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
Φ = 0,47 - for smooth surface planets without atmosphere
Φ = 1 - for gases planets and for heavy cratered without atmosphere 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
The Planet's Without-Atmosphere Mean Surface Temperature Equation
from the incomplete effective temperature equation
Te = [ (1-a) S / 4 σ ]¹∕ ⁴
which is in common use right now, but actually it is an incomplete planet's Te equation and that is why it gives us very confusing results.
to the Planet's Without-Atmosphere Mean Surface Temperature Equation
Tmean = [ Φ (1-a) S (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴ (1)
The Planet's Without-Atmosphere Mean Surface Temperature Equation is also based on the radiative equilibrium and on the Stefan-Boltzmann Law.
The Equation is being completed by adding to the incomplete Te equation the new parameters Φ, N, cp and the constant β.
Φ - is the dimensionless Solar Irradiation accepting factor
N - rotations /day, is the planet’s axial spin
cp – is the planet's surface specific heat
β = 150 days*gr*oC/rotation*cal – is the Rotating Planet Surface Solar Irradiation Absorbing-Emitting Universal Law constant.