### Calisto 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 **

**Tsat.mean.europa = 102 K**

** Let's calculate Europa's effective temperature old blackbody equation:**

** Te.europa = [ (1-a) So (1/R²) /4σ ]¹∕ ⁴ **

**Τe.europa = [ (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 **

**So here it is what happens: **

**Io and Europa have the same albedo a = 0,63 **

**They both are at the same distance from the sun.**

** So Te.io = Te.europa = 95,16 K …. logical is not it? **

**Tsat.mean.io = 110 K **

**Tsat.mean.europa = 102 K **

**Why Io is warmer than Europa then? **

** Let's look closer, we would understand even more, look how close the Te = 95,16 K is to the Europa's Tsat.mean.europa =102 K**

** And compare it with the Tsat.mean.io = 110 K ...**

** Ganymede and Calisto don't fit in the play, because they have different albedo a. ganymede = 0,43 and a.calisto = 0,22**

** Also Ganymede and Calisto are at larger distance from Jupiter.**

** But still Tsat.mean.ganymede = 110 K **

**Tsat.mean.calisto = 134 K ± 11**

** Let's check it too, let's calculate Ganymede's effective temperature old blackbody equation:**

** Te.ganymede = [ (1-a) So (1/R²) /4σ ]¹∕ ⁴ **

**Τe.ganymede = [ (1-0,43)1.362 W/m² *0.0369 /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ = **

**= (126.309.285,7)¹∕ ⁴ = 106,01 K**

** Te.ganymede = 106,01 K**

** Tsat.mean.ganymede = 110 K **

**Again very close fit Te.ganymede = 106 K **

**and Tsat.mean.ganymede = 110 K**

** Let's calculate Calisto's effective temperature old blackbody equation:**

** Te.calisto = [ (1-a) So (1/R²) /4σ ]¹∕ ⁴**

**Τe.calisto = [ (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.calisto = 134 K ± 11 **

**Calisto does not fit, that is why the 134 K ± 11**

**There is a big difference of **

**134 K - 114,66 K = 19,34**

**So Calisto is warmer, no matter what. **

**Calisto 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. **

**Calisto rotates 10 times less than Io, but Calisto has cp =1, compared to Io having cp = 0,145 also Calisto has (1 - 0,22) = 0,78 and Io has (1 - 0,63) = 0,37 **

**That means Calisto "absorbs" twice as much solar energy and the (β*N*cp)¹∕ ⁴ for Calisto is (150*0,0599 *1)¹∕ ⁴ = 1,7313**

** the (β*N*cp)¹∕ ⁴ for Io is (150*0,5559 *0,145)¹∕ ⁴ = 1,8647 **

**Io coefficient is ( 0,37 * 1,8647 )¹∕ ⁴ = 0,6899¹∕ ⁴ = 0,91137**

**Calisto coefficient is ( 0,78 * 1,7313 )¹∕ ⁴ = 1,3504¹∕ ⁴ = 1,07799**

**Calisto coeff /Io coeff = 1,07799 /0,91137 = 1,1828**

**Tsat.mean.calisto /Tsat.mean.io = 134 K /110 K = 1,2181**

**1,2181 /1,1828 = 1,029 or only 2,9 % difference !**

**Io and Calisto have Φ = 1**

**And that explains the reasons Calisto is the warmest Jupiter's satellite. **

**Canymede and Europa have Φ = 0,47 .**

**A smooth planet has Φ = 0,47 so the old blackbody equation Te temperature (calculated without inserting the actual Φ = 0,47) is closer to the satellite measured Tmean.**

** That is how the tragic coincidences happen, like - the Mars' Te.old tragic coincidence, when Tsat.mean.mars = 210 K and Te.old.mars = 209,8 K appeared almost equal, which led to the wrong conclusion that the planets' Tmean = Te.**

**Actually the Tsat.mean.mars = 210 K should be compared with the Te.correct.mars = 174 K.**