A Planet Effective Temperature Complete Formula Te = [ Φ (1-a) S (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴

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Jupiter’s Effective Temperature Te.jupiter

Jupiter’s Effective Temperature Complete Formula Te.jupiter is:

Te.jupiter = [Φ (1-a) So (1/R²) (β*N*cp)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 = 1.362 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)

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

Jupiter has not surface

β = 150 days*gr*oC/rotation*cal – it is the Rotating Planet Surface Solar Irradiation Absorbing-Emitting Universal Law constant

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

So we have:

Planet Jupiter’s effective temperature Te.jupiter is:

Te.jupiter = {1*(1-0,503)1.362*0,0369(W/m²) [150*(24h/9,925h)*3,1388]¹∕ ⁴ /4*5,67*10⁻⁸(W/m²K⁴) }¹∕ ⁴ =

Te.jupiter = 159 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).

 

Let's for comparison reason calculate Jupiter’s Effective Temperature Incomplete Formula Te.jupiter.incompl is:

Te.jupiter.incompl = [ (1-a) So (1/R²) /4σ]¹∕ ⁴

Te.jupiter.incompl = [(1-0,503)1.362*0,0369(W/m²)  /4*5,67*10⁻⁸(W/m²K⁴) ]¹∕ ⁴ =

Te.jupiter.incompl = 102,44 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).

And comparing with the Effective Temperature Complete Formula Te.jupiter.compl = 159 K

we may conclude here that the without-atmosphere Effective Temperature Complete Formula, when applied to Gaseous Giant Jupiter gives us much closer to the measured by satellites result.