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

Tethys as imaged by Cassini on 11 April 2015

Saturn: Pictured in natural color approaching equinox, photographed by Cassini in July 2008; the dot in the bottom left corner is Titan.

### Tethys' (Saturn’s satellite) Mean Surface Temperature Calculation

Tethys' (Saturn’s satellite) Surface Mean Temperature Equation Te.tethys is:

Tmean.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’ mean surface temperature equation Tmean.tethys is:

Tmean.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

Tmean.tethys = 87,48 K is the calculated.

And below is the measured by satellites

Tsat.tethys = 86 ± 1 K