Newton’s Cannon

By: Aiden Shiu

Isaac Newton conceived a thought experiment, Newton’s Cannon. Imagine a cannon firing a cannonball horizontally from a high mountain. When the ball is fired, the forces of air resistance and gravity will act upon it, and its vertical position will drop (still being pushed forward by the initial cannon fire). Newton said that if the speed of the cannonball is too low, it’ll simply fall to the ground. If the speed of the cannonball is too high (being higher than Earth’s escape velocity) then it’ll leave Earth’s orbit. However, if the velocity of the cannonball was high enough so that it wouldn’t fall at a rate matching the bend of the Earth, it would circle the globe  parallel to the ground as it curves out from under it due to the force of gravity. It would eventually make its way back to the original cannon’s position.
This thought experiment helped Newton realize that the moon was in a similar situation, and helped influence his Universal Law of Gravitation. For example, the moon is constantly falling into the Earth’s center. Though the rate of its fall was matched by the curvature of its orbit and therefore has what we know as the moon orbiting around the Earth. This orbit is a result of the tangential velocity and acceleration due to the force of gravity (of the Earth). It orbits Earth in a circular motion just like how when Newton’s cannon fired the cannonball, it made a circular orbit around the Earth.

In this image, points A and B didn’t have enough initial velocity from the cannon to get out of Earth’s escape velocity. In point E, it had too much energy and left Earth’s orbit entirely. In point D, it was able to go around the Earth in an orbit, though it was shot with too much energy and will eventually fall back to Earth. In point C, its rate of fall matches the Earth’s curvature orbit and therefore orbits in a circle around the body. Point C could also demonstrate the moon (granted it would have to be further away from Earth) showing the same concepts the cannonball follows when it comes to Earth’s gravity and the velocity of certain moving objects.

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