Observed stellar velocities estimate $T$, while visible mass and size predict $V$. Galaxies and clusters often have far more kinetic energy than luminous matter can bind under the <virial theorem>. The additional gravitational potential is evidence for unseen dark matter.

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 4 / 9B / b / Solution

 Solution (source code)