Calculate redshift of a Galaxy using recession velocity and distance

Question

A galaxy is receding away from us with a recession velocity of 100,000 km s^−1. What is the distance to this galaxy? (Don't input the distance, just calculate it.) What is the redshift z of this galaxy?

Answer 1

The first part of this problem is find the distance to the galaxy. The recessional velocity of a galaxy (assuming a cosmological red shift) is given by: v = H₀ D The distance can be found by rearranging this equation as D = v ⁄ H₀

where D is the distance to the galaxy, v is the recessional velocity, and H_o is the Hubble Constant (which really isn't a constant at all) ≈ 65 km/s/Mpc (Mpc = megaparsecs, 1 Mpc = 3.2 × 10⁶ light years

D = v ⁄ H₀ = (100,000 km/s) ⁄ 65 km/s/Mpc =1540 Mpc = 4.9 × 10⁹ light years

The equation for the redshift is z = sqrt[ (c +v ) / (c - v)] - 1

c = 3 x 10⁸ m/s (2.998 x 10⁸) = 300,000 km/s

z = sqrt[ (300,000 + 100,000) / (300,000 - 100,000)] -1 = sqrt[ 4 / 2 ] - 1 = 0.41