I wanted to figure out the temperature(t_{2}) of any object based on things such as its specific heat capacity, re-entry speed, etc. Work: W = Fy Force by Air: F_{D} = 1/2pv^{2}C_{D}A Energy-temperature relationship: Q = mc(t_{2} - t_{1}) Setting things equal & solving for t_{2} gives: t_{2} = (1/2pv^{2}C_{D}Ay+mct_{1}) / mc (I'm sorry I could not get latex to format all of the formulas correctly so I formatted none of them...) So, how accurate is this equation in describing temperature gain through freefall back down to earth?
I'm going to take a guess and say you get an estimate by finding the dynamic pressure (q = 0.5 * density * velocity^2) and solving for the adiabatic heating due to the pressure rise. This doesn't take any skin friction into account however.