### 4. Mercury’s Effective Temperature calculation

**Te.mercury**

N = 1/58,646 rotations/per day, Planet Mercury completes one rotation around its axis in 58,646 days.

Mercury average distance from the sun is R=0,387AU. The solar irradiation on Mercury is (1/R)² = (1AU/0,387AU)²= 2,584²= 6,6769 times stronger than that on Earth.

Mercury’s albedo is: amercury = 0,088

Mercury is a rocky planet, Mercury’s surface irradiation accepting factor: Φmercury = 0,47

Cp.mercury = 0,19cal/gr oC, Mercury’s surface is considered as a dry soil

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

Mercury’s Effective Temperature Complete Formula is:

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

Planet Mercury’s effective temperature Te.mercury is:

Te.mercury = { 0,47(1-0,088) 1.362 W/m²*6,6769*[150* (1/58,646)*0,19]¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ }¹∕ ⁴ =

**Te.mercury = 346,11 K**

The calculated Mercury’s Effective Temperature Te.mercury = 346,11 K is only 1,80% higher than the measured by satellites

**Tsat.mean.mercury = 340 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 ← T↓max**

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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 = 213,59 K

** Te.mars = 213,59 K**

The calculated Mars’ effective temperature Te.mars = 213,59 K is only by 1,7% higher than that measured by satellites

**Tsat.mean.mars = 210 K !**

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