a Planet-Without-Atmosphere Effective Temperature Complete Formula** was working on all the planets and moons without atmosphere **in the solar system.**

I dare to assume now that this Formula works for all planets and moons without atmosphere **in the whole universe…**

A Planet Effective Temperature Complete Formula succesfully calculates **planet's effective temperature.**

### A Planet Effective Temperature Complete Formula. Earth's and Moon's Effective Temperature Calculation.

A **Planet-Without-Atmosphere Effective Temperature Complete Formula** derives from the **incomplete Te formula **which is based on the **radiative equilibrium** and on the Stefan-Boltzmann Law.

from the** Te = [ (1-a) S / 4 σ ]¹∕ ⁴**** **

which is in common use right now, but actually it is an incomplete Te formula and that is why it gives us very confusing results.

A** Planet-Without-Atmosphere Effective Temperature Complete Formula** is also based on the **radiative equilibrium **and on the Stefan-Boltzmann Law.

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

to the** complete Te = [ Φ (1-a) S (β*N*cp)¹∕ ⁴ ****/4σ ]¹∕ ⁴**** (1) **

**(.......)¹∕ ⁴ ** is the fourth root

**S = So(1/R²**), where **R** is the average distance from the sun in **AU** (astronomical units)

**S** - is the solar flux **W/m²**

**So = 1.362 W/m²** (So is the Solar constant)

Planet’s albedo: **a **

**Φ** - is the dimensionless **solar irradiation spherical surface accepting factor**

**Accepted** by a Hemisphere with radius **r** sunlight is **S*Φ*π*r²****(1-a)**, where **Φ = 0,47** for smooth surface planets, like **Earth, Moon, Mercury and Mars…**

**(β*N*cp)¹∕ ⁴** is a dimensionless** Rotating Planet Surface Solar Irradiation Warming Ability**

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

**N rotations/day**, is planet’s sidereal rotation period

**cp** – is the planet surface **specific heat **

**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.

** cp = 0,19 cal/gr*oC,** for dry soil rocky planets, like **Moon and Mercury**.

Mars has an iron oxide **F2O3** surface, **cp.mars = 0,18 cal/gr*oC**

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

This **Universal** Formula **(1)** is the instrument for calculating **a Planet-Without-Atmosphere Effective Temperature**. The results we get from these calculations are almost **identical** with those measured by satellites.

**1. Earth’s-Without-Atmosphere Effective Temperature Calculation:**

** So = 1.362 W/m²** (So is the Solar constant)

Earth’s albedo: **aearth = 0,30 **

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

(**Accepted** by a Smooth **Hemisphere** with radius **r** sunlight is **S*Φ*π*r²(1-a)**, where** Φ = 0,47**)

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

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

**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

**Earth’s-Without-Atmosphere Effective Temperature Complete Formula Te.earth is **

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

**Τe.earth = [ 0,47(1-0,30)1.362 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 = **

**Τe.earth = [ 0,47(1-0,30)1.362 W/m²(150*1*1)¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ = **

**Te.earth = 288,36 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**.

**2. Moon’s Effective Temperature Calculation:**

** So = 1.362 W/m²** (**So** is the Solar constant)

Moon’s albedo: **amoon = 0,136**

Moon’s sidereal rotation period is 27,3216 days. But Moon is Earth’s satellite, so **the lunar day is 29,5 days**

Moon is a rocky planet, Moon’s surface solar irradiation accepting factor

**Φmoon = 0,47**

(**Accepted** by a Smooth **Hemisphere** with radius **r** sunlight is **S* Φ*π*r²*(1-a), **where** Φ = 0,47)**

** cp.moon = 0,19cal/gr oC,** moon’s surface is considered as a dry soil

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

** N = 1/29,5 rotations per/ day**

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

**Moon’s Effective Temperature Complete Formula ****Te.moon:**

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

** Te.moon = { 0,47 (1-0,136) 1.362 W/m² [150* (1/29,5)*0,19]¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ }¹∕ ⁴ = **

**Te.moon = 221,74 Κ**

The newly calculated **Moon’s Effective Temperature** differs only by **0,8%** from that measured by satellites!

