Newton’s cannonball: why the Moon doesn’t fall

This thought experiment is over three hundred years old and is still the shortest route to understanding spaceflight. Newton sketched it in his "Treatise of the System of the World": a cannon on a mountain so tall it reaches above the atmosphere. Fire — the ball falls beyond the horizon. Fire harder — it falls farther. And at a certain speed, something strange happens. Try it yourself: move the slider and fire.

A fall that keeps missing

A cannonball always falls — gravity makes no exceptions. But the Earth is round, so its surface drops away beneath the flight path: over every 8 kilometres of horizontal distance, the ground "falls" by about 5 metres. Now for the key coincidence: a freely falling body drops about 5 metres in its first second. So if the ball flies horizontally at 8 kilometres per second, it falls by exactly as much as the ground curves away. It keeps falling — and it keeps missing.

The Moon has been falling for 4.5 billion years

The Moon does exactly the same. Every second it falls towards the Earth by a fraction of a millimetre — precisely enough to bend its straight path into a circle. Newton computed that fraction, compared it with a falling apple, and the numbers agreed: the same force governs the orchard and the heavens. That was the moment terrestrial and celestial physics became one science.

An orbit is a fall that forever misses the ground.

From cannon to rocket

This picture corrects the most common misconception about rockets: getting to orbit is not a problem of altitude but of speed. You could, in principle, take an elevator a hundred kilometres up — and you would fall straight back down. Rockets launch vertically only to get out of the thick atmosphere, then pitch over and accelerate along the horizon to those ~7.8 km/s. Almost all the fuel is spent on horizontal speed, not on height.

In the figure you will also find a third regime: above 11.2 km/s the ball’s energy is positive and no ellipse will ever bring it back — that is escape velocity, a one-way ticket out of Earth’s gravity. Between the circular orbit and escape stretches a whole family of ellipses — the very paths flown by the GPS satellites of our next article.

A simplificationWe ignore air resistance (Newton’s mountain deliberately reaches above the atmosphere — near the surface the ball would burn up in seconds), treat the Earth as a uniform sphere, and fire perfectly horizontally. The mountain’s height in the figure is exaggerated for clarity. The core stays exact: the entire flight path follows from one law — Newtonian gravity.