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

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Europa: Imaged on 7 September 1996 by Galileo spacecraft.

Jupiter: Near-true colour view in 2019[a]

7. Europa’s (Jupiter’s satellite) Effective Temperature Calculation

Te.europa

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

Europa’s albedo: aeuropa = 0,63

As we know the strong reflectors are poor emitters. But it is not the case for Europa. Europa is an ice crust planet, and we know for sure that ice is not a poor emitter,

ε = 0,90

(1/0,90)¹∕ ⁴ = 1,027

Europa is an ice-crust planet (rocky) without atmosphere, Europa’s surface irradiation accepting factor Φeuropa = 0,47

Europa’s surface consists of water ice crust

Cp.europa = 1cal/gr*oC

1/R² = 1/5,2044² = 0,0369 times lesser is the solar irradiation on Jupiter than that on Earth, the same on its satellite Europa.

Europa’s orbital period is 3,5512 d

Europa’s sidereal rotation period is synchronous

N = 1/3,5512 rotation /day

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

Europa’s effective temperature complete formula Te.europa is:

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

Τe.europa = { 0,47(1-0,63)1.362 W/m² *0.0369*[150* (1/3,5512)*1]¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴}¹∕ ⁴ = 

Te.europa = 99,557 K

Tsat.mean.europa = 102 K (- 171 oC)

As we know the strong reflectors are poor emitters. But it is not the case for Europa. Europa is an ice crust planet, and we know for sure that ice is not a poor emitter,

ε = 0,90

(1/0,90)¹∕ ⁴ = 1,027

(Te.europa = 99,557 K * 1,027 = 102,214 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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1. Earth's Without-Atmosphere effective temperature ( equilibrium temperature ) calculation formula

1. Earth’s Without-Atmosphere Effective Temperature Calculation:

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

Earth’s albedo: aearth = 0,30

Earth is a rocky planet, Earth’s surface solar irradiation accepting factor Φearth = 0,47 (Accepted by a Smooth Hemisphere with radius r sunlight is S*Φ*π*r²(1-a), where Φ = 0,47)

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

N = 1 rotation /per day, is Earth’s sidereal rotation period

cp.earth = 1 cal/gr*oC, it is because Earth has a vast ocean.

Generally speaking almost the whole Earth’s surface is wet. We can call Earth a Planet Ocean.

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

Earth’s Without-Atmosphere Effective Temperature Complete Formula Te.earth is:

 

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

 

Τe.earth = [ 0,47(1-0,30)1.362 W/m²(150 days*gr*oC/rotation*cal *1rotations/day*1 cal/gr*oC)¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =

Τe.earth = [ 0,47(1-0,30)1.362 W/m²(150*1*1)¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =

Τe.earth = ( 6.914.170.222,70 )¹∕ ⁴ =

Te.earth = 288,36 Κ

And we compare it with the

Tsat.mean.earth = 288 K, measured by satellites.

These two temperatures, the calculated one, and the measured by satellites are almost identical.

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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 = 0,9783 rotations/per day, Planet Mars completes one rotation around its axis in about 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*0,9783*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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