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

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A Blackbody Surface Equilibrium Temperature (A Blackbody Effective Temperature)

A blackbody planet surface is meant as a classical blackbody surface approaching.

Here are the blackbody's properties:

1. Blackbody does not reflect the incident on its surface radiation.

2. Blackbody interracts with the entire incident on the blackbody's surface radiation.

3. Blackbody's emission temperature depends only on the quantity of the incident radiative energy per unit area. 

4. Blackbody is considered only as blackbody's surface physical properties. Blackbody is only a surface without "body".

5. Blackbody does not consist from any kind of a matter. Blackbody has not a mass. Thus blackbody has not a specific heat.

Blackbody's cp = 0.

6. Blackbody has surface dimensions. So blackbody has the radiated area and blackbody has the emitting area.

7. The whole blackbody's surface area is the blackbody's emitting area.

8. The blackbody's surface has an infinitive conductivity.

9. All the incident on the blackbody's surface radiative energy is instantly and evenly distributed upon the whole blackbody's surface.

10. The radiative energy incident on the blackbody's surface the same very instant the blackbody's surface emitts this energy away.

The emission temperature the blackbody's surface has according to the Stefan-Boltzmann Law is:

Te = (Total incident W /Total area m² *σ)¹∕ ⁴ K

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

Planet is not a blackbody.

Planet reflects the (1-a)Φ part of the incident on the planet's surface solar irradiation. Here "a" is the planet's average albedo and "Φ" is the planet's solar irradiation accepting factor.

For smooth planet without thick atmosphere, Earth included,

Φ=0,47

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

Tmin→ T↑mean ← Tmax

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