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

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

**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 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) **