🚀 Hubble’s Law & The Big Bang
What we’ll learn:
- Recall the formula \$v = H_0 d\$.
- Use SI units for velocity, distance, and the Hubble constant.
- Show how this simple relationship points to a universe that started from a single point – the Big Bang.
🔭 1. What is Hubble’s Law?
Hubble’s Law tells us that galaxies are moving away from us at a speed proportional to how far they are:
\$v = H_0 \, d\$
- \$v\$ – recession velocity (m s⁻¹)
- \$d\$ – distance to the galaxy (m)
- \$H_0\$ – Hubble constant (s⁻¹)
In everyday terms: the farther a galaxy is, the faster it’s moving away – like the dots on an inflating balloon moving apart as the balloon expands.
📏 2. Units & Typical Values
| Parameter | SI Unit | Typical Value |
|---|
| \$H_0\$ | s⁻¹ | ≈ 2.3 × 10⁻¹⁸ s⁻¹ (≈ 70 km s⁻¹ Mpc⁻¹) |
| \$d\$ | m (or light‑years, parsecs) | e.g., 1 Mpc ≈ 3.09 × 10²² m |
| \$v\$ | m s⁻¹ | e.g., 70 km s⁻¹ ≈ 7 × 10⁴ m s⁻¹ |
🧮 3. Quick Example
Calculate the recession velocity of a galaxy 10 Mpc away.
- Convert distance to metres: \$d = 10 \times 3.09\times10^{22}\,\text{m} = 3.09\times10^{23}\,\text{m}\$
- Use \$H_0 = 2.3\times10^{-18}\,\text{s}^{-1}\$
- Apply Hubble’s Law: \$v = H_0 d = 2.3\times10^{-18}\,\text{s}^{-1} \times 3.09\times10^{23}\,\text{m} \approx 7.1\times10^{5}\,\text{m s}^{-1}\$
- Convert to km s⁻¹: \$v \approx 710\,\text{km s}^{-1}\$
🌌 4. From Hubble’s Law to the Big Bang
Imagine rewinding the universe’s expansion. If galaxies are moving apart now, they must have been closer together in the past. Extrapolating back in time using Hubble’s Law shows that all galaxies would converge to a single point at a finite time in the past.
\$t{\text{past}} = \frac{1}{H0}\$
With \$H0 \approx 2.3\times10^{-18}\,\text{s}^{-1}\$, we get \$t{\text{past}} \approx 4.3\times10^{17}\,\text{s}\$, which is about 13.8 billion years – the age of the universe. This is the Big Bang: a single, hot, dense beginning that has been expanding ever since.
📝 5. Exam Tips
Remember:
- Always use SI units – metres for distance, metres per second for velocity, seconds for the Hubble constant.
- Show the step‑by‑step calculation when converting units.
- Explain the Big Bang idea as a time‑reverse of Hubble’s Law.
- Use the balloon analogy to illustrate expansion.
- Check your answer’s magnitude: 10 Mpc → ~700 km s⁻¹ is a good sanity check.
Good luck! 🌠