Mathematical snapshots motivated by “dark matter”

A standard difficulty in astronomy is the inability to observationally verify basic assumptions about the dynamics such as that the moment of inertia of a system can be set equal to a constant, or that $2T = U$ where T and U are, respectively, the system’s kinetic energy and self‐potential. To address these kinds of problems, the approach developed here is to introduce long term consequences of the assumptions. To be useful, the consequences must be of the type that can be observationally checked. The choices of illustrating assumptions come from aspects of how mass is computed for dark matter considerations.