The average radial velocity of galaxies in the Hercules cluster is 10,800 km/s. (a) using H0 = 73 km/s/Mpc, find the distance to the Hercules cluster in Mpc. (b) How would your answer to (a) differ if the Hubble constant had a smaller value?

a) 147.95 Mpc

Explanation:

Using Hubble's formula

where;

v = radical velocity

= Hubble's constant

d = distance

Given that:

The average radial velocity of galaxies in the Hercules cluster v =  10,800 km/s

Also using = 73 km/s/ Mpc ; we  make distance d the subject of the formula:

Then distance d can be written as:

d = 147.95 Mpc

b)

Now, if the Hubble constant had a smaller value, then for a  given velocity the distance to the galaxy will increase because distance d is inversely proportional to

i.e  

d  ∝

total distance travelled = 60 miles

total time taken =1.5 hours

average speed = total distance / total time

60 / 1.5

= 40

therefore, average speed = 40 m/h

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