science

Hooke–Newton inverse square law controversy

Hooke–Newton inverse square law controversy is a science 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 Hooke–Newton inverse square law controversy rather than just read about it. In short: In 1686, when the first book of Isaac Newton's Principia was presented to the Royal Society, Robert Hooke accused Newton of plagiarism by claiming that he had taken from him the "notion" of "the rule of the decrease of Gravity, being reciprocally as the squares of the distances from the Center". At the same time (according to Edmond Halley's contemporary report) Hooke agreed that "the Demonstration of the Curves gen…

Key takeaways

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

Reference excerpt

In 1686, when the first book of Isaac Newton's Principia was presented to the Royal Society, Robert Hooke accused Newton of plagiarism by claiming that he had taken from him the "notion" of "the rule of the decrease of Gravity, being reciprocally as the squares of the distances from the Center". At the same time (according to Edmond Halley's contemporary report) Hooke agreed that "the Demonstration of the Curves generated thereby" was wholly Newton's. The modern view is that the hypothesis of the inverse square relation was known before either Newton or Hooke came to be involved. Newton's work, by reasoning along multiple avenues and casting the relationship in mathematical terms, converted this hypothesis into an inverse square law, in modern terms a scientific theory, refined to the point of abstraction. Hooke's work lacked mathematical rigor and was inconsistent in its physical reasoning. Newton gave credit in his Principia to two people: Ismaël Bullialdus (who wrote without proof that there was a force on the Earth towards the Sun), and Giovanni Alfonso Borelli (who wrote that all planets were attracted towards the Sun). The main influence may have been Borelli, whose book Newton had a copy of.

Hooke's work and claims Robert Hooke published his ideas about the "System of the World" in the 1660s, when he read to the Royal Society on March 21, 1666, a paper "concerning the inflection of a direct motion into a curve by a supervening attractive principle", and he published them again in somewhat developed form in 1674, as an addition to "An Attempt to Prove the Motion of the Earth from Observations". Hooke announced in 1674 that he planned to "explain a System of the World differing in many particulars from any yet known", based on three suppositions: that "all Celestial Bodies whatsoever, have an attraction or gravitating power towards their own Centers" and "also attract all the other Celestial Bodies that are within the sphere of their activity"; that "all bodies whatsoever that are put into a direct and simple motion, will so continue to move forward in a straight line, till they are by some other effectual powers deflected and bent..." and that "these attractive powers are so much the more powerful in operating, by how much the nearer the body wrought upon is to their own Centers". Thus Hooke postulated mutual attractions between the Sun and planets, in a way that increased with nearness to the attracting body, together with a principle of linear inertia. Hooke's statements up to 1674 made no mention, however, that an inverse square law applies or might apply to these attractions. Hooke's gravitation was also not yet universal, though it approached universality more closely than previous hypotheses. He also did not provide accompanying evidence or mathematical demonstration. On the latter two aspects, Hooke himself stated in 1674: "Now what these several degrees [of attraction] are I have not yet experimentally verified"; and as to his whole proposal: "This I only hint at present", "having my self many other things in hand which I would first compleat, and therefore cannot so well attend it" (i.e. "prosecuting this Inquiry"). It was later on, in writing on 6 January 1680 to Newton, that Hooke communicated his "supposition ... that the Attraction always is in a duplicate proportion to the Distance from the Center Reciprocall, and Consequently that the Velocity will be in a subduplicate proportion to the Attraction and Consequently as Kepler Supposes Reciprocall to the Distance." (The inference about the velocity was incorrect.) Hooke's correspondence with Newton during 1679–1680 not only mentioned this inverse square supposition for the decline of attraction with increasing distance, but also, in Hooke's opening letter to Newton, of 24 November 1679, an approach of "compounding the celestial motions of the planets of a direct motion by the tangent & an attractive motion towards the central body".

Newton's work and claims

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Worked examples

Example 1 — a first encounter with Hooke–Newton inverse square law controversy

Start with the simplest possible case. Write down what Hooke–Newton inverse square law controversy claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, 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 Hooke–Newton inverse square law controversy 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 Hooke–Newton inverse square law controversy 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 Hooke–Newton inverse square law controversy

In research: Hooke–Newton inverse square law controversy appears in science 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 Hooke–Newton inverse square law controversy 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: Hooke–Newton inverse square law controversy is common in secondary-school and first-year university syllabi. It links to neighbouring topics Discovery and invention controversies, Gravity, Isaac Newton, so understanding it makes those chapters shorter.
In everyday life: Look for Hooke–Newton inverse square law controversy 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 Hooke–Newton inverse square law controversy in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Hooke–Newton inverse square law controversy means in your own words.
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Work through the three examples above with pen and paper.
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Frequently asked questions

What is Hooke–Newton inverse square law controversy in simple terms?

Why does Hooke–Newton inverse square law controversy matter?

Because it connects several science 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 Hooke–Newton inverse square law controversy?

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 Hooke–Newton inverse square law controversy.