Guided Earth–Moon mission: teacher’s guide
A lesson in which the class takes a spacecraft from Earth orbit into orbit around the Moon, with real physics and the numbers in front of them. Here you will find objectives, a lesson plan, the answers to the guide’s questions and a printable sheet for the pupils.
At a glance
| Duration | one 50–60 minute lesson (the mission itself takes less than ten minutes) |
| Age | lower secondary (last year) and upper secondary school |
| Equipment | interactive whiteboard or projector with internet access; or one computer or tablet per group |
| Link for the class | https://sextans.eu/simulatore/?guida&lang=en |
| Languages | Italian, English, Spanish, French and German |
Objectives
The guide uses the simulator’s real physics: the gravity of the Earth, the Moon and the Sun, an engine with finite thrust and limited propellant. Adapt the objectives to the class.
Lower secondary
- an orbit is a continuous fall: the ship falls, but moves sideways so fast that it always misses the Earth;
- the Moon moves: to reach it you must aim where it will be, not where it is;
- fuel is limited and every manoeuvre has a cost;
- the Apollo missions as an example of scientific work and teamwork.
Upper secondary
- orbital speed and the law of gravitation (v = √(GM/r));
- conservation of energy: the ship slows as it climbs and speeds up as it nears the Moon;
- Δv and the rocket equation (Tsiolkovsky): why departure costs more than braking;
- the point where Earth and Moon pull equally, light travel time, orders of magnitude.
Links: physics (gravitation, circular motion, energy), mathematics (ratios, scientific notation, roots), history (the space race), STEM.
Before the lesson
- Fly the mission once yourself: it takes a few minutes and shows you what the pupils will see.
- Check the connection: the simulator computes the positions of the Earth and the Moon on the server.
- Choose the format: a whiteboard demonstration with a different “pilot” at each stop, or groups with one device each.
- Print the pupil sheet (button at the top): one per pupil or per group.
Lesson plan
| Time | Stop | Teacher | Pupils |
|---|---|---|---|
| 5′ | Introduction | Tells the story of Apollo 11 (July 1969) and shows the goal: an orbit 100 km above the Moon. | Guess how long the trip takes and how much fuel it needs. |
| 10′ | 1 · Earth orbit | Starts a lap and asks the first question. | Note altitude and speed; discuss why the ship does not fall. |
| 5′ | 2 · Launch window | Shows that the Moon moves; starts the window search. | Answer “what if we aimed straight at it?”. |
| 10′ | 3 · Departure | Chooses “Do it yourself”: a pupil fires and stops the engine. | Watch the apoapsis climb; compare their result with the computer’s; note the propellant. |
| 10′ | 4–6 · Journey, correction, approach | Lets time run; stops on the journey and approach questions. | Watch the speed drop and rise again; note the values halfway. |
| 5′ | 7 · Braking | Executes the braking burn and shows the yellow orbit around the Moon. | Note the propellant left and the orbit altitude. |
| 5′ | Summary | Asks the final question and collects the sheets. | Work out the propellant used for departure and braking. |
Questions and answers
Stop 1 · At 400 km gravity is almost 90% of what it is on the ground: why does the ship not fall?
It actually falls all the time. But it moves sideways at about 7.7 km/s: while it falls, the curved surface of the Earth drops away beneath it by the same amount, so the ship never reaches it. This is “Newton’s cannon”. Astronauts float because they fall together with the ship, not because there is no gravity (at 400 km it is about 8.7 m/s², 89% of the value on the ground).
Stop 2 · What would happen if we pointed the ship straight at the Moon right now?
The trip takes 3–5 days and meanwhile the Moon moves about 13 degrees per day along its orbit, that is 40–65 degrees: we would arrive where the Moon was, not where it is. Besides, the ship does not travel in a straight line: it follows an ellipse around the Earth. It is like passing a ball to a running team-mate: you aim ahead of them.
Stop 4 · Why does the speed drop even though nothing is braking the ship?
The Earth’s gravity keeps pulling it back: energy of motion turns into energy of position, as for a stone thrown upwards. After departure the ship travels at almost 11 km/s; halfway it drops below 1 km/s.
Stop 6 · Where does the Moon start pulling the ship harder than the Earth?
The Moon has about 81 times less mass than the Earth. Gravity falls with the square of distance, so the two pulls are equal when the ship is 9 times closer to the Moon than to the Earth (√81 = 9): about 38,000 km from the Moon, 346,000 km from the Earth. From there on the ship “falls” towards the Moon and speeds up.
Summary · Why does leaving the Earth cost so much more than stopping at the Moon? How long does light take for the same trip?
To get away from the Earth you have to climb out of a deep gravity “well”: from low orbit it takes about 3.1 km/s more. The Moon’s gravity is much weaker (escape speed 2.4 km/s against 11.2 for the Earth), so removing about 0.8 km/s is enough to be captured. Light covers the 384,400 km in about 1.3 seconds; the ship took more than four days, about 300,000 times longer.
“Do it yourself” departure · Why does stopping a little earlier or later change the apoapsis so much?
Close to escape speed very little is enough: 25 m/s more or less (under 1% of the push) moves the farthest point of the orbit by tens of thousands of kilometres. That is why real missions always plan course corrections.
Useful numbers
| Mean Earth–Moon distance | 384,400 km |
| Radius of the Moon | 1,737 km |
| Orbital speed at 400 km | 7.7 km/s, one lap in about 92 minutes |
| Departure push | about 3.1 km/s, a burn of just over 5 minutes |
| Braking at the Moon | about 0.8 km/s |
| Trip duration | 3–5 days (Apollo 11: about 76 hours to lunar orbit) |
| Simulator spacecraft | 28 t, of which 25 t propellant; 180 kN engine, specific impulse 350 s |
| Earth–Moon light time | about 1.3 s |
If something goes wrong
- “Astronomy engine unavailable”
- Check the connection and press Start again.
- No launch window
- Press “Find the launch window” again, or start again from another date.
- “Too much push” or “Too little push” after a hand-flown departure
- Press “Try the burn again”: the ship goes back to the departure point. A great moment to discuss why.
- The correction or the braking burn fails
- Press “Advance one hour” and try again: from another point of the trajectory the manoeuvre changes.
- The ship crashes
- This happens if the manoeuvres were changed by hand: press Start again.
Back to the top ↑ · Open the guided mission · Simulator manual
Earth–Moon mission · pupil sheet
During the mission write down the values you see in the “What to watch” box.
| Moment | Altitude (km) | Speed (km/s) | Propellant (kg) | What do you notice? |
|---|---|---|---|---|
| In Earth orbit | ||||
| Just after departure | ||||
| Halfway | ||||
| Near the Moon | ||||
| In lunar orbit |
- Why does the ship in orbit not fall onto the Earth?
- Why is the ship not pointed straight at the Moon?
- Your departure: apoapsis reached ______ km; computer’s target ______ km. What did you learn?
- Why does the speed drop during the journey and then rise again?
- Propellant used for departure: ______ kg; for braking: ______ kg. Why the difference?