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 atmospheric temperature was 270 K. Calculate the temperature at the stagnation point of the vehicle, assuming a calorically perfect gas with γ = 1.4. Do you think this is an accurate calculation? If not, why? If not, is your answer an overestimate or underestimate?

The temperature at stagnation point is 78246K. The answer is an overestimate of the actual value.

Explanation:

Given:

Mach number, M = 38

Atmospheric temperature, Tₐ = 270K

γ = 1.4

Temperature at the station point, Tₓ = ?

We know,

Tₓ = 270 X [ 1 + (38*38) X (1.4-1) /2]

Tₓ = 270 X [ 1 + 577.6/2]

Tₓ = 270 X [1 + 288.8]

Tₓ = 270 X 289.8

Tₓ = 78246K

Therefore, the temperature at stagnation point is 78246K which seems to be inaccurate because the assumption of a calorically perfect gas holds good up to M = 5.

The answer is an overestimate of the actual value.

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