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The speed of light

Waves, sound and light · level 5, lesson 3 of 6

A question to start

When engineers send a command to a rover, the rover does not get it for several minutes. Radio travels at the speed of light, the fastest speed there is. So why the wait?

The idea

Light, and radio, travel through empty space at about

\[c = 3.00\times10^8 \text{ m/s},\]

300,000 km every second. That is fast enough to go round the Earth seven times in a second. But Mars is so far away that even light takes minutes.

Light travel times Mars Earth
Average distance from the Sun 227.9 million km 149.6 million km
Sunlight takes 12.7 minutes 8.3 minutes

Between Mars and Earth, the distance swings from 54.6 to 401.4 million km, so a radio signal takes from 3.0 to 22.3 minutes. The distance changes because they travel round the Sun at different speeds. Sometimes they are on the same side of the Sun, sometimes on opposite sides.

closest: 3 minutesopposite sides:22 minutes

Worked examples

1. Sunlight to Mars. \(t = d/c = 227.9\times10^9/3.00\times10^8 = 760\) s, about 12.7 minutes.

2. Closest. \(54.6\times10^9/3.00\times10^8 = 182\) s, about 3.0 minutes.

3. Farthest. \(401.4\times10^9/3.00\times10^8 = 1338\) s, about 22.3 minutes.

Try it

  1. How fast does light travel in empty space?
  2. How long does a radio signal take to go to Mars and back when Mars is closest?
  3. A signal takes 10 minutes to reach Mars. How far away is it?
  4. Why is the light travel time to Mars not always the same?
Answers
  1. About \(3.00\times10^8\) m/s.
  2. About 6 minutes.
  3. \(3.00\times10^8 \times 600 = 1.8\times10^{11}\) m, 180 million km.
  4. The distance between Earth and Mars keeps changing as they orbit the Sun.

Common mistake

Mixing up km and m. 1 million km is \(10^9\) m. Change to metres before dividing by \(3.00\times10^8\) m/s.

Where it leads