Virial Theorem, Dark Matter, and N-Body Problems

While the Virial Theorem relates the time averages of the kinetic and potential energies as time goes to infinity, it is typical to make simplifying assumptions to convert this conclusion into a working tool for astronomy to determine, for instance, a galaxy’s “virial mass.” As described here, consequences associated with these assumptions may impose undesired dynamical behavior and lead to larger virial mass estimates. The N‐body “configurational measure” is also described.