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A message to Mars

Space and time · level 3, lesson 5 of 6

A question to start

You send a "hello" by radio to a friend on Mars. How long before they hear it? How long before you hear their reply?

The idea

Radio travels at the speed of light. But Mars is so far away that even light takes minutes:

  • When Mars is closest, about 54.6 million km away: about 3 minutes.
  • When Mars is farthest, about 401 million km away: about 22 minutes.

A reply takes just as long to come back. So a chat with Mars has a long, awkward pause in it: from about 6 minutes to about 45 minutes between saying "hello" and hearing "hello" back.

"hello": 3 to 22 minutesreply: 3 to 22 minutesEarthMars

Worked examples

1. Closest. \(54{,}600{,}000 \div 300{,}000 = 182\) seconds: about 3 minutes.

2. Farthest. \(401{,}000{,}000 \div 300{,}000 \approx 1{,}337\) seconds: about 22 minutes.

3. A middle distance. Suppose Mars is 225 million km away. \(225{,}000{,}000 \div 300{,}000 = 750\) seconds: 12 and a half minutes each way, 25 minutes there and back.

Try it

  1. About how long does a message take to reach Mars at its closest?
  2. And at its farthest?
  3. Why can you not have a normal phone call with someone on Mars?
  4. Mars is 90 million km away. How long does a message take?
Answers
  1. About 3 minutes.
  2. About 22 minutes.
  3. Each message takes minutes to arrive, so every reply comes much later.
  4. \(90{,}000{,}000 \div 300{,}000 = 300\) seconds: 5 minutes.

Common mistake

"The delay is always the same." It changes all the time, from about 3 minutes to about 22, as Earth and Mars move round the Sun.

Where it leads