Thx!

]]>No, at this point in time Hooke does not explicitly mention an inverse square law, although five years later he appears to be well acquainted with it, see next episode.

]]>Huygens is almost certainly the source for Wren, Halley et al considering an inverse square law, which seems to have been common knowledge in the early 1680s. See next episode.

]]>Indeed, it is intensely annoying that the public should not have access to research undertaken at public universities funded by the public. There are entries in ResearchGate for these 2 papers which give one the option of requesting the full text from the author.

Niccolò Guicciardini (2005) Reconsidering the Hooke-Newton Debate on Gravitation: Recent Results

Michael Nauenberg (2005) Hooke’s and Newton’s Contributions to the Early Development of Orbital Dynamics and the Theory of Universal Gravitation

]]>He writes “Of course, at the time, the constant M in Kepler’s third law was not known to be the mass of the sun, but it was clear that if both Huygens’s law of centrifugal force and Kepler’s third law were to be satisfied for circular orbits, the force of attraction must be proportional to the reciprocal of the square of the distance.”

From: https://www.mathpages.com/home/kmath658/kmath658.htm

Indeed — it’s trivial to demonstrate inverse for circular orbits given Kepler’s 3rd law and and Huygens expression for centrifugal force.

However demonstrating the same for the ellipse and other conic sections is more difficult. I believe that was one of Newton’s major accomplishments.

]]>