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

Planet's Surface Radiative Equilibrium Temperature

Planet's Surface Radiative Equilibrium Temperature

What solar irradiated planet's surface does is to achieve a radiative equilibrium with the incoming solar energy.

It is an equation:

energy in = energy out

The mechanisms planet has to achieve the surface radiative equilibrium:

1. The negative feedbacks.

a). The rising precipitation, due to warming from the excess energy, rises the Earth's cloud cover.

This in turn magnifies the planet's albedo.

So some less energy reaches the surface.

b). The loss of Arctic oceanic ice cover, due to warming from the excess energy, opens the Arctic oceanic waters.

This in turn magnifies the Arctic oceanic surface emissivity (water has higher emissivity compared to the ice, and water has a much higher emissivity compared to the snow covered Arctic oceanic ice fields).

So some more energy is emitted to space from the Earth's surface to come closer to the radiative equilibrium (radiative balance).

2. The heat accumulation and the rise of the planet's average temperature.

Some of the solar energy that is not emitted out to space forms the accumulated heat, mostly in the oceanic waters and also in the land masses.

The heat accumulation rises the planet's temperature.

When the planet's temperature risen planet's infrared radiation energy emissions rise too.

Thus the Planet's Surface Radiative Equilibrium Temperature being formatted.


Earth's Without-Atmosphere Mean Surface Temperature calculation

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

S (W/m²) is the planet's solar flux. For Earth S = So

Earth’s albedo: aearth = 0,306

Earth is a smooth 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 axial spin = 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 Mean Surface Temperature Equation is: [ Φ (1-a) So (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴

Τ = [ 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 =

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

Τ = ( 6.854.905.906,50 )¹∕ ⁴ = 287,74 K = 287,74 Κ

And we compare it with the = 288 K, measured by satellites.

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


The mean surface temperature equation

Tmean = [ Φ (1-a) S (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴ produces remarkable results. The calculated planets temperatures are almost identical with the measured by satellites.


Mercury....439,6 K…….325,83 K…..340 K

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 288 K – 255 K = Δ 33 oC difference does not exist in the real world.

There are only traces of greenhouse gasses.

The Earth’s atmosphere is very thin. There is not any measurable Greenhouse Gasses Warming effect on the Earth’s surface.


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

Tmin→ T↑mean ← Tmax