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From Vendetta Online Wiki
The formula is complicated because it is more naturally expressed in terms of instantaneous extraction rate and heating rate; to get a time value you have to integrate. That has been done already, so here it is:
TimeToCrate(NumCrates, initialT, ThermalMass, GunHeatingRate, GunEfficiency): let dQ = Ho*GunHeatingRate/ThermalMass - BlackBodyRadiation(ThermalMass) if dQ == 0 then NumCrates*initialT/Ke else initialT*(exp(NumCrates*dQ/(Ke*GunEfficiency)) - 1)/dQ
where initialT is the asteroid temperature when you start mining, ThermalMass is the heating rate constant of the asteroid (typical values range from 200 to 700), Ke and Ho are global constants calculated based on several parameters; Ke is currently 2.3010 and Ho is 36.945. GunHeatingRate and GunEfficiency are both 1 for the default gun. BlackBodyRadiation we can ignore as 0 for now, although here's the formula we use if you want to be more accurate:
