Heat Flow from planets and moons
Tearth(D) = Tsurface + 30*D
Tearth(D=35 km) = 288 K + 30*35 K
Tearth(35 km) = 1338 K

What about Io?
Tio(D) = 124 K + dT/dD * D


Tio(D) = 124 K + 5 * D
D = [Tio(D) -124 K] / 5 (k per km)
if the melting point of rock is 1200 K, then we want to solve for the situation at which
Tio(D) = 1200 K
then
D = [1200 K -124 K]  / 5 (K per km) = 215 km



What about Europa?
Teuropa(D) = 124 K + dT/dD * D


Teuropa(D) = 124 K + 1 * D
D = [Teuropa(D) -124 K] / 1 (K per km)

 
if  the melting point of water is 300 K, then we wan to solve for the situation at which

Teuropa(D) = 300 K

then


D = [300 K -124 K]  / 1 (K per km) = 176 km


 
so as long as a thermal gradient of 1 K per km is possible, and provided water exists within Europa, we would get liquid water at a depth of only 176 km.


Heat Flow Models: