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

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Titan in natural color. The thick atmosphere is orange due to a dense organonitrogen haze.

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

9. Titan’s (Saturn’s satellite) Without-Atmosphere Effective Temperature calculation

Te.titan

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

Titan’s albedo: atitan = 0,22

1/R² = 1/9,04² = 1/81 = 0,01234567

Titan’s sidereal rotation period is 15,9 days

Titan does N = 1/15,9 rotations per day (synchronous rotation)

Titan is a rocky planet, it has atmosphere of 95% N2 and 5% CH4, but very opaque. Titan’s atmosphere is 8 times larger with respect to square meter planet’s surface compared to Earth, so we consider Titan a gaseous planet and Titan’s surface irradiation accepting factor Φtitan = 1.

Titan can be considered as a liquid methane ocean planet,

Cp.methane = 0,4980 cal/gr*oC

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

Titan's Without-Atmosphere effective temperature complete formula Te.titan is

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

Τe.titan = { 1*(1-0,22)*1.362 W/m² *0.01234*[150 *(1/15,945)*0,4980]¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ }¹∕ ⁴ =

Te.titan = 96,03 K

Tsat.mean.titan = 93,7 K (- 179,5 oC)

Titan has an atmosphere of 95% N2 nitrogen plus 5% of greenhouse gas methane CH4. Titan has a minor greenhouse effect phenomenon. This phenomenon is so insignificant that it hasn't appeared in calculations.

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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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