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.