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

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Pluto (dwarf planet): Northern hemisphere of Pluto in true color[

Charon (Pluto's satellite): Charon in true color, imaged by New Horizons in 2015

12. Pluto’s (dwarf planet) Surface Mean Temperature calculation

Tmean.pluto

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

Pluto’s albedo: apluto = 0.49 to 0.66 (geometric) Let’s have apluto = 0.50

1/R² = 1/39,48² = 1/1.558 = 0,0006418

Pluto’s sidereal rotation period is 6,38723 days

Pluto does N = 1/6,38723 rotations/ per day

Pluto is a nitrogen ice crust surface planet, very cratered, and Pluto’s surface solar irradiation accepting factor Φpluto = 1.

Pluto's surface is composed of more than 98 percent nitrogen ice.  

Pluto can be considered as a nitrogen ice crust surface planet,

Cp.nitrogen N2 = 0,24845 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

Surface temp.    min          mean               max  

Kelvin                 33 K     44 K (−229 °C)    55 K

Pluto’s surface mean temperature equation Tmean.pluto is: 

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

Τmean.pluto = { 1*(1-0,50)*1.362 W/m² *0,0006418*[150 *(1/6,38723)* 0,24845]¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ }¹∕ ⁴ =

Tmean.pluto = 41,59 K

Tsat.mean.pluto = 44 K (- 229 oC) 

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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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Mar's 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 = 0,9747 rotations/per day, Planet Mars completes one rotation around its axis in 24 hours 37 min 22 s.

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*0,9747*0,18)¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =

= ( 2.066.635.457,46 )¹∕ ⁴ = 213,21 K

Te.mars = 213,21 K

The calculated Mars’ effective temperature Te.mars = 213,21 K is only by 1,53% higher than that measured by satellites

Tsat.mean.mars = 210 K !

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