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One way and round trip

Space and time · level 6, lesson 2 of 6

A question to start

A rover team sends "take a picture" when Mars is 15 light-minutes away. How soon can they see the picture?

The idea

Mission teams use two delays:

  • One-way light time: how long a signal takes to go from Earth to Mars, or back.
  • Round-trip light time: there and back, twice as long.
\[t_\text{one way} = \frac{d}{c}, \qquad t_\text{round trip} = \frac{2d}{c}.\]

The one-way time tells you how old the news is. A picture arriving now shows Mars as it was one light time ago. The round trip tells you how long any question takes to answer: you cannot see the effect of a command sooner than one round trip, plus the time the rover spends doing it.

Across the range of Earth to Mars distances:

  • closest, 54.6 million km: about 3.0 min one way, 6.1 min round trip;
  • farthest, 401 million km: about 22.3 min one way, 44.6 min round trip.
EarthMarssendtake picturepicture arrivesone wayone way

Worked examples

1. The picture. 15 minutes there, say 5 minutes to take it, 15 minutes back: at least 35 minutes.

2. From distance. Mars is 300 million km away. \(300{,}000{,}000 \div 300{,}000 = 1{,}000\) s one way, about 16.7 minutes. Round trip: about 33 minutes.

3. How old is the news? A weather report from Mars arrives when the one-way time is 10 minutes. It describes the weather 10 minutes ago, before any change since.

Try it

  1. What is the difference between one-way and round-trip light time?
  2. Which one tells you how old a picture is?
  3. Mars is 120 million km away. Find both delays.
  4. A command reaches the rover, which spends 20 minutes on it. The one-way time is 8 minutes. When does the team see the result, counting from sending?
Answers
  1. Round trip is there and back: twice the one-way time.
  2. One-way.
  3. One way \(120{,}000{,}000 \div 300{,}000 = 400\) s, about 6.7 min. Round trip about 13.3 min.
  4. \(8 + 20 + 8 = 36\) minutes.

Common mistake

Forgetting the way back. The command needs one light time to arrive, and the reply needs another one to come home.

Where it leads