The average thermal energy of a particle in an ideal gas depends on temperature. We can pull average velocity out of the energy if we know the mass of the gas particle.

Thermal energy = kinetic energy

3/2 k_b T = 1/2 m v^2

Rearrange:

v = sqrt( 3 k_b T / m)

• k_b = boltzmann constant = 1.4e-23 J/K
• m for a nitrogen molecule = 28 amu = 4.6e-26 kg
• T in the stratosphere is around 220-270K, lets pick 250 arbitrarily

Plugging in yields v = 477 m/s. Oxygen would be slightly slower due to being more massive.

At sea level, the speed of sound is around 340m/s, and it decreases as you go up. In other words, the average air molecule is already bouncing around in the stratosphere at supersonic speeds. A collision with a supersonic aircraft would be absolutely unremarkable in terms of accelerating a gas molecule out of the atmosphere.

UV photochemistry and solar wind are the main ways gas is able to escape the atmosphere. Also, the above velocity is the average velocity. There are rare gas particles going much faster such that some gas can escape the atmosphere just by bouncing off other gas molecules ("thermal escape").

There is no formal definition for the end of the atmosphere and the beginning of space, but an altitude can be arbitrarily chosen. A common choice is the Kármán Line which is an altitude of 100km. But 101km above would still have low amounts of atmosphere in it and I wouldn't consider it in space if it stays near the earth.

The link states that the Kármán Line is well above the altitude that traditional aircraft are able to fly at.

The X-15 and SpaceShipOne reached space, if we count them then the answer is (pretty trivially) yes.

For non-rocket flight we are looking at the 25-40 km region. In principle the sound waves still have a non-zero amplitude at 100 km, increasing the chance to go above for some molecules beyond briefly, but that's a mathematical result without practical relevance.

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