In Light-Years, Stars and Galaxies you met the light-year as a distance. Here is the other side of that idea: because light needs time to reach us, every look into space is a look into the past. Light is part of the electromagnetic spectrum, and all of it, from radio to gamma rays, travels through space at the same speed, $c = 3.00 \times 10^{5}$ km/s.
Why it works
Light is fast but not instant. In 1676 Ole Rømer noticed that the eclipses of Jupiter's moon Io came several minutes late when Jupiter was far from Earth and early when it was near: the light carrying the news needed extra time to cross the wider gap. Travel time is distance divided by speed, $t = \dfrac{d}{c}$. A light-year is how far light goes in one year: $3.00 \times 10^{5}\ \text{km/s} \times 3.156 \times 10^{7}\ \text{s} = 9.46 \times 10^{12}$ km. So light from an object $N$ light-years away left it $N$ years ago. The numbers are huge, so operations in scientific notation do most of the work.
Key idea
Light takes time $t = d/c$ to reach us, so we see every object as it was when its light left: the Sun as it was $8.3$ minutes ago, the nearest star $4.2$ years ago, the Andromeda Galaxy about $2.5$ million years ago.
Worked examples
Worked example: Sunlight
The Sun is $1.496 \times 10^{8}$ km away. How long does its light take to reach us?
- $t = \frac{1.496 \times 10^{8}\ \text{km}}{3.00 \times 10^{5}\ \text{km/s}} = 4.99 \times 10^{2}$ s.
- $499 \div 60 = 8.3$ min.
- If the Sun vanished, we would keep seeing it, and Earth would keep orbiting, for about 8 minutes.
Answer: About $8.3$ minutes.
Worked example: Driving on Mars
Mars is $2.25 \times 10^{8}$ km away. How long must a rover driver wait for a reply to a command?
- The signal goes there and back: $4.50 \times 10^{8}$ km.
- $t = \frac{4.50 \times 10^{8}}{3.00 \times 10^{5}} = 1.50 \times 10^{3}$ s $= 25$ min.
- With a 25-minute delay, nobody can steer a rover live, so rovers carry software to drive themselves between commands.
Answer: $25$ minutes.
Common mistake
It is natural to think we see the stars as they are now. We never do. The light from Betelgeuse left it centuries ago; if it exploded tonight, nobody on Earth would know for hundreds of years. Check the units: a light-year is a distance, and the travel time in years equals the distance in light-years. The farther away we look, the older the view, which is how astronomers study the young universe: they look very far.
| Object | Distance | Light travel time |
|---|---|---|
| Moon | $3.84 \times 10^{5}$ km | $1.3$ s |
| Sun | $1.50 \times 10^{8}$ km | $8.3$ min |
| Neptune | $4.5 \times 10^{9}$ km | $4.2$ h |
| Proxima Centauri | $4.2$ ly | $4.2$ yr |
| Center of the Milky Way | $26{,}000$ ly | $26{,}000$ yr |
| Andromeda Galaxy | $2.5$ million ly | $2.5$ million yr |