(Note: this exercise is a continuation of Exercise 12.)

Through other investigations, you convince yourself that the
galaxy described in Question 3(b) above is indeed gravitationally
bound to Abell 2218.  This means that its velocity, 950 km/sec,
is probably close to its orbital velocity around the center of
the cluster.

(a) Using the assumptions above, how much total mass exists 
within a 1000 kpc radius of the center of Abell 2218?  

(b) Remember your estimate of the mass of the visible matter in the 
cluster from Question 2(b) above.  How many times greater or smaller 
is the total mass compared to the mass of visible matter?  How does
the overall density of the cluster compare to the density of the visible 
matter in the cluster?

(c) Does this series of calculations confirm the existence of "dark matter"
in Abell 2218?  Give well reasoned arguments for and against this conclusion.