An observer on Earth observes the hydrogen- \(\beta\) line of a distant galaxy shifted from its laboratory measured value of \(434 \mathrm{~nm}\) to a value of \(510 \mathrm{~nm}\). How fast was the galaxy receding from the Earth at the time the light was emitted? (You may neglect the effects of the cosmological redshift due to the expansion of the universe during the time of flight of the photons.)