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mach 37 is not escape velocity of Earth's atmosphere

"The name 'MACH37' is a reference to the escape velocity of Earth's atmosphere.[5]"

Escape velocity is not "of Earth's atmosphere", it is from a certain distance from the center of a planet (or other celestial body). Escape velocity from Earth's surface is approximately Mach 33, not Mach 37. There are other possible speeds that might be involved (e.g., low earth orbit orbital speed, solar escape velocity) but none that I know of that are approximately Mach 37.

Theater Arts at CalTech appears to have it right. See https://tacit.caltech.edu/mach33/why

See https://en.wikipedia.org/wiki/Escape_velocity for more about escape velocity.