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The trip to Mars

Rockets and landing · level 4, lesson 3 of 6

A question to start

The Perseverance rover left Earth on 30 July 2020 and landed on Mars on 18 February 2021, 203 days later. In that time it travelled about 470 million km. But Mars was never more than about 400 million km away. Why the long way round?

The idea

A ship going to Mars does not fly in a straight line. Like everything near the Earth, it is already going round the Sun with the Earth, at 30 km/s. When it leaves, it moves onto a new orbit round the Sun, a long curve that reaches out to Mars's orbit. The cheapest curve is half an ellipse, and takes about 8.5 months; real missions often push a little harder to take 6 to 8 months.

The steps of the trip:

  1. Launch into an orbit round the Earth, or straight onto the path to Mars.
  2. The departure burn: about 3.6 km/s added in a few minutes, to leave the Earth for Mars.
  3. Cruise. Months of coasting round the Sun, with no engine running. A few small burns, called trajectory correction manoeuvres, fine-tune the aim. Perseverance made several.
  4. Approach. In the last weeks, the navigators work out exactly where the ship will hit the top of the air of Mars, to within a few kilometres.
  5. Entry, descent and landing: the seven minutes, in the next lesson.

Leaving at the right time. The ship must leave when Mars is in the right place, about 44° ahead of the Earth, so that Mars arrives at the meeting point at the same time. That happens about every 26 months: these are the launch windows.

Talking to the ship. Radio signals travel at the speed of light, but Mars is so far away that a message takes 3 to 22 minutes to arrive, depending on where the planets are. When Perseverance landed, a signal took 11 minutes 22 seconds to reach Earth.

With a crew. People on the trip would float for months, so they would exercise every day to keep their bones and muscles. Outside the Earth's magnetic field, they would be exposed to more radiation, and the ship would need shielding. They would carry all their food, water and air, and recycle as much as they could.

Worked examples

1. The long way. The ship travels about half way round the Sun on an orbit about 1.26 times as big as the Earth's. Half of that ellipse is roughly 590 million km on the cheapest path; Perseverance's faster path was about 470 million km.

2. Light delay. At 225 million km (about the average), light takes \(225{,}000{,}000 \div 300{,}000 = 750\) s, which is 12.5 minutes.

Try it

  1. How long did Perseverance take to reach Mars?
  2. Why doesn't a ship to Mars fly in a straight line?
  3. What is a trajectory correction manoeuvre?
  4. Mars is 100 million km from Earth. How long does a radio message take?
  5. Why can't the ship leave whenever it is ready?
Answers
  1. 203 days.
  2. It is in orbit round the Sun the whole time; every path it can take is a curve round the Sun.
  3. A small engine burn during cruise to fine-tune the ship's path.
  4. \(100{,}000{,}000 \div 300{,}000 \approx 333\) s, about 5.5 minutes.
  5. Mars must reach the meeting point at the same time as the ship; that only lines up about every 26 months.

Common mistake

"Ships to Mars fire their engines all the way." They fire for a few minutes to leave, then coast for months. In space nothing slows them down, so there is no need to keep pushing.

Where it leads