### Jupiter’s Effective Temperature Calculation

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:

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.

**I**

**http://www.cristos-vournas.com**

** The faster a planet rotates (n2>n1) **

** Tmin↑→ T↑mean ← T↓max**