The Planet's Effective Temperature and the Planet's Mean Surface Temperature Equation: Tmean = [ Φ (1-a) S (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴

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FullMoon 2010

Mercury / Moon / Mars satellite measured mean temperatures 340 K, 220 K and 210 K comparison

These ( Tmean, R, N, and albedo ) planets' parameters are all satellites measured. These planets' parameters are all observations.

Planet….Mercury….Moon….Mars

Tsat.mean.340 K….220 K…210 K

R…......0,387 AU..1 AU..1,525 AU

1/R²…..6.6769….....1….…0,430

N…1 /175,938..1 /29,531..0,9747

a......0,068......0,11......0,250

coeff..1,1636...0,8093...0,8090

 

Comparison coefficient calculation

[ (1/R²) (N)¹∕ ⁴ ]¹∕ ⁴

 

Mercury:

Tsat.mean = 340 K

[ (1/R²) (N)¹∕ ⁴ ]¹∕ ⁴ = [ 6,6769*(1/175,938)¹∕ ⁴ ] ¹∕ ⁴ = 1,1636

 

Moon:

Tsat.mean = 220 K

[ (1/R²) (N)¹∕ ⁴ ]¹∕ ⁴ = [ 1*(1/29,531)¹∕ ⁴ ] ¹∕ ⁴ = 0,8093

 

Mars:

Tsat.mean = 210 K

[ (1/R²) (N)¹∕ ⁴ ]¹∕ ⁴ = [ 0,430*(0,9747)¹∕ ⁴ ] ¹∕ ⁴ = 0,8090

 

Let's compare

Mercury coeff. / Moon coeff. =

= 1,1636 /0,8093 = 1,4378

 

And

Tmean.mercury /Tmean.moon =

= 340 K/220 K = 1,5454…

 

They are close enough, because Mercury and Moon have close (1-albedo) values: amoon = 0,11 and amercury = 0,068. For Moon (1-0,11)=0,89 and for Mercury (1-0,068)=0,932.

The Mercury's coefficient (1,1636) is calculated for Mercury's Semi-major axis which is 0,387 AU. But half of the time, Mercury comes closer to the sun at its Perihelion of 0,307 AU. The fact Mercury's orbit has high eccentricity e = 0,205 partly explains the difference between the calculated (1,4378) and the measured (1,5454).

 

Moon coeff. /Mars coeff. =

= 0,8093 /0,8090 = 1,00037

or 0,037 %

If Moon and Mars had the same albedo amoon = 0,136 they would both have the same satellite measured mean temperature Tmean = 220 K. Mars' albedo is amars = 0,25.

And

It is the confirmation that the planet's axial spin (rotations per day) "N" should be considered in the Tmean planet's surface mean temperature equation in the fourth root:

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

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