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

Cassini mosaic of Rhea

Size comparison of Earth (right), the Moon (left top), and Rhea (left down)

10. Rhea’s (Saturn’s satellite) Mean Surface Temperature calculation

Tmean.rhea

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

Rhea’s albedo: arhea = 0,949 (geometric)

1/R² = 1/9,5826² = 1/91,826 = 0,010890

Rhea is a heavy cratered planet, so the Φ = 1

Rhea's surface is ice crust

cp.rhea = 1 cal/gr*oC

Rhea’s sidereal rotation period is 4,518212 days

Rhea performs N = 1/4,518212 rotations /per day, synchronous

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

Rhea’s mean surface temperature equation Tmean.rhea is

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

Τmean.rhea = { 1*(1-0,949)*1.362 W/m² *0.010890*[150*(1/4,518212)*1]¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ }¹∕ ⁴ = 

Tmean.rhea = 53,19 K

Tsat.rhea = min 53 K, max 99 K

The temperature on Rhea is 99 K (−174 °C) in direct sunlight and between 73 K (−200 °C) and 53 K (−220 °C) in the shade.

We don’t have data for the Rhea’s Bond albedo. We have data only for Rhea’s Geometric albedo: arhea = 0,949 (geometric) But such a high albedo doesn’t leave enough sunlight in our equation; therefore the Planet- Without-Atmosphere Mean Surface Temperature Equationa is based on the Bond Albedo and not on Geometric Albedo.

Tsat.rhea = min 53 K, max 99 K

 

Te.rhea = [ Φ (1-a) So (1/R²) /4σ ]¹∕ ⁴

Τe.rhea = [ 1*(1-0,949)*1.362 W/m² *0.010890* /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =

Te.rhea = 42,735 K

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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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