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

### (β*N*cp)¹∕ ⁴ is a dimensionless Rotating Planet Surface Solar Irradiation Warming Ability

### Mars' and Mercury's Effective Temperature Calculation

**3. Mars’ Effective Temperature Calculation:**

**Te.mars**

**(1/R²)** = (1/1,5²) = 1/2,25 Mars has 2,25 times less solar irradiation intensity than Earth has

Mars’ albedo: **amars = 0,25**

**N = 1 rotations/per day,** Planet Mars completes one rotation around its axis in about 24 hours

Mars is a rocky planet, Mars’ surface solar irradiation accepting factor:** Φmars = 0,47**

**cp.mars = 0,18 cal/gr oC,** on Mars’ surface is prevalent the **iron oxide**

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

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

**So = 1.362 W/m²** the Solar constant

**Mar’s Effective Temperature Complete Formula is:**

**Te.mars = [ Φ (1-a) So (1/R²) (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴**

**Planet Mars’ Effective Temperature**

**Te.mars is:**

**Te.mars = [ 0,47 (1-0,25) 1.362 W/m²*(1/2,25)*(150*1*0,18)¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =**

**Te.mars = 215,23 K**

The calculated Mars’ effective temperature **Te.mars = 215,23 K** is only by **2,4%** higher than that measured by satellites

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

**4. Mercury’s Effective Temperature Calculation:**

**Te.mercury**

**N = 1/58,646 rotations/per day,** Planet Mercury completes one rotation around its axis in 58,646 days.

Mercury average distance from the sun is **R=0,387AU.** The solar irradiation on Mercury is (1/R²) = (1AU/0,387AU)²= 2,584²= **6,6769** times stronger than that on Earth.

Mercury’s albedo is: **amercury = 0,088**

Mercury is a rocky planet, Mercury’s surface solar irradiation accepting factor: **Φmercury = 0,47**

**Cp.mercury = 0,19 cal/gr oC,** Mercury’s surface is considered as a dry soil

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

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

**So = 1.362 W/m²** the Solar constant

**Mercury’s Effective Temperature Complete Formula is:**

**Te.mercury = [ Φ (1-a) So (1/R²) (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴**

**Planet Mercury’s effective temperature**

**Te.mercury is:**

**Te.mercury = { 0,47(1-0,088) 1.362 W/m²*6,6769*[150* (1/58,646)*0,19]¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ }¹∕ ⁴ =**

**Te.mercury = 346,11 K**

The calculated Mercury’s Effective Temperature **Te.mercury = 346,11 K** is only **1,80%** higher than the measured by satellites

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

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

### We can confirm now with great confidence

So, we can confirm now with great confidence, that a **Planet or Moon Without-Atmosphere Effective Temperature Complete Formula, according to the Stefan-Boltzmann Law, is:**

** Te.planet = [ Φ (1-a) So (1/R²) (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴ (1)**

We have collected the results now:

**Comparison of results the planet Te calculated by the Incomplete Formula, the planet Te calculated by the Complete Formula, and the planet Te (Tsat.mean) measured by satellites: **

**Planet or Te. incomplete Te.complete Te (sat.mean)**

** Moon calculated by calculated by Measured by**

** Incomplete formula Complete formula satellites **

**Mercury 437 K 346,11 K 340 K **

**Earth 255 K 288,36 K 288 K **

**Moon 271 Κ 221,74 Κ 220 Κ **

**Mars 211,52 K 215,23 K 210 K**

These data, the calculated with a Planet Without-Atmosphere Effective Temperature **Complete Formula** and the **measured** by satellites are almost the same, very much alike.

They are almost identical, within limits, which makes us conclude that the **Planet-Without-Atmosphere Effective Temperature Complete Formula**

** Te.planet = [ Φ (1-a) So (1/R²) (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴ (1)**

can calculate a **planet mean temperatures.**

It is a situation that happens once in a lifetime in science. Although the evidences existed, were measured and remained isolated information so far.

It was not obvious one could combine the evidences in order to calculate the planet’s temperature.

A planet-without-atmosphere effective temperature calculating formula

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. **

Those two parameters **are not enough** to calculate a **planet effective temperature**. Planet is a celestial body with more major features when calculating planet effective temperature to consider.

The planet-without-atmosphere effective temperature calculating formula has to include **all the planet’s major properties and all the characteristic parameters. **

3. The sidereal rotation period **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 geometrical quality). **

Altogether these parameters are combined in a **Planet-Without-Atmosphere Effective Temperature Complete Formula:**

**Te.planet = [ Φ (1-a) So (1/R²) (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴ (1)**

A Planet-Without-Atmosphere Effective Temperature Complete Formula produces very reasonable results:

**Te.earth = 288,36 K, **calculated with the** Complete Formula,** which is identical with the **Tsat.mean.earth = 288 K, **measured by** satellites. **

