explain why redshift leads to the idea that the Universe is expanding

What is Redshift? 🔭

When a star or galaxy moves away from us, the light it emits stretches to longer wavelengths. This shift towards the red end of the spectrum is called redshift.

The amount of shift is measured by the ratio $z = \dfrac{\lambda_{\text{observed}} - \lambda_{\text{emitted}}}{\lambda_{\text{emitted}}}$.

Think of it like a stretching rubber band that gets longer as the source moves away.

Redshift and Distance: Hubble’s Law 🚀

Edwin Hubble found that the redshift of a galaxy is proportional to its distance: $v = H_0 \, d$, where $v$ is the recession velocity, $H_0$ is the Hubble constant, and $d$ is distance.

Using the Doppler approximation for small speeds, $v \approx c\,z$, we can rewrite Hubble’s Law as $z \approx \dfrac{H_0}{c}\, d$.

This means the farther a galaxy is, the more its light is redshifted—just like the sound of a siren gets lower as an ambulance drives away.

Why Does This Imply an Expanding Universe? 🌍

1. All galaxies show a redshift that increases with distance.
2. There is no preferred direction—every galaxy sees the same trend.
3. From Einstein’s equations, a uniform expansion stretches space itself, not just objects moving through space.

Imagine inflating a balloon with dots on it. As the balloon expands, every dot moves away from every other dot, and the distance between them grows. The dots are like galaxies; the balloon’s surface is like space.

Exam Tip Box 📚

• Remember the key equation: $z = \dfrac{v}{c}$ for small velocities.
• Use Hubble’s Law to calculate distances if given a redshift.
• Explain the balloon analogy when asked why the universe is expanding.
• Show that redshift is not due to motion through space but due to space itself stretching.

Quick Recap 🎯

• Redshift = stretching of light wavelengths.
• Hubble’s Law links redshift to distance.
• Uniform redshift in all directions → Universe expanding.

Keep the balloon analogy handy; it’s a favourite for explaining cosmic expansion in exams!