Light-years and look-back time: seeing the past

Light is fast, but not instant. In empty space it travels at exactly 299,792,458 m/s, about 300,000 km/s (this value defines the metre). In one year it covers

299,792,458 m/s × 31,557,600 s ≈ 9.46 × 10¹⁵ m, or about 9.46 trillion km.

That distance is one light-year (ly). It is a unit of distance, not time. A star "ten light-years away" is a star that is 10 × 9.46 × 10¹⁵ m away.

Distance becomes time. Because light takes time to arrive, the time it needed is simply t = d / c. We always see an object as it was when the light left it.

Check the first two lines: the Moon is 3.844 × 10⁸ m away, and 3.844 × 10⁸ / 2.998 × 10⁸ ≈ 1.28 s. For the Sun, 1.496 × 10¹¹ / 2.998 × 10⁸ ≈ 499 s.

Looking far means looking back. The light we collect from the Andromeda Galaxy left it about 2.5 million years ago, around the time the first stone tools appeared on Earth. We cannot see what Andromeda looks like today. The picture is not wrong, it is just old, and there is no way to get a fresher one sooner.

This turns telescopes into time machines. The farther away a galaxy is, the earlier in cosmic history we see it. In later worlds we will see the oldest light of all.

The parsec. Astronomers also use the parsec (pc). One parsec is the distance at which one astronomical unit would look like an angle of one arcsecond (an arcsecond is 1/3,600 of a degree). It works out to 3.26 light-years, or 3.09 × 10¹⁶ m. We write kpc (thousand parsecs) and Mpc (million parsecs): the Andromeda Galaxy is about 0.78 Mpc away, and 1 Mpc is about 3.26 million light-years.