**Te.moon = 221,74 K, **calculated with the** Complete Formula, **which is almost the same with the **Tsat.mean.moon = 220 K, **measured by **satellites.**

**A Planet-Without-Atmosphere Effective Temperature Complete Formula** gives us a planet effective temperature **values** very close to the **satellite measured** planet **mean** temperatures **(**the satellite measured planet **effective** temperatures**). **

Thus we have to **conclude **here that the** satellites measured planet mean temperatures **should be considered** as the satellite measured Planet Effective Temperatures.**

**It is a Stefan-Boltzmann Law Triumph! And it is a Milankovitch Cycle coming back! And as for NASA, all these new discoveries were possible only due to NASA satellites planet temperatures precise measurements!**

### The Fast Rotating Planet Earth

So far we came to the end of this presentation. Its topic was to present the **Planet-Without-Atmosphere Effective Temperature Complete Formula:**

** Te = [ Φ (1-a) So (1/R²) (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴ (K)**

This Formula is based on the **incomplete** effective temperature formula:

Te = [ (1-a) S / 4 σ ]¹∕ ⁴

And also it is based on the discovered of the **Rotating Planet Spherical Surface Solar Irradiation Absorbing-Emitting Universal Law:**

**Jemit = σΤe⁴/(β*N*cp)¹∕ ⁴ (W/m²)**

Here the **(β*N*cp)¹∕ ⁴** is a dimensionless **Rotating Planet Surface Solar Irradiation Warming Ability.**

** Φ** - is the dimensionless solar irradiation spherical surface accepting factor.

Accepted by a Hemisphere with radius** r** sunlight is **S*Φ*π*r²(1-a)**, where **Φ = 0,47** for smooth surface planets, like **Earth, Moon, Mercury and Mars…**

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

** N rotations/day,** is planet’s sidereal rotation period

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

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

The** Rotating Planet Surface Solar Irradiation Absorbing-Emitting Universal Law** is based on a simple thought. It is based on the thought, that physical phenomenon which **distracts** the black body surfaces from the **instant **emitting the absorbed solar radiative energy back to space, warms the black body surface up.

In our case those **distracting physical phenomena** are the planet’s sidereal rotation, **N rotations/day,** and the planet’s surface specific heat, **cp cal/gr oC.**

Thus we have the measured by satellites Earth’s **Tmean.earth = 288 K** to be the same as the calculated by the effective temperature complete formula **Te.earth = 288,36 K.**

Those physical phenomena **distracting** Earth from the **instant emitting back to space** are the Earth’s **rotation around its axis** and the Earth’s **surface specific heat. **

Also we should mention here, that a **smooth surface spherical body,** as the planet Earth is, doesn’t accept and absorb all the solar radiation falling on the hemisphere. Only the **0,47*So** of the solar energy’s amount is **accepted** by the hemisphere. The rest **0,53*So** is reflected back **to space.** That is why **Φ= 0,47** what is left for surface to absorb.

Now we have to say about the planet’s **albedo (a).** The **planet’s albedo** describes the **dispersed on the surface secondary reflection to space fraction** of the falling on the hemisphere solar light.

Thus a planet’s surface **absorbs** only the **Φ*(1– a)** **fraction** of the **incident** on the hemisphere solar energy. That is why we have the **Φ (1-a) So (1/R²)** expression in the **complete effective temperature formula.**

**Conclusions: **

We had to answer those two questions:

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

It is proven now by the **Planet Effective Temperature Complete Formula** calculations. There **aren’t** any atmospheric factors in the **Complete Formula.** Nevertheless the **Planet-Without-Atmosphere Effective Temperature Complete Formula** produces very reasonable **results:**

** Te.earth = 288,36 K,** calculated by the **Complete Formula,** which is the same as the **Tsat.mean.earth = 288 K,** measured by satellites.

** Te.moon = 221,74 K,** calculated by the **Complete Formula,** which is almost identical with the **Tsat.mean.moon = 220 K,** measured by satellites.

Earth has a very **thin** atmosphere; Earth has a very **small** greenhouse phenomenon in its atmosphere and it **doesn’t** warm the planet.

