physics

Newton's cannonball

Newton's cannonball is a physics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Newton's cannonball rather than just read about it. In short: Newton's cannonball was a thought experiment Isaac Newton used to hypothesize that the force of gravity was universal, and it was the key force for planetary motion. It appeared in his posthumously published 1728 work De mundi systemate (also published in English as A Treatise of the System of the World).

Key takeaways

Newton's cannonball belongs to physics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Newton's cannonball to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Newton's cannonball from memory before moving on to harder problems.

Reference excerpt

Newton's cannonball was a thought experiment Isaac Newton used to hypothesize that the force of gravity was universal, and it was the key force for planetary motion. It appeared in his posthumously published 1728 work De mundi systemate (also published in English as A Treatise of the System of the World).

Theory In this experiment described near the start of his De mundi systemate, Newton visualizes a stone being projected from the top of a high mountain, and "that there is no air about the earth, or at least that it is endowed with little or no power of resisting". As a gravitational force acts on the projectile, it will follow a different path depending on its initial velocity. If the speed is low, it will simply fall back on Earth. If the speed is the orbital speed at that altitude, it will go on circling around the Earth along a fixed circular orbit "and return to the mountain from which it was projected". If the speed is higher than the orbital velocity, but not high enough to leave Earth altogether (lower than the escape velocity), it will continue revolving around Earth along an elliptical orbit. If the speed is very high, it will leave Earth in a parabolic (at exactly escape velocity) or hyperbolic trajectory.

Source Newton's original plan for Philosophiæ Naturalis Principia Mathematica was that it should consist of two books, the first analyzing basic laws of motion, and the second applying them to the Solar System. In order to include more material on motion in resisting media, the first book was split into two; the succeeding (now third) book, originally written in a more popular style, was rewritten to be more mathematical. However, manuscripts of an earlier draft of this last book survived, and a version of it was published in 1728 as De mundi systemate; an English translation was also published earlier in 1728 under the name A Treatise of the System of the World. The thought experiment occurs near the start of this work.

Other appearances

An image of the page from A Treatise of the System of the World showing Newton's diagram of this experiment was included on the Voyager Golden Record, as image #111.

Illustrations

Worked examples

Example 1 — a first encounter with Newton's cannonball

Start with the simplest possible case. Write down what Newton's cannonball claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Newton's cannonball before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Newton's cannonball ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Newton's cannonball

In research: Newton's cannonball appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Newton's cannonball in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Newton's cannonball is common in secondary-school and first-year university syllabi. It links to neighbouring topics Fictional weapons, Isaac Newton, Space guns, so understanding it makes those chapters shorter.
In everyday life: Look for Newton's cannonball outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Newton's cannonball in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Newton's cannonball means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Newton's cannonball out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Newton's cannonball in simple terms?

Why does Newton's cannonball matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Newton's cannonball?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Newton's cannonball.