During the entry of the Apollo space vehicle into the Earth's atmosphere, the Mach number at a given point on the trajectory was \(M=38\) and the atmosphere temperature was \(270 \mathrm{~K}\). Calculate the temperature at the stagnation point of the vehicle, assuming a calorically perfect gas with \(\gamma=1.4\). Do you think this is an accurate calculation? If not, why? If not, is your answer an overestimate or underestimate?