Corrected Effective Temperatures of the Planets' and the 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

Jupiter, image taken by NASA's Hubble Space Telescope, June 2019

Saturn during Equinox

Gaseous Planets Jupiter, Saturn, Neptune T1bar mean temperatures 165 K, 134 K, 72 K comparison

All data are satellites measurements.

R – semi-major axis in AU (Astronomical Units)

a – planet’s average albedo

N – rotations /day – planet’s spin

T1bar – planet atmosphere at 1 bar average temperature in Kelvin

Planet.…Jupiter…..Saturn….Neptune

R………....5,2044…..9,5826.….30,33

1/R²…….0,0369…0,01089…0,001087

a……………0,503…0,342…….0,290

1-a………..0,497…0,658…….0,710

N………….2,4181…2,2727….1,4896

T 1 bar…...165 K….134 K……72 K

Coeff...0,388880... 0,306264…0,170881

 

Comparison coefficient calculation

[ (1-a) (1/R²) (N)¹∕ ⁴ ]¹∕ ⁴

 

Jupiter

[ (1-a) (1/R²) (N)¹∕ ⁴ ]¹∕ ⁴ =

= [ 0,497*0,0369*(2,4181)¹∕ ⁴ ]¹∕ ⁴ =

= ( 0,497*0,0369*1,2470 ]¹∕ ⁴ = ( 0,0228691 )¹∕ ⁴ =

= 0,388880

 

Saturn

[ (1-a) (1/R²) (N)¹∕ ⁴ ]¹∕ ⁴ =

= [ 0,658*0,01089*(2,2727)¹∕ ⁴ ]¹∕ ⁴ =

= ( 0,658*0,01089*1,2278 )¹∕ ⁴ = ( 0,0087980 )¹∕ ⁴ =

= 0,306264

 

Neptune

[ (1-a) (1/R²) (N)¹∕ ⁴ ]¹∕ ⁴ =

= [ 0,710*0,001087*(1,4896)¹∕ ⁴ ]¹∕ ⁴ =

= ( 0,710*0,001087*1,1048 )¹∕ ⁴ = ( 0,000852651 )¹∕ ⁴ =

= 0,170881

 

Let’s compare

Jupiter coeff. /Saturn coeff. =

= 0,388880 /0,306264 = 1,2698

T1bar.jupiter /T1bar.saturn = 165 /134 = 1,2313

 

Jupiter coeff. / Neptune coeff. =

= 0,388880 /0,170881 = 2,2757

T1bar.jupiter /T1bar.neptune = 165 /72 = 2,2917

 

Saturn coeff. /Neptune coeff. =

= 0,306264 /0,170881 = 1,7923

T1bar.saturn /T1bar.neptune = 134 /72 = 1,8611

 

Conclusion:

Gaseous planets Jupiter, Saturn and Neptune average T1bar temperatures relate the same way as the rocky inner planets Mercury, Moon and Mars average surface temperatures, and also as the Earth with Europa average surface temperatures.

 

The comparison coefficient is the same:

[ (1-a) (1/R²) (N)¹∕ ⁴ ]¹∕ ⁴

 

The planets are being separated in groups (Jupiter, Saturn and Neptune - H2), (Mercury, Moon and Mars - regolith), and (Earth with Europa - H2O) only by their similar specific heat.

 

And It is a confirmation that the planet's axial spin (rotations per day) "N" should be considered in the Tmean planet's surface mean temperature in the fourth root:

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

Neptune - Voyager 2 (29347980845) flatten crop