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The Mach number is defined as $$M = \frac{v_\infty}{a}$$

$v_\infty$ is the flow speed wrt the aircraft, and $a$ is the local speed of sound.

For lower altitudes (within the troposphere) Mach number increases with altitude even when a constant TAS (true airspeed, identical to $v_\infty$) is maintained due to the decreasing speed of sound.

As one goes higher (past the Karman line) what happens to the Mach number?

I think it should be infinite (or at least very large), as there will always be some $v_\infty$ (the atmosphere never really ends, satellites encounter drag in orbit), and the speed of sound is tremendously small. My friend thinks otherwise and says reentering vehicles have to cross the sonic barrier all over again (essentially starting from Mach 0).

Who is right?

Qmechanic
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William R. Ebenezer
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1 Answers1

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Sound requires fluid dynamics, and fluid dynamics requires collisions between molecules so that he notion of a local pressure exerted by one bit of the gas on its neigbour makes sense. Once the size of the moving object becomes comparable to the mean-free-path of the gas molecules, fluid dynamics become inapplicable and a Mach number cannot be defined. The key parameter is the Knudsen number.

mike stone
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