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The residual gas damping of the test mass (TM) in the free molecular flowregime is studied in the finite open systems for high-precision gravity-relatedexperiments. Through strict derivation, we separate the damping coefficientsfor two finite open systems, i.e., the bi-plate system and the sensor coresystem, into base damping and diffusion damping. This elucidates therelationship between the free damping in the infinite gas volume and theproximity damping in the constrained volume, unifies them into one microscopicpicture, and allows us to point out three pathways of energy dissipation in thebi-plate gap. We also provide the conditions that need to be met to achievethis separation. In applications, for space gravitational wave detection, ourresults for the residual gas damping coefficient for the 4TM torsion balanceexperiment is the closest one to the experimental and simulation data comparedto previous models. For the LISA mission, our estimation for residual gasacceleration noise at the sensitive axis is consistent with the simulationresult, within about $5\%$ difference. In addition, in the test of thegravitational inverse-square law, our results suggest that the constraint onthe distance between TM and the conducting membrane can be reduced by about$28\%$.

Damping Separation of Finite Open Systems in Gravity-Related Experiments in the Free Molecular Flow Regime