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

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Planet 5261 Eureka’s ( Mars’ Trojan ) Effective Temperature Te calculation equilibrium formula

5261 Eureka’s ( Mars’ Trojan ) Effective Temperature Calculation:

Te.eureka

(1/R²) = (1/1,524²) = 1/2,32

Eureka has 2,32 times less solar irradiation intensity than Earth has

Eureka’s albedo: aeureka = 0,39 geom. ( not bond )

N = (24h /2,6902h) rotations/per day, Eureka completes one rotation around its axis in 2,6902 hours (0,11209 day)

Eureka is a rocky planet, Eureka’s surface irradiation accepting factor: Φeureka = 0,47

cp.eureka = 0,203cal/gr oC, on Eureka’s surface is rock

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

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

Eureka’s Effective Temperature Complete Formula is:

Te.eureka = [ Φ (1-a) So (1/R²) (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴

Eureka’s Effective Temperature Te.eureka is:

Te.eureka = [ 0,47 (1-0,39) 1.362 W/m²*(1/2,32)*[150*(24h /2,6902h)*0,203 ]¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =

Te.eureka = 234,28 K

Tsat. eureka ~ 250 K.

 

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

Tmin→ T↑mean ← Tmax

 

 

1. Earth's Without-Atmosphere effective temperature ( equilibrium temperature ) calculation formula

Te.earth

So = 1.362 W/m² (So is the Solar constant)

Earth’s albedo: aearth = 0,30

Earth is a rocky planet, Earth’s surface solar irradiation accepting factor Φearth = 0,47 (Accepted by a Smooth Hemisphere with radius r sunlight is S*Φ*π*r²(1-a), where Φ = 0,47)

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

N = 1 rotation /per day, is Earth’s sidereal rotation period

cp.earth = 1 cal/gr*oC, it is because Earth has a vast ocean.

Generally speaking almost the whole Earth’s surface is wet. We can call Earth a Planet Ocean.

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

Earth’s Without-Atmosphere Effective Temperature Complete Formula Te.earth is:

 

Te.earth = [ Φ (1-a) So (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴

 

Τe.earth = [ 0,47(1-0,30)1.362 W/m²(150 days*gr*oC/rotation*cal *1rotations/day*1 cal/gr*oC)¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =

Τe.earth = [ 0,47(1-0,30)1.362 W/m²(150*1*1)¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =

Τe.earth = ( 6.914.170.222,70 )¹∕ ⁴ =

Te.earth = 288,36 Κ

And we compare it with the

Tsat.mean.earth = 288 K, measured by satellites.

These two temperatures, the calculated one, and the measured by satellites are almost identical.

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