The Planet Surface Rotational Warming Phenomenon

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

Enceladus: View of trailing hemisphere in natural color[a]

Saturn: Pictured in natural color approaching equinox, photographed by Cassini in July 2008.

Enceladus (Saturn’s satellite) Mean Surface Temperature Calculation

Enceladus (Saturn’s satellite) Mean Surface Temperature Equation Tmean.enceladus is:

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

Enceladus’ orbital period is 1,370218 days

Enceladus’ sidereal rotation period is synchronous 1,370218 days

N = 1/1,370218 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 Enceladus

So = 1.361 W/m² is Solar constant

Enceladus’ albedo, aenceladus = 0,81 ± 0,04 Bond

Let's have aenceladus =0,85

Enceladus is a heavy cratered planet, Enceladus’s surface irradiation accepting factor Φenceladus = 1

Cp.enceladus = 1 cal/gr oC , Enceladus surface is mostly covered by fresh, clean ice.

Enceladus is mostly covered by fresh, clean ice, making it one of the most reflective bodies of the Solar System. Consequently, its surface temperature at noon only reaches −198 °C (−324 °F), far colder than a light-absorbing body would be. Despite its small size, Enceladus has a wide range of surface features, ranging from old, heavily cratered regions to young, tectonically deformed terrains.

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:

ENCELADUS' mean surface temperature equation Tmean.enceladus is:

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

Let's substitute and calculate

Tmean.enceladus = {1*(1-0,85)1.361*0,01089(W/m²) [150*(1/1,370218)*1]¹∕ ⁴ /4*5,67*10⁻⁸(W/m²K⁴) }¹∕ ⁴ = 75,06 K

Tmean.enceladus = 75,06 K is the calculated.

And below is the measured by satellites

Tsat.mean.enceladus = 75 K


 The faster a planet rotates (n2>n1) the higher is the planet’s average (mean) temperature T↑mean:

Tmin→ T↑mean ← Tmax