Light-Years and Speed of Light

Astronomical distances are huge, so scientists use the light-year. Despite its name, a light-year is a distance, not a time. It is how far light travels in one year through space.

Key ideas

• Speed of light (c): light moves in space at about $3.0\times10^{8}\,\text{m s}^{-1}$.
• Definition: 1 light-year (ly) is the distance light travels in 1 year.
• Scale: $1\,\text{ly} \approx 9.46\times10^{15}\,\text{m} \approx 9.46\times10^{12}\,\text{km}$.

From speed to distance

Use distance–speed–time: $$s = v\,t$$

For one light-year: $$1\,\text{ly} = c \times (1\,\text{year})$$

With $c \approx 3.0\times10^{8}\,\text{m s}^{-1}$ and $1\,\text{year} \approx 365\times24\times3600 = 3.156\times10^{7}\,\text{s}$: $$1\,\text{ly} \approx 3.0\times10^{8}\times3.156\times10^{7} = 9.46\times10^{15}\,\text{m}.$$

Why use light-years?

• The Milky Way is about 100 000 ly across.
• Proxima Centauri (nearest star beyond the Sun) is about 4.2 ly away.
• Using kilometres would give extremely large numbers that are hard to read.

Converting and calculating

• To convert ly to metres: multiply by $9.46\times10^{15}$.
• To convert ly to kilometres: multiply by $9.46\times10^{12}$.
• Time for light to arrive from a star is the distance in light-years (e.g. 10 ly takes 10 years of light travel time).
• If a spacecraft travels at a fraction of $c$, time in years $=$ distance in ly divided by that fraction.

Common misconception

Incorrect: A light-year measures time. Correct: A light-year measures distance, based on the speed of light.