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Spherical gas in vacuum

A sphere of radius $R$ is filled with low pressure ideal gas, such that the mean free path is $l\approx R$. Inside the sphere, at a distance $h$ from its center, a small pressure sensor is placed, with its radius $r \ll R$. From the sensor, the gas molecules are bouncing off perfectly elastically. The detector calculates the pressure $p$ by averaging over a very long time period, longer than any relevant characteristic time parameters.

1 Determine the measured pressure value $p$ as a function of $h$.