Gaseous Planets Jupiter, Saturn, Neptune at 1 bar level mean temperatures T1bar 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 at 1bar level (satellite measured) temperatures T1bar relate (everything else equals) as their rotational spins' (N) sixteenth root.
It is a demonstration of the Planet Rotational Warming Phenomenon.
It happens the same exactly 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, He), (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 mean surface temperature in the sixteenth root:
Tmean.planet = [ Φ (1-a) So (1/R²) (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴.
Notice:
The observed Jupiter and Neptune having the closest coefficient - planet's temperatures at 1 bar level comparison rates, can be explained by the fact that Jupiter and Neptune have the closest atmospheric gases content.