# 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

### Earth’s Without-Atmosphere Corrected Effective Temperature calculation Te.correct.earth = 210 Κ

Earth's Corrected Effective Temperature is Te.correct.earth = 210 Κ

To calculate Earth's Corrected Effective Temperature we should use the following data values

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

Φ = 0,47 solar irradiation accepting factor (dimensionless)

a = 0,306 Earth's average albedo

So = 1.361 W/m², solar flux on the top of the Earth's atmosphere

Earth’s Without-Atmosphere Corrected Effective Temperature Equation Te.correct.earth is:

Te.correct.earth = [ Φ (1-a) So /4σ ]¹∕ ⁴

Te.correct.earth = [ 0,47 (1-0,306) 1.361 W/m² /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =

Te.correct.earth = [ 0,47 (0,694) 1.361 W/m² /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =

Te.correct.earth = ( 1,957.367.636,68 )¹∕ ⁴ = 210,34 K

Te.correct.earth = 210,34 K

or

Te.correct.earth = 210 K

### The Planet Corrected Effective Temperature : Te.correct = [ Φ (1-a) S /4σ ]¹∕ ⁴

Te - planet effective temperature

Te = [ (1-a) S /4σ ]¹∕ ⁴

Te.correct - the planet corrected effective temperature

Te.correct = [ Φ (1-a) S /4σ ]¹∕ ⁴

Φ - is the solar irradiation accepting factor (it is the planet surface spherical shape, and planet surface roughess coefficient)

Φ = 0,47 - for smooth surface planets without atmosphere

Φ = 1 - for heavy cratered without atmosphere planets

Φ = 1 - for gases planets

.......................................

Te.correct = [ Φ (1-a) S /4σ ]¹∕ ⁴

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

Or

Tmean = Te.correct * [ (β*N*cp)¹∕ ⁴ ]¹∕ ⁴

Table 1.

Comparison of Predicted (Tmean) vs. Measured (Tsat) Temperature for All Rock-type Planets

......................Φ....Te.correct ..[(β*N*cp)¹∕ ⁴]¹∕ ⁴..Tmean ...Tsat

...................................°K ........................................°K .........°K

Mercury .....0,47....364,0 ........0,8953............. 325,83 ...340

Earth ..........0,47....211 ...........1,368................287,74 ....288.

Moon ..........0,47....224 ...........0.9978.............223,35 .....220

Mars ...........0,47....174 ...........1,227..............213,11 .....210

Io ..................1.......95,16 ........1,169..............111,55 .....110

Europa ........0,47....78,83 ........1,2636.............99,56 .....102

Ganymede...0,47....88,59 ........1,209.............107,14 ....110

Calisto ..........1.....114,66 ........1,1471...........131,52 ....134 ±11

Enceladus .... 1 ......55,97 ........1,3411............75,06 .......75

Tethys ..........1.......66,55 .........1,3145 ...........87,48 .......86 ± 1

Titan .............1.......84,52 .........1,1015 ...........96,03 .......93,7

Pluto .............1.......37 ..............1,1164 ...........41,6 .........44

Charon .........1......41,90 ...........1,2181 ...........51,04 .......53

Conclusion:

We can calculate planet mean surface temperature obtaining very close to the satellite measured results.

Tmean = Te.correct * [ (β*N*cp)¹∕ ⁴ ]¹∕ ⁴

where [ (β*N*cp)¹∕ ⁴ ]¹∕ ⁴ - is the planet surface warming factor Warming Factor = (β*N*cp)¹∕₁₆