Fire Newton's cannon. Put it in orbit.

The lesson opens on Newton's own thought experiment: a cannon on a tower above the air, fired flat at three speeds. Each shot comes down further round the Earth, and the screen asks how fast it must go never to land. Then every phone sets a speed, from 0 to 12,000 m/s, and an angle above flat, from 0° to 90°, and predicts whether its shot will crash, orbit or escape. When the launches lock, the big screen fires up to 24 of them from the one cannon at once, in model time at one hour every two seconds: some come down, some loop round and come back to the tower, some leave the frame for good. In a bigger room the 24 are a declared sample, spread by speed, and the screen says so.

Then every launch lands as a mark at its speed and angle, shaped and coloured by what happened, and the pen inks the model's two boundaries: the escape line, vertical at 7,910 m/s, and the crash boundary, which starts at 4,567 m/s for a flat shot and meets the escape line at 45°, above which every shot slower than escape comes back down. Beside it, a small table sets what each person predicted against what happened. Only now does each phone show its owner's own result: where the shot went, how high it climbed and how long it took to come back.

Why is the escape line vertical? Whether a shot escapes depends on its energy, and its energy depends only on its speed at the tower, never on its direction: aiming up gives a shot nothing extra. From the tower, two Earth radii from the centre, the escape speed is √(2μ/r) = 7,910 m/s at every angle, which happens to equal the speed of a circular orbit at the ground. The angle decides the shape instead. Round 2 asks for a circle, the same height all the way round, and only a flat shot at the circular speed, √(μ/r) = 5,593 m/s, gives one: aimed up, or a little faster or slower, it becomes an oval.

The finale is Kepler's third law. A board on log scales plots how long each orbit takes to come back against its size, half its long axis, and every orbit of both rounds falls on one line, Newton's T = 2π√(a³/μ), with three real satellites on it too: the ISS, a GPS satellite and a geostationary one, each a dated published value. The room's orbits lie exactly on the line because they are model orbits; the satellites are the evidence. Then the twin shot flies two of the room's launches at one speed, one flat and one aimed up, or the model's own pair where no two match. Their paths look nothing alike, and they come back to the tower together: the same speed is the same energy, so the same size and the same period.

Every number is a model: Newton's gravity around a point-mass Earth, with no air, and the Earth does not spin. From a tower one Earth radius high. No mountain is this tall: Newton imagined one above the air, and the height makes the paths easy to see. The screen shows the room's launches as anonymous marks, and the lesson keeps counts only; each phone is told only its own launch's outcome, once the screen has shown the room's.

Try the screen-and-phone preview, where your phone fires one launch and fictional classmates fire theirs through the same runtime as the lesson; they are illustrative, not observations of a real class. To fire the cannon alone, use the bench above.