We present a simple analysis of the force noise associated with the mechanical damping of the motion of a test body surrounded by a large volume of rarefied gas. The calculation is performed considering the momentum imparted by inelastic collisions against the sides of a cubic test mass, and for other geometries for which the force noise could be an experimental limitation. In addition to arriving at an accurated estimate, by two alternative methods, we discuss the limits of the applicability of this analysis to realistic experimental configurations in which a test body is surrounded by residual gas inside an enclosure that is only slightly larger than the test body itself.
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