# The Planet Surface Rotational Warming Phenomenon

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

Titan in natural color. The thick atmosphere is orange due to a dense organonitrogen haze.

Saturn: Pictured in natural color approaching equinox, photographed by Cassini in July 2008; the dot in the bottom left corner is Titan.

### 9. Titan’s (Saturn’s satellite) Without-Atmosphere Mean Surface Temperature calculation

Tmean.titan

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

Titan’s albedo: atitan = 0,22

1/R² = 1/9,5826² = 1/91,826 = 0,010890

Titan’s sidereal rotation period is 15,9 days

Titan does N = 1/15,9 rotations per day (synchronous rotation)

Titan is a rocky planet, it has atmosphere of 95% N2 and 5% CH4, but very opaque. Titan’s atmosphere is 8 times larger with respect to square meter planet’s surface compared to Earth, so we consider Titan a gaseous planet and Titan’s surface irradiation accepting factor Φtitan = 1.

Titan can be considered as a liquid methane ocean planet,

Cp.methane = 0,4980 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

Titan's Without-Atmosphere mean surface temperature equation Tmean.titan is

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

Τmean.titan = { 1*(1-0,22)*1.362 W/m² *0.010890*[150 *(1/15,945)*0,4980]¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ }¹∕ ⁴ =

Tmean.titan = 93,10 K

Tsat.mean.titan = 93,7 K (- 179,5 oC)

Titan has an atmosphere of 95% N2 nitrogen plus 5% of greenhouse gas methane CH4. Titan has a minor greenhouse effect phenomenon. This phenomenon is so insignificant that it hasn't appeared in calculations.