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.