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+----- Thread: Hooke–Newton inverse square law controversy (/showthread.php?tid=1881)
Hooke–Newton inverse square law controversy - mklabgr - 09-07-2026
Summary
The Hooke–Newton inverse-square law controversy concerns who deserves credit for recognizing that gravitational attraction decreases with the square of distance, approximately $F\propto 1/r^2$. Robert Hooke had developed important ideas about planetary motion during the 1660s and 1670s, arguing that celestial bodies attract one another and that planetary orbits could be understood as a combination of inertial motion along a tangent and attraction toward a central body. In correspondence with Isaac Newton in 1679–1680, Hooke explicitly proposed that attraction varied inversely with the square of the distance. However, Hooke did not provide a rigorous mathematical derivation, and some of his associated conclusions were incorrect.
The dispute erupted in 1686, shortly before the publication of Newton's Principia, when Hooke claimed that Newton had taken the inverse-square idea from him. Newton strongly rejected this claim, pointing out that inverse-square ideas had already appeared in earlier work by scientists such as Ismaël Bullialdus, and that Newton himself had investigated related inverse-square relations during the 1660s. More importantly, Newton transformed the hypothesis into a comprehensive mathematical theory. He demonstrated that an inverse-square central force produces the observed properties of planetary orbits and proved that a spherically symmetric body attracts an external object as though its mass were concentrated at its centre. Thus Newton established the universal gravitational law in the form
$F=G\frac{m_1m_2}{r^2}$.
Modern historians therefore generally distinguish between suggesting the idea and proving the theory. Hooke deserves significant credit for independently proposing the inverse-square relationship and for encouraging Newton to reconsider planetary dynamics in terms of centripetal attraction, but the inverse-square concept itself predates both men. Newton's decisive contribution was to connect the idea with mathematics, Keplerian orbital motion and observational evidence, turning a plausible hypothesis into a predictive theory of universal gravitation. Newton did acknowledge Hooke, Christopher Wren and Edmond Halley in the Principia, although debate continues over exactly how much Newton's thinking was stimulated by Hooke's correspondence.
Key takeaways
- Hooke: clearly proposed $1/r^2$ gravitational attraction by 1680, but did not mathematically prove its consequences.
- Newton: supplied the rigorous mathematical framework connecting inverse-square gravity with planetary orbits.
- Neither man invented the inverse-square idea from nothing; related proposals existed earlier.
- The controversy illustrates the crucial distinction between having an insightful hypothesis and demonstrating that it forms a quantitative scientific theory.
ARTICLE