Planet's Without-Atmosphere Mean Surface Temperature New Equation: Tmean = [ Φ (1-a) S (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴ (K)

Neptune’s Mean Temperature Calculation at 1 bar level

Neptune’s Mean Temperature at 1 bar level Equation Tmean.neptune is:

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

Neptune’s sidereal rotation period is16 h 6 min 36 sec, or 0,6713 day

N = 1/0,6713 rotations/per day

R = 30,33 AU, 1/R² = 1/30,33² = 0,001087 times lesser is the solar irradiation on Neptune than that on Earth.

So = 1.361 W/m² is Solar constant

Neptune’s albedo, aneptune = 0,290 

Neptune is a gaseous planet, Neptune’s surface irradiation accepting factor Φneptune = 1

(Neptune 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 80% ± 3,2% H₂, 19% ± 3,2% He, 1,5% ± 0,5% CH₄.

 

B = 850 days/rotation – it is the Rotating Gaseous Planet at 1 bar level (Jupiter, Saturn, Uranus and Neptune very similar atmosphere composition) Rotating Planet Solar Irradiation INTERACTING-Emitting constant

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

So we have 

Neptune’s mean temperature at 1 bar level Tmean.neptune.1bar is:

Tmean.neptune.1bar = {1*(1-0,290)1.361*0,001087(W/m²) [850*(1/0,6713)]¹∕ ⁴ /4*5,67*10⁻⁸(W/m²K⁴) }¹∕ ⁴ =

Tmean.neptune.1bar = [0,71*1,48(W/m²) (850*1,493)¹∕ ⁴ /4*5,67*10⁻⁸(W/m²K⁴) ]¹∕ ⁴ =

Tmean.neptune.1bar = [0,71*1,48(W/m²) 5,97 /4*5,67*10⁻⁸(W/m²K⁴) ]¹∕ ⁴ =

Tmean.neptune.1bar = (27.659.947,08)¹∕ ⁴ = 72,52 K

Tmean.neptune.1bar = 72,52 K is the calculated.

 

And below is the measured by satellites

Tsat.mean.neptune = 73 K (at 1bar level).

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https://www.cristos-vournas.com

The faster a planet rotates (n2>n1) the higher is the planet’s average (mean) temperature T↑mean:

Tmin↑→ Tmean Tmax

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