A Planet Effective Temperature Complete Formula Te = [ Φ (1-a) S (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴

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Cassini mosaic of Rhea

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

10. Rhea’s (Saturn’s satellite) Effective Temperature calculation

Te.rhea

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

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

1/R² = 1/9,04² = 1/81 = 0,01234567

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 effective temperature complete formula Te.rhea is

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

Τe.rhea = { 1*(1-0,949)*1.362 W/m² *0.01234*[150*(1/4,518212)*1]¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ }¹∕ ⁴ = 

Te.rhea = 54,881 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 formula; therefore the Planet- Without-Atmosphere Effective Temperature Formula is based on the Bond Albedo and not on Geometric Albedo.

Tsat.rhea = min 53 K, max 99 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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Mars' Effective Temperature calculation

Te.mars

(1/R²) = (1/1,524²) = 1/2,32

Mars has 2,32 times less solar irradiation intensity than Earth has

Mars’ albedo: amars = 0,25

N = 0,98971 rotations/per day, Planet Mars completes one rotation around its axis in 24 hours 15 min.

Mars is a rocky planet, Mars’ surface solar irradiation accepting factor: Φmars = 0,47

cp.mars = 0,18 cal/gr oC, on Mars’ surface is prevalent the iron oxide

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

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

So = 1.362 W/m² the Solar constant

Mar’s Effective Temperature Complete Formula is:

 

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

 

Planet Mars’ Effective Temperature Te.mars is:

Te.mars = [ 0,47 (1-0,25) 1.362 W/m²*(1/2,32)*(150*0,98971*0,18)¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =

= ( 2.074.546.264,23 )¹∕ ⁴ = 213,42 K 

Te.mars = 213,42 K

The calculated Mars’ effective temperature Te.mars = 213,42 K is only by 1,63% higher than that measured by satellites

Tsat.mean.mars = 210 K !

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