### 6. Io’s (Jupiter’s satellite) Effective Temperature Calculation

**Te.io**

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

Io’s albedo: aio = 0,63

Io is a rocky planet without atmosphere, Io’s surface irradiation accepting factor Φio = 0,47

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

The Io’s surface is a very strong reflector. Therefore the Io’s global emissivity plays a major role too. Since the planet’s albedo is aio = 0,63 we can assume Io's emissivity value as εio = 0,45

Io’s effective temperature complete formula Te.io is:

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

Τe.io = { 0,47(1-0,63)1.362 W/m² *0.0369*[150*(1/1,799)*0,145]¹∕ ⁴ /4*0,45*5,67*10⁻⁸ W/m²K⁴ }¹∕ ⁴ =

**Te.io = 112,77 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 ← T↓max**

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