The Relationship between Distance and Redshift of Distant Galaxies

Introduction

The redshift of a galaxy is a measure of how much its light has been stretched or “reddened” as it travels through an expanding universe.
A larger redshift implies a longer distance travelled, hence redshift can be used as a scale to measure the distance of very far away galaxies.

Hubble’s Law and Redshift

Hubble’s Law is a cornerstone of modern cosmology stating that the redshift of a galaxy is proportional to its distance from us.
It was discovered by Edwin Hubble in the 1920s and can be represented in simple terms as velocity = Hubble constant x distance.
The Hubble constant is the proportionality factor in this equation, measuring the rate at which the universe is expanding.

Interpretation of Distance-Redshift Relationship

The further away a galaxy is from us, the more the universe has expanded while the light from that galaxy was travelling to us. Thus, the light gets stretched more, resulting in a higher redshift.
This stretching of light, or redshift, is what we measure and it is this measurement that leads us to conclude the universe is expanding.
The greater the distance, the greater the redshift, indicating that the universe is not just expanding, but the expansion is also accelerating.

Importance of Redshift

Understanding this relationship between distance and redshift powers some of our most fundamental measures of the universe, such as its age, size, and expansion rate.
By plotting redshift against distance for a large number of galaxies, scientists can determine the slope of the graph, hence the Hubble constant, and therefore the rate of expansion of the universe.

Cosmic Redshift and the Big Bang Theory

This understanding of cosmic redshift offers strong support for the Big Bang Theory, which posits all matter and energy were once compacted in an extremely dense point that exploded and began expanding.
If the universe is expanding from an initial point, then the further away a galaxy is from us, the more time light from it has had to travel and thus the more it shifted towards red, which is exactly what we observe.

Remember to understand not only the concepts of redshift and distance but also how they relate and how this relationship supports the idea of an expanding, and indeed accelerating, universe. This is crucial for your understanding of cosmology.