To determine the distance to this quasar using the Hubble relation (assuming
the redshift is cosmological in origin) we do the following steps:
1. Measure the redshift off the spectrum above:
3C 273 Hydrogen beta line redshift Dl = l
- lo = 77.9 nm
2. Use the doppler relation to determine the radial
velocity: v/c = Dl/lo
(lo
= 486.1 nm, Hb
rest wavelength) v = (77.9 nm / 486.1 nm) x
300,000 km/s = 48,000 km/s
3. Use the
Hubble relation with the current best value of Hubble's constant (Ho
= 71 km/s/Mpc) to determine the distance: D = v/Ho
; D = 48,000 km/s / 71 km/s/Mpc ;
D = 677 Mpc = 2.2 billion light years