Editing Virial theorem (section)

==== Theoretical analysis ====
He approximated the Coma cluster as a spherical "gas" of <math>N</math> stars of roughly equal mass <math>m</math>, which gives <math display="inline">\langle T \rangle= \frac 12 Nm \langle v^2 \rangle</math>. The total gravitational potential energy of the cluster is <math>U = -\sum_{i < j} \frac{Gm^2}{r_{i,j}}</math>, giving <math display="inline">\langle U\rangle = -Gm^2 \sum_{i < j} \langle {1}/{r_{i,j}}\rangle</math>. Assuming the motion of the stars are all the same over a long enough time ([[ergodicity]]), <math display="inline">\langle U\rangle = -\frac{1}2 N^2 Gm^2\langle {1}/{r}\rangle</math>.

Zwicky estimated <math>\langle U\rangle</math> as the gravitational potential of a uniform ball of constant density, giving <math display="inline">\langle U\rangle = -\frac 35 \frac{GN^2m^2}{R}</math>.

So by the virial theorem, the total mass of the cluster is<math display="block">Nm = \frac{5\langle v^2\rangle}{3G\langle \frac{1}{r}\rangle}</math>