The Planet's 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.

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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.