### 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

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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**http://www.cristos-vournas.com**

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

** Tmin↑→ T↑mean ← T↓max**

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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 = 1 rotations/per day, Planet Mars completes one rotation around its axis in about 24 hours

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*1*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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