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

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

Io, Jupiter's moon, highest resolution true color

Jupiter’s Mean Temperature Calculation at 1 bar level

Jupiter’s Mean Temperature Equation Tmean.jupiter.1bar is:

Tmean.jupiter.1bar = [Φ (1-a) So (1/R²) (B*N)¹∕ ⁴ /4σ]¹∕ ⁴

Jupiter’s sidereal rotation period is 9,925 h 

N = 24h/9,925h  rotations/per day 

R = 5,2044 AU, 1/R² = 1/5,2044² = 0,0369 times lesser is the solar irradiation on Jupiter than that on Earth.

So = 1.361 W/m² is Solar constant

Jupiter’s albedo, ajupiter = 0,503

Jupiter is a gaseous planet, Jupiter’s surface irradiation accepting factor Φjupiter = 1

(Jupiter has not surface to reflect the incident sunlight.  Accepted by a Gaseous Hemisphere with radius r sunlight is S*Φ*π*r²(1-a), where Φ = 1)

Atmosphere composition 89% ± 2,0% H, 10% ± 2,0% He, 0,3% ± 0,1% CH.

Jupiter has not surface

B = 850 days/rotation – it is the Rotating Gaseous Planet at 1 bar level Solar Irradiation Absorbing-Emitting Universal constant

σ = 5,67*10⁻⁸ W/m²K⁴, a Stefan-Boltzmann constant

So we have:

Jupiter’s mean temperature at 1 bar level Tmean.jupiter.1bar is:

Tmean.jupiter.1bar = {1*(1-0,503)1.361*0,0369(W/m²) [850*(24h/9,925h)]¹∕ ⁴ /4*5,67*10⁻⁸(W/m²K⁴) }¹∕ ⁴ =

Tmean.jupiter.1bar = {1*(0,497)1.361*0,0369(W/m²) [850*2,417]¹∕ ⁴ /4*5,67*10⁻⁸(W/m²K⁴) }¹∕ ⁴ =

Tmean.jupiter.1bar = {1*(0,497)1.361*0,0369(W/m²) [2.054,45]¹∕ ⁴ /4*5,67*10⁻⁸(W/m²K⁴) }¹∕ ⁴ =

Tmean.jupiter.1bar = {1*(0,497)1.361*0,0369(W/m²) *6,732 /4*5,67*10⁻⁸(W/m²K⁴) }¹∕ ⁴ =

Tmean.jupiter.1bar = (740.869.877)¹∕ ⁴ = 165 K

Tmean.jupiter.1bar = 165 K is the calculated.

 

And below is the measured by satellites

Tsat.mean.jupiter = 165 K (at 1bar level)

 

Tsat.mean.jupiter = 112 K (at 0,1 bar level).

 

Here is an abstract from Wikipedia:

Atmosphere Main article: Atmosphere of Jupiter

Jupiter has the largest planetary atmosphere in the Solar System, spanning over 5,000 km (3,000 mi) in altitude.[55][56] Because Jupiter has no surface, the base of its atmosphere is usually considered to be the point at which atmospheric pressure is equal to 100 kPa (1.0 bar).

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Jupiter's Atmosphere composition

89% ± 2,0% H₂, 10% ± 2,0% He, 0,3% ± 0,1% CH₄.

Cp.H₂ = 3,1388 cal/gr. oC , H₂ specific heat at 175 K,

Cp.He = 1,243 cal/gr. oC , He specific heat,

Cp.CH₄ = 0,531 cal/gr. oC , CH₄ specific heat.

Cp.jupiter = 90%*Cp.H₂ + 10%*Cp.He = 0,9*3,14 + 0,1*1,243 = 2,825 + 0,12416 = 2,95 cal/gr.oC

Jupiter has not surface

Here is an abstract from Wikipedia:

Atmosphere Main article: Atmosphere of Jupiter

Jupiter has the largest planetary atmosphere in the Solar System, spanning over 5,000 km (3,000 mi) in altitude.[55][56] Because Jupiter has no surface, the base of its atmosphere is usually considered to be the point at which atmospheric pressure is equal to 100 kPa (1.0 bar). 

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http://www.cristos-vournas.com

The faster a planet rotates (n2>n1) 

Tmin↑→ Tmean Tmax

 

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