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).
.
https://www.cristos-vournas.com
The faster a planet rotates (n2>n1) the higher is the planet’s average (mean) temperature T↑mean:
Tmin↑→ T↑mean ← T↓max
.