Newton's Cannon

Everything in this view is to scale: Earth, the Moon and the distance between them (384,400 km, about 60 Earth radii). The Moon is 60 times farther from Earth's center than the ground is, so its acceleration is g ÷ 60² = g ÷ 3600, about 0.0027 m/s². Newton used this "Moon test" to show that the gravity pulling the cannonball down also holds the Moon in orbit. Arrows here use different scales than the mountain view.

Launch speed: 5000 m/s

0speed (m/s)

0height above ground (km)

0|a| (m/s²)

0v²/r (m/s²)

—angle between v and ΣF

0time (min)

Vectors

Velocity v Force of gravity F_G Net force ΣF Acceleration a

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Path Line to Earth's center Satellite orbits (iPhone SOS, GPS, geostationary)

Zoom out: 1×

ISS orbit, to scale

ISS: about 420 km up, 7,660 m/s, one lap every 93 min (about 15 laps a day). Our friend Dr. Jessica Meir, the NASA astronaut who livestreamed with our school, is doing science up there, falling around Earth just like the cannonball. Newton's mountain (1,100 km) is taller than the ISS flies. Mount Everest (8.8 km) would be a quarter of a pixel.

Mt. Everest, to scale

Mt. Everest is 8.85 km high, the highest point on Earth. Newton's mountain is about 1,100 km, roughly 125 times as tall. On this Earth, Everest is a quarter of a pixel tall, so the close-up box compares the heights at a larger scale.

Slow motion

Gravity can be switched on or off at any time, even mid-flight. The mountain is drawn very tall, as in Newton's drawing (about 1100 km). Arrows are not drawn to the same scale as each other.
Keys: F fire, Space pause, G gravity, C clear, M switch view.
Drawing: Isaac Newton, A Treatise of the System of the World (1728); scan from Daniel Schroeder's Newton's Cannon.