Earth / Mars satellite measured mean surface temperatures 288 K and 210 K comparison
These ( Tmean, R, N, cp and albedo ) planets' parameters are all satellites measured.
These planets' parameters are all observations.
Planet…....Earth.….Moon….Mars
Tsat.mean.288 K….220 K…210 K
R…...............1... AU..1 AU..1,525 AU
1/R²…..........1…........1….…0,430
N…..............1....1 /29,531..0,9747
cp................1.........0,19.......0,18
a..............0,306......0,11......0,250
1-a…........0,694……0,89…….0,75
coeff...........1...................0,72748
As we can see Earth and Mars have very close (1-a); for Earth 0,694 and for Mars 0,75.
Also Earth and Mars have very close N; for Earth N = 1 rotation /day, and for Mars N = 0,9747 rotation /day.
Earth and Mars both have the same Φ = 0,47 solar irradiation accepting factor.
Thus the comparison coefficient can be limited as follows:
Comparison coefficient calculation
[ (1/R²) (cp)¹∕ ⁴ ]¹∕ ⁴
Earth:
Tsat.mean = 288 K
[ (1/R²)*(cp)¹∕ ⁴ ]¹∕ ⁴ =
= [ 1*(1)¹∕ ⁴ ] ¹∕ ⁴ = 1
Mars:
Tsat.mean = 210 K
[ (1/R²)*(cp)¹∕ ⁴ ]¹∕ ⁴ =
= [ 0,430*(0,18)¹∕ ⁴ ] ¹∕ ⁴ = ( 0,430*0,65136 )¹∕ ⁴ =
= ( 0,2801 )¹∕ ⁴ = 0,72748
Let's compare
Earth coeff. / Mars coeff. =
= 1 /0,72748 = 1,3746
And
Tmean.earth /Tmean.mars =
= 288 K /210 K = 1,3714
Conclusion:
Everything is all right. Everything is based on observations in the comparison coefficient
[ (1/R²) (cp)¹∕ ⁴ ]¹∕ ⁴
And
It is the confirmation that the planet surface specific heat "cp" should be considered in the (Tmean) planet mean surface temperature equation in the fourth root:
Tmean.planet = [ Φ (1-a) So (1/R²) (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴.
.