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I'm reading Richard Conn Henry's article called "Circular Motion." In it he states that in his De vi Centrifuga Huygens discovered the formula $a=v^2/r$ and that

Edmund Halley, Christopher Wren, and Robert Hooke were all able to immediately substitute the result into Kepler's third law and deduce that the gravitational force must vary inversely as the square of the distance from the sun.

He does not give any references about where he got this information. Do you know any historical documents showing that Halley, Wren, or Hooke arrived at inverse square law by substituting $a=v^2/r$ into Kepler's Rule?

If there exist such a document, I assume, it would be in the language of proportions and not equations.

Note: This question has nice information about Huygens' discovery but not about its application by the above people.

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    $\begingroup$ Hooke, at least, inferred the inverse square law before (1666) the (the ratio form of) the centripetal acceleration formula became public (1673). Most likely, from the spherical surface area formula that Kepler used to infer the inverse square falling off of the intensity of light, which Bullialdus then adapted to gravity (1645). Of course, once the acceleration formula became known it could have been used to get a confirmation. $\endgroup$
    – Conifold
    Commented Aug 23, 2022 at 11:23
  • $\begingroup$ So, you don't believe the story told in the article that Hooke learned the centripetal acceleration formula from Huygens and he already knew Kepler's Rule (the 3. law) and plugged it in Kepler's Rule and discovered the inverse square relation? $\endgroup$
    – zeynel
    Commented Aug 23, 2022 at 12:00
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    $\begingroup$ No, Micrographia has multiple allusions to Kepler's argument for light and nothing about centripetal acceleration, see The Archaeology of the Inverse Square Law. In 1682 Hooke explicitly wrote "I conceive the Power thereof to be always reciprocal to the Area or Superficies of the Orb of Propagation, that is duplicate of the Distances", see Hooke, orbital motion, and Newton's Principia. $\endgroup$
    – Conifold
    Commented Aug 23, 2022 at 23:26
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    $\begingroup$ Newton did infer the inverse square law from the acceleration formula ($a\sim R / T^2$ in his version) and Kepler's third law in unpublished On Circular Motion (1666), see Gal, Inverse square law:"Finally since in the primary planets the cubes of their distances from the sun are as the squares of the numbers of revolutions in a given time: the endeavours of receding from the sun will be reciprocally as the squares of the distances from the sun." Perhaps, many authors simply assume that others did the same. $\endgroup$
    – Conifold
    Commented Aug 23, 2022 at 23:38

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