6.2.2 Stars – Distance and Light‑Years 🚀
Objective
Know that one light‑year is equal to \$9.5 \times 10^{15}\,\text{m}\$.
Why a Light‑Year Matters
A light‑year is the distance light travels in one year. Light moves at a constant speed of \$c = 3.0 \times 10^8\,\text{m/s}\$ (≈ 300,000 km/s). Because space between stars is huge, we use light‑years instead of metres to keep numbers manageable. 🌌
Analogy: The Marathon Runner
- Imagine a marathon runner who covers 42 km in a day. If that runner kept running for an entire year (365 days), they would travel about 15,300 km.
- Now think of light as a runner that can cover 300,000 km in just one second! Over a year, it would cover a distance that is 9.5 quadrillion metres – that’s a light‑year.
- So, a light‑year is like the runner’s “year‑long marathon” but with light’s incredible speed.
How to Calculate a Light‑Year
- Speed of light: \$c = 3.0 \times 10^8\,\text{m/s}\$
- Seconds in a year: \$1\,\text{yr} = 3.15 \times 10^7\,\text{s}\$
- Multiply: \$c \times 1\,\text{yr} = 3.0 \times 10^8 \times 3.15 \times 10^7\$
- Result: \$9.5 \times 10^{15}\,\text{m}\$
| Step | Formula | Result |
|---|
| 1 | \$c = 3.0 \times 10^8\,\text{m/s}\$ | \$3.0 \times 10^8\,\text{m/s}\$ |
| 2 | \$1\,\text{yr} = 3.15 \times 10^7\,\text{s}\$ | \$3.15 \times 10^7\,\text{s}\$ |
| 3 | \$c \times 1\,\text{yr}\$ | \$9.5 \times 10^{15}\,\text{m}\$ |
Exam Tip 💡
Remember: 1 light‑year = \$9.5 \times 10^{15}\,\text{m}\$.
Use this value directly when converting distances in exam questions.
Check units carefully – metres are the standard unit in physics, but the exam may ask for kilometres or astronomical units (AU).
Practice converting between metres, kilometres, and light‑years to build confidence.
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