6.2.3 The Universe – Redshift & Galaxy Speeds
What is Redshift?
When a galaxy moves away from us, the light it emits stretches, making its wavelength longer. This shift towards the red part of the spectrum is called redshift (🌈).
The Doppler Effect for Light
Just like a car’s horn sounds lower as it drives away, light from a receding galaxy sounds “redder” because its waves are stretched.
Speed from Redshift
For speeds much less than the speed of light, the relationship is:
\$v = c \times \frac{\Delta \lambda}{\lambda_0}\$
- \$v\$ – galaxy’s recessional speed
- \$c\$ – speed of light (\$3.0 \times 10^8\ \text{m/s}\$)
- \$\Delta \lambda = \lambda{\text{observed}} - \lambda0\$ – change in wavelength
- \$\lambda_0\$ – original (rest) wavelength
Step‑by‑Step Example
- Choose a spectral line: Hydrogen alpha line at \$\lambda_0 = 656.3\ \text{nm}\$.
- Measure the observed wavelength: \$\lambda_{\text{obs}} = 700.0\ \text{nm}\$.
- Calculate \$\Delta \lambda = 700.0 - 656.3 = 43.7\ \text{nm}\$.
- Compute the ratio: \$\frac{\Delta \lambda}{\lambda_0} = \frac{43.7}{656.3} \approx 0.0666\$.
- Find the speed: \$v = 3.0 \times 10^8 \times 0.0666 \approx 2.0 \times 10^7\ \text{m/s}\$.
- Convert to km/s: \$v \approx 20\,000\ \text{km/s}\$.
Quick Reference Table
| Galaxy | Observed λ (nm) | Δλ (nm) | Speed v (km/s) |
|---|
| Galaxy A | 700.0 | 43.7 | 20 000 |
| Galaxy B | 650.0 | -6.3 | -2 900 |
Key Takeaways
- Redshift tells us how fast a galaxy is moving away.
- Use the simple formula \$v = c\,\Delta\lambda/\lambda_0\$ for low speeds.
- Positive Δλ → moving away (redshift); negative Δλ → moving toward (blueshift).
- Remember: the farther a galaxy, the larger its redshift and speed.
Practice Question
For a galaxy whose hydrogen alpha line is observed at \$680.0\ \text{nm}\$, calculate its recessional speed in km/s.
Answer: ≈ 12 000 km/s (show steps in class).