Question

After analyzing the spectrum of a distant galaxy, an astronomer identifies a spectral line as being CaII (singly ionized Calcium) with a measured wavelength of 410.0 nm. The true, rest wavelength of this spectral line, measured in a lab, is 393.3 nm.

a) What would be this galaxy’s recessional velocity, in km/s? b) Using a Hubble constant of H0 = 70 km/s/Mpc, calculate the distance to this cluster. Give your answer in megaparsecs and in light-years. c) How would your answer to part b) differ if the Hubble constant had a smaller value? A larger value? Explain.

Answer 1

Hello,

a) Solution:

The expression of the recessional velocity of galaxy is

Where, v is the recessional velocity of galaxy

c is speed of light

   .....(1)

Here,

Substitute the all values in equation (1) and find v

The recessional velocity of galaxy is.

b) Solution:

Given: Hubble constant

We have to find the distance to the cluster.

The expression of the relation between recessional velocity, Hubble constant and distance to cluster is

The distance to the cluster in pc is .

The relation between pc and light year is

The distance to the cluster in light year is .

c) Solution:

From this expression, distance to the cluster is inversely propotional to Hubble constant.

If the value of Hubble constant is large then the value of distance to the cluster is small and when the value of Hubble constant is small then the value of distance to the cluster is large.

Thanking You!