Question

Measurements of the radial recession velocities of five galaxies in a cluster give velocities of 9700, 8600, 8200, 8500, and 10,000 km/s. What is the distance to the cluster if the Hubble parameter is H0​?

Answer 1

To find the distance to the cluster, we can use Hubble's law. Rearranging the equation, we get the distance = recessional velocity / Hubble parameter.

Step-by-step explanation:

To find the distance to the cluster, we can use Hubble's law, which states that the recessional velocity of a galaxy is proportional to its distance from us. The equation for Hubble's law is given as v = H0 * d, where v is the recessional velocity, H0 is the Hubble parameter, and d is the distance to the galaxy or cluster. Rearranging the equation, we get d = v / H0.

In this case, we are given the recessional velocities of five galaxies in the cluster: 9700 km/s, 8600 km/s, 8200 km/s, 8500 km/s, and 10,000 km/s. Let's take the average of these velocities and substitute it into the formula. The average is (9700 + 8600 + 8200 + 8500 + 10,000) / 5 = 9000 km/s.

Now, we can plug in the values into the equation: d = 9000 km/s / H0.

Therefore, the distance to the cluster is 9000 km/s divided by the value of the Hubble parameter, H0.