Know that one light-year is equal to 9.5 × 10^15 m

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

1. Speed of light: $c = 3.0 \times 10^8\,\text{m/s}$
2. Seconds in a year: $1\,\text{yr} = 3.15 \times 10^7\,\text{s}$
3. Multiply: $c \times 1\,\text{yr} = 3.0 \times 10^8 \times 3.15 \times 10^7$
4. Result: $9.5 \times 10^{15}\,\text{m}$

Exam Tip 💡