Callisto is the warmest Jupiter's satellite. Calisto /Io satellite Tmean temperatures comparison 134 K and 110 K
Tsat.mean.io = 110 K
Let's calculate Io's effective temperature old blackbody equation:
Te.io = [ (1-a) So (1/R²) /4σ ]¹∕ ⁴
Τe.io = [ (1-0,63)1.362 W/m² *0.0369 /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =
= (81.990.238,1)¹∕ ⁴ = 95,16 K
There is a big difference of
110 K - 95,6 K = 14,4 °C
Tsat.mean.callisto = 134 K ± 11
Let's calculate Callisto's effective temperature old blackbody equation:
Te.callisto = [ (1-a) So (1/R²) /4σ ]¹∕ ⁴
Τe.callisto = [ (1-0,22)1.362W/m² *0.0369 /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =
= (172.844.285,7)¹∕ ⁴ = 114,66 K
Tsat.mean.callisto = 134 K ± 11
There is a big difference of
134 K - 114,66 K = 19,34 °C
So Callisto is warmer, no matter what.
Callisto is at the outmost distance from the Jupiter, so it cannot be warmed from the planet's IR, also because of the distance it has the lowest tidal effect.
But here it is what happens:
Callisto has (1 - 0,22) = 0,78 and Io has (1 - 0,63) = 0,37
That means Callisto "absorbs" twice as much solar energy
Callisto rotates 10 times less than Io, but Callisto has cp =1,
which is bid when compared to Io having cp = 0,145
Thus the (β*N*cp)¹∕ ⁴ for Calisto is (150*0,0599 *1)¹∕ ⁴ = 1,7313
does not differ much from the (β*N*cp)¹∕ ⁴ for Io, which is (150*0,5559 *0,145)¹∕ ⁴ = 1,8647
Io coefficient is ( 0,37 * 1,8647 )¹∕ ⁴ = 0,6899¹∕ ⁴ = 0,91137
Callisto coefficient is ( 0,78 * 1,7313 )¹∕ ⁴ = 1,3504¹∕ ⁴ = 1,07799
Callisto coeff /Io coeff = 1,07799 /0,91137 = 1,1828
Tsat.mean.callisto /Tsat.mean.io = 134 K /110 K = 1,2181
1,2181 /1,1828 = 1,029 or only 2,9 % difference !
Also the Io and Callisto have Φ = 1, when Europa and Ganymede have Φ = 0,47
So, all that together explains the reasons Callisto is the warmest Jupiter's satellite.