I wanted to figure out the temperature(t2) of any object based on things such as its specific heat capacity, re-entry speed, etc.
Work: W = Fy
Force by Air: FD = 1/2pv2CDA
Energy-temperature relationship: Q = mc(t2 - t1)
Setting things equal & solving for t2 gives:
t2 = (1/2pv2CDAy+mct1) / 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?