What is the predicted mass of the Coma cluster using a simple model?

[rohanlol7]

Homework Statement

An estimate of the mass of the Coma cluster can be made from the velocity of the galaxies relative to the centre of mass of the cluster; the velocities are around 2000 km s-1. The stars that form the cluster have been together for a long time. Show that a simple model will predict a mass of the cluster of the order of 2*10^43kg. The radius of the Coma cluster is about 10^21m.

Homework Equations

GMm/R^2 =Mv^2/R

The Attempt at a Solution

Tried a few things. First i tried to consider that as a spherical hollow shell. I calculated by using the above equation ( just plugin in values ) and i was off by a factor of 3. Next i tried to consider 2000 as being the AVERAGE speed. This time i was wrong by a factor of about 10.
I tried to model it as a disk but that seemed to complex

 

[fresh_42]

Wikipedia says the Coma cluster has est. $10^{14} - 10^{15}$ sun masses, i.e. $\; 2\cdot 10^{44}-2\cdot 10^{45}\,kg$.
Isn't this your factor $10$?

 

[rohanlol7]

Wikipedia says the Coma cluster has est. $10^{14} - 10^{15}$ sun masses, i.e. $\; 2\cdot 10^{44}-2\cdot 10^{45}\,kg$.
Isn't this your factor $10$?

Maybe but the problem wants me to obtain 2*10^43