# The Planet 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

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. 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).

### In progress

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. 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).