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

Plus the introduction to the Reversed Milankovitch Cycle. Click above on the box for more

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.