Final answer:
Distance measurements can determine the age of the Universe by using the redshift of light from galaxies to calculate their distance. By understanding how long ago the light was emitted (look-back time) and assuming a consistent expansion rate, we can piece together the age of the Universe.
Step-by-step explanation:
Distance measurements inform us about the age of the Universe through a process that involves observing galaxies at various distances. The redshift observed in the light from a galaxy, which indicates how much the wavelength has been stretched due to the expansion of the universe, is directly related to its distance from us. Using Hubble's Law, which correlates the redshift to the speed at which a galaxy is moving away from us, astronomers can determine how far away a galaxy is. Moreover, as the speed of light is constant, we can calculate how long the light has taken to reach us, which tells us how long ago the galaxy emitted the light we are now observing. Hence, by measuring distances to these distant galaxies, we obtain a 'look-back time,' which reflects the state of the universe at various stages in its development, allowing us to piece together its overall age.
For example, if we observe a galaxy that is 400 million light-years away moving with a velocity calculated using the Hubble constant of 20 km/s per million light-years, its velocity would be 8,000 km/s. If it has always been receding at this rate, we can estimate that it was next to our own Galaxy approximately 20 billion years ago. While this is an oversimplification and assumes a constant rate of expansion (which we know has changed over time), it gives us a rough estimate and evidences the techniques used to age the universe.