What is Astronomical unit and light-year? — Physics

Definition 1.13 High School Physics · Chapter 1 — Orders of Magnitude: Measuring the Universe

The astronomical unit ( $1\,\mathrm{au} = 1.496 \times 10^{11}\,\mathrm{m}$ ) is the average Earth–Sun distance. The light-year ( $\mathrm{ly}$ ) is the distance light travels in one year. Light moves in vacuum at

c = 3.00 \times 10^{8}\,\mathrm{m}/\mathrm{s},

the fastest speed nature allows — so the light-year is a distance, not a time.

Distances from Earth on the multiplicative ruler, with light’s travel time in red beneath each: the Moon is light-seconds away, the planets light-hours, the stars light-years.

Examples

Example 1.14 (The light-year in metres)

A year holds $365.25 \times 24 \times 3600 = 3.156 \times 10^{7}\,\mathrm{s}$ (pleasantly close to $\pi \times 10^{7}\,\mathrm{s}$ ). Hence

1\,\mathrm{ly} = c \times 3.156 \times 10^{7}\,\mathrm{s} = 3.00 \times 10^{8}\,\mathrm{m}/\mathrm{s} \times 3.156 \times 10^{7}\,\mathrm{s} = 9.47 \times 10^{15}\,\mathrm{m}.

Proxima Centauri, the nearest star after the Sun, lies $4.2\,\mathrm{ly} \approx 4.0 \times 10^{16}\,\mathrm{m}$ away: light, which crosses an Earth–Sun distance in eight minutes, needs over four years to arrive from there.

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