How does Hubble's Law relate to red-shift?

Hubble's Law states that the further away a galaxy is, the faster it is moving away from us.

Hubble's Law is a key concept in understanding the expanding universe. It was discovered by Edwin Hubble in the 1920s when he observed that galaxies are moving away from us, and the speed at which they are receding is proportional to their distance from us. This relationship is expressed mathematically as \( v = H_0 \times d \), where \( v \) is the velocity at which a galaxy is moving away, \( H_0 \) is the Hubble constant, and \( d \) is the distance to the galaxy.

Red-shift is a phenomenon where the light from an object moving away from us is shifted towards the red end of the spectrum. This happens because the wavelengths of the light are stretched, making them longer and thus redder. In the context of galaxies, the red-shift is a direct indicator of their velocity relative to us. The greater the red-shift, the faster the galaxy is moving away.

Hubble's Law and red-shift are closely related because the red-shift provides the evidence for the velocities of galaxies. By measuring the red-shift of a galaxy's light, astronomers can determine how fast it is moving away. When they plot these velocities against the distances of the galaxies, they find a linear relationship, which is Hubble's Law. This relationship supports the idea that the universe is expanding, with galaxies moving away from each other over time.

Understanding Hubble's Law and red-shift helps us grasp the scale and dynamics of the universe. It shows that the universe is not static but constantly changing, with galaxies drifting apart as space itself expands. This discovery has profound implications for cosmology, the study of the origin and development of the universe.