Estimate how long a galaxy in the Coma cluster would take to travel from one side of the cluster to the other. Assume that the galaxy moves with a constant speed equal to the cluster’s radial velocity dispersion. How does this compare with the Hubble time, t H ? What can you conclude about whether the galaxies in the Coma cluster are gravitationally bound?
Carroll, Bradley W.; Ostlie, Dale A.. Introduction to Modern Astrophysics, An: Pearson New International Edition (Page 1184)
The Attempt at a Solution
The first 2 questions are simple, with values(from some very not reliable encyclopedia)
diameter is 6 mpc
radial dispersion velocity is 1000km/h
hubble time = 13.8 billion years
I reached a conclusion of the time needed is about 0.4 Hubble time.
But I have no clue how does it imply anything about gravitational bound.