Newton's Cannonball

How can a moon "fall" toward a planet forever and never hit it? In the seventeenth century Isaac Newton answered this with a brilliant thought experiment involving an impossibly powerful cannon on an impossibly tall mountain. It revealed that orbiting is nothing more than falling — done correctly.

The mountain and the cannon

Newton asked his readers to imagine a cannon placed atop a mountain so tall it pokes above the atmosphere, so that air resistance can be ignored. The cannon fires horizontally. With a small charge, the cannonball arcs out and falls to the ground a short distance away, following the familiar curved path of any projectile.

Now fire it harder. The ball travels farther before landing, its curved path stretching out across the landscape. Fire it harder still, and it lands farther yet. Because the Earth is round, something interesting begins to happen: as the ball flies farther, the ground itself curves away beneath it.

The crucial insight

Newton's stroke of genius was to ask: what if you fire the ball so fast that the Earth's surface curves away just as quickly as the ball falls toward it? Then the ball never gets any closer to the ground. It falls continuously, but the ground continuously falls away beneath it by the same amount. The cannonball circles the entire planet and — if nothing stops it — comes back around and strikes the cannon from behind. It has entered orbit.

Falling forever

This reframes one of the most counter-intuitive facts about space. Astronauts on the Space Station are not beyond Earth's gravity — gravity there is nearly as strong as on the ground. They float because they, and their station, are in continuous free fall around the Earth, moving sideways at about 28,000 kilometres per hour. They are falling, endlessly, and endlessly missing the planet. The Moon does exactly the same thing, just farther out and slower.

Unifying heaven and earth

The deepest significance of Newton's cannonball is what it unified. Before Newton, the heavens and the Earth were thought to obey different laws — earthly objects fell, while celestial bodies moved by some separate divine clockwork. Newton's cannonball showed they are the same. The force that makes an apple fall is the very same force that holds the Moon in its orbit. A single law of gravitation governs both. This unification of the terrestrial and the cosmic was one of the greatest intellectual achievements in history.

From thought to reality

For nearly three centuries Newton's cannon remained imaginary. Then, in the twentieth century, humanity built rockets powerful enough to do exactly what he described — fling objects sideways fast enough to fall around the Earth forever. Every satellite, every space station, every GPS signal you rely on is a real-world Newton's cannonball.

Key takeaways

• Newton imagined a cannon firing horizontally from above the atmosphere.
• Fired fast enough, the ball falls toward Earth as fast as the surface curves away.
• The result is an orbit — perpetual falling while missing the ground.
• This showed that the same gravity governs falling apples and orbiting moons alike.