Mercury / Moon / Mars satellite measured mean surface 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 = 0,11 they would both have the same satellite measured mean surface temperature Tmean = 220 K. Mars' albedo is amars = 0,25.
Conclusion:
Everything is all right.
It is a demonstration of the Planet Surface Rotational Warming Phenomenon!
And
It is the confirmation that the planet axial spin (rotations per day) "N" should be considered in the (Tmean) planet mean surface temperature equation in the sixteenth root:
Tmean.planet = [ Φ (1-a) So (1/R²) (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴.