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

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Io: Galileo spacecraft true-color image of Io.

Jupiter: Near-true colour view in 2019[a]

6. Io’s (Jupiter’s satellite) Surface Mean Temperature Calculation

Tmean.io

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

Io’s albedo: aio = 0,63

Io is a rocky planet without atmosphere heavy cratered, Io’s surface irradiation accepting factor Φio = 1 

Most of Io's surface is composed of  sulfur and sulfur dioxide frost.

Cp.sulfur = 0,17 cal/gr.oC, Cp.sulfur.dioxide = 0,12 cal/gr.oC 

cp.io = 0,17 cal/gr.oC *0,5 + 0,12 cal/gr.oC *0,5 =

cp.io = 0,145 cal/gr.oC

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

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

1/R² = 1/5,2044² = 0,0369 times lesser is the solar irradiation on Jupiter than that on Earth, the same on its satellite Io.

Io’s orbital period is 1,799 days. Io’s sidereal rotation period is synchronous.

N = 1/1,799 rotations/per day

Io’s surface mean temperature equation Tmean.io is:

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

Τmean.io = { 1*(1-0,63)1.362 W/m² *0.0369*[150*(1/1,799)*0,145]¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ }¹∕ ⁴ = 

Tmean.io = 111,55 K

Tsat.mean.io = 110 K (- 163 oC)

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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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