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

The Global Warming is happening due to the **orbital forcing**. It is not happening because of the atmosphere. We have **the prove** - a newly discovered for the **Rotating Planet Surface Solar Irradiation Absorbing-Emitting Universal Law:**

**Jemit = σΤe⁴/(β*N*cp)¹∕ ⁴ (W/m²)**

And knowing that **Jemit = Jabs **

And **Jabs = [ Φ (1-a) So (1/R²) /4 ] (W/m²)**

**Solving for Te we obtain the ****Planet without Atmosphere Effective Temperature Complete Formula:**

** Te.earth = [ Φ (1-a) So (1/R²) (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴ = 288,36 K**

The calculations made by the Planet without Atmosphere Effective Temperature Complete Formula also **correspond to the next conclusion:**

**The measured by satellites Earth’s mean temperature T = 288 K is the Earth’s surface radiative equilibrium temperature.**

And… what keeps the Earth warm at **Te.earth = 288 K,** when the Moon is at **Te.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.**

### I dedicate this work to the great mathematician and astronomer of the 20th century Milutin Milankovitch

### The Original Milankovitch Cycle

According to **Milankovitch** Ice Ages are generally triggered by **minima** in high-latitude **Northern Hemisphere summer insolation,** enabling winter snowfall to persist through the year and therefore accumulate to build Northern Hemisphere glacial ice sheets. Similarly, times with **especially intense** high-latitude Northern Hemisphere summer insolation, **determined by orbital changes,** are thought to **trigger** **rapid deglaciations,** associated climate change and sea level rise. But, at second thought, I concluded that **Earth cannot** accumulate heat on the **continents’ land masses.** Earth instead accumulates heat **in the oceanic waters.**

### The Reversed Milankovitch Cycle

Milankovitch’s **main idea** was that the glacial periods are ruled by **planet’s movements forcing.** At the right we have the Reversed Milankovitch cycle. **The minimums in the reversed Milankovitch cycle are the maximums in the original.** These two cycles, the original Milankovitch cycle and the reversed differ in time only by a half of a year. According to the reversed Milankovitch cycle there are long and very deep glacial periods and small and very short interglacial. The reversed cycle complies with the **paleo geological findings.** As we can see in the reversed Milankovitch cycle, we are getting now **to the end of a long and a slow warming period.** What we are witnessing as a **Global Climate Change** are the **culmination moments** at the end of that warming period.

### The NASA planets surface temperatures measurements are all we have to work with.

And we believe **in NASA measurements**, because they are very precise and very professionally performed.

And I underline here again, **we have to rely only on the NASA measurements.** The NASA planets surface temperatures measurements are all we have to work with.

### Resume

A Planet-Without-Atmosphere Effective Temperature Calculating Formula, the Te formula which is based on the radiative equilibrium and on the Stefan-Boltzmann Law, and which is in common use right now:

Te = [ (1-a) S / 4 σ ]¹∕ ⁴

is actually an incomplete Te formula and that is why it gives us very confusing results.

A planet-without-atmosphere effective temperature calculating formula

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.

Those two parameters are not enough to calculate a planet effective temperature. Planet is a celestial body with more major features when calculating planet effective temperature to consider.

The planet-without-atmosphere effective temperature calculating formula has to include all the planet’s major properties and all the characteristic parameters.

3. The sidereal rotation period 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 geometrical quality). For Mercury, Moon, Earth and Mars without atmosphere Φ = 0,47.

Earth is considered without atmosphere because Earth’s atmosphere is very thin and it does not affect Earth’s Effective Temperature.

Altogether these parameters are combined in a Planet-Without-Atmosphere Effective Temperature Complete Formula:

Te.planet = [ Φ (1-a) So (1/R²) (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴ (1)

A Planet-Without-Atmosphere Effective Temperature Complete Formula produces very reasonable results:

Te.earth = 288,36 K, calculated with the Complete Formula, which is identical with the Tsat.mean.earth = 288 K, measured by satellites.

Te.moon = 221,74 K, calculated with the Complete Formula, which is almost the same with the Tsat.mean.moon = 220 K, measured by satellites.

A Planet-Without-Atmosphere Effective Temperature Complete Formula gives us a planet effective temperature values very close to the satellite measured planet mean temperatures (the satellite measured planet effective temperatures).

Thus we have to conclude here that the satellites measured planet mean temperatures should be considered as the satellite measured Planet Effective Temperatures.

We have collected the results now:

Comparison of results the planet Te calculated by the Incomplete Formula, the planet Te calculated by the Complete Formula, and the planet Te (Tsat.mean) measured by satellites:

Planet or Te.incomplete Te.complete Te.satellites

moon formula formula measured

Mercury 437,30 K 346,11 K 340 K

Earth 255 K 288,36 K 288 K

Moon 271 Κ 221,74 Κ 220 Κ

Mars 211,52 K 215,23 K 210 K

As you can see Te.complete.earth = 288,36 K.

That is why I say in the real world the Δ 33 oC difference does not exist.