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 roughness 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....210 ...........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
.