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

Mercury imaged in enhanced color by MESSENGER in 2008

Mars pictured in natural color in 2007

### 4. Mercury’s Mean Surface Temperature calculation

Tmean.mercury

Surface temp..Tmin..Tmean..Tmax

Kelvin...........100.K...340.K...700.K

N = 1/175,938 rotations/per day, planet Mercury solar day is 175,938 earth 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 = 0,068

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

Cp.mercury = 0,20cal/gr oC, Mercury’s surface is considered as rock basalt

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 Mean Surface Temperature Equation is:

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

Tmean.mercury = { 0,47 (1-0,068) 1.361 W/m²*6,6769*[150* (1/175,938)*0,20]¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ }¹∕ ⁴ = (11.271.047.334,17)¹∕ ⁴ = 325,83 K

Tmean.mercury = 325,83 K

The calculated Mercury’s Surface Mean Temperature Tmean.mercury = 325,83 K is only 4,35% lower than the measured by satellites

Tsat.mean.mercury = 340 K !

The Tmean.mercury = 325,83 K is calculated for Mercury's Semi-major axis which is 0,387 AU.

But half of the time, Mercury comes closer to the sun at its Perihelion of 0,307 AU.

The fact Mercury's orbit has high eccentricity e = 0,205 partly explains the difference between the calculated Tmean.mercury = 325,83 K and the measured Tsat = 340 K .