How do I calculate the thickness of the upper ice layer on cold ocean worlds like Europa, Enceladus, Ganymede, ...? I'm asking this for a programm I'm currently writing.
Given/Known is: mass, radius, average density of metal (assume Fe) core, rock (assume MgSiO3) layer, ice (assume H2O) layer; internal heat from tidal heating, radioactive decay and residual formation heat; external heating from solar radiation (assume equal constant heating distributed over the entire surface or ignore it if it is irrelevant/minuscule); pressure of the atmosphere above (assume pure N2 with variable pressure or no atmosphere)
Wanted is: thickness frozen (crust) and molten layer
Bonus stuff: If easy adaptation of the formula for the calculation of the rocky layers crust thickness is possible I would appreciate it. Should it be possible, an adaptation to find the rocky crust thickness and the ice crust thickness on wolds where both are needed would be helpful.
Thanks for any answer and time spent of solving this.