### Tethys' (Saturn’s satellite) Effective Temperature Calculation

Tethys' (Saturn’s satellite) Effective Temperature Complete Formula Te.tethys is:

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

Tethys’ orbital period is 1,887 802 days

Tethys’ sidereal rotation period is synchronous 1,887 802 days

N = 1/1,887 802 rotations/per day

R = 9,5826 AU, 1/R² = 1/9,5826² = 0,01089 times lesser is the solar irradiation on Saturn than that on Earth. The same is on Saturn’s satellite Tethys

So = 1.362 W/m² is Solar constant

Tethys’ albedo, atethys = 0,80 ± 0,15 (bond)

Let’s assume atethys = 0,70

Tethys is a heavy cratered planet, Tethy’s surface irradiation accepting factor Φtethys = 1

Cp.tethys = 1 cal/gr oC , Tethys’ surface is ice crust

The density of Tethys is 0.98 g/cm³, indicating that it is composed almost entirely of water-ice.

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

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

So we have:

Tethys’ effective temperature complete formula Te.tethys is:

Te.tethys = {1*(1-0,70)1.362*0,01089(W/m²) [150*(1/1,887802)*1]¹∕ ⁴ /4*5,67*10⁻⁸(W/m²K⁴) }¹∕ ⁴ = 87,48 K

**Te.tethys = 87,48 K is the calculated.**

And below is the measured by satellites

** Tsat.tethys = 86 ± 1 K**

**I**

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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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