structural:summarization
Gravitation

While many of Hooke's contemporaries, such as Isaac Newton, believed in aether as a medium for transmitting attraction and repulsion between separated celestial bodies, Hooke argued for an attracting principle of gravitation in Micrographia (1665). In a communication to the Royal Society in 1666, he wrote:

I will explain a system of the world very different from any yet received. It is founded on the following positions. 1. That all the heavenly bodies have not only a gravitation of their parts to their own proper centre, but that they also mutually attract each other within their spheres of action. 2. That all bodies having a simple motion, will continue to move in a straight line, unless continually deflected from it by some extraneous force, causing them to describe a circle, an ellipse, or some other curve. 3. That this attraction is so much the greater as the bodies are nearer. As to the proportion in which those forces diminish by an increase of distance, I own I have not discovered it....

Hooke's 1674 Gresham lecture, An Attempt to Prove the Motion of the Earth by Observations (published 1679), said gravitation applies to "all celestial bodies" and restated these three propositions.

Hooke's statements up to 1674 make no mention, however, that an inverse square law applies or might apply to these attractions. His model of gravitation was also not yet universal, though it approached universality more closely than previous hypotheses. Hooke did not provide accompanying evidence or mathematical demonstration; he stated in 1674: "Now what these several degrees are I have not yet experimentally verified", indicating he did not yet know what law the gravitation might follow; and about his whole proposal, he said: "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").

In November 1679, Hooke initiated a notable exchange of letters with Newton that was published in 1960. Hooke's ostensible purpose was to tell Newton he (Hooke) had been appointed to manage the Royal Society's correspondence; Hooke therefore wanted to hear from members about their research or their views about the research of others. Hooke asked Newton's opinions about various matters. Among other items, Hooke mentioned "compounding the celestial motions of the planets of a direct motion by the tangent and an attractive motion towards the central body"; his "hypothesis of the lawes or causes of springinesse"; a new hypothesis from Paris about planetary motions, which he described at length; efforts to carry out or improve national surveys; and the difference of latitude between London and Cambridge.

Newton's reply offered "a fansy of my own" about a terrestrial experiment rather than a proposal about celestial motions that might detect the Earth's motion; the experiment would use a body suspended in air and then dropped. Hooke wanted to discern how Newton thought the falling body could experimentally reveal the Earth's motion by its direction of deviation from the vertical but Hooke went on hypothetically to consider how its motion could continue if the solid Earth had not been in the way, on a spiral path to the centre. Hooke disagreed with Newton's idea of the body's continuing motion. A further short correspondence developed; towards the end of it, writing on 6 January 1680 to Newton, 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". (Hooke's inference about the velocity is incorrect.)

In 1686, when the first book of Newton's Principia was presented to the Royal Society, Hooke said he had given Newton 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 contemporaneous report, Hooke agreed "the Demonstration of the Curves generated thereby" was wholly Newton's.

According to a 2002 assessment of the early history of the inverse square law: "by the late 1660s, the assumption of an 'inverse proportion between gravity and the square of distance' was rather common and had been advanced by a number of different people for different reasons". In the 1660s, Newton had shown for planetary motion under a circular assumption, force in the radial direction had an inverse-square relation with distance from the centre. Newton, who in May 1686 was presented with Hooke's claim to priority on the inverse square law, denied he was to be credited as author of the idea, giving reasons including the citation of prior work by others. Newton also said that, even if he had first heard of the inverse square proportion from Hooke (which Newton said he had not), he would still have some rights to it because of his mathematical developments and demonstrations. These, he said, enabled observations to be relied upon as evidence of its accuracy while according to Newton, Hooke, without mathematical demonstrations and evidence in favour of the supposition, could only guess it was approximately valid "at great distances from the centre".

Newton did accept and acknowledge, in all editions of the Principia, Hooke and others had separately appreciated the inverse square law in the solar system. Newton acknowledged Wren, Hooke and Halley in this connection in his "Scholium to Proposition 4" in Book 1. In a letter to Halley, Newton also acknowledged his correspondence with Hooke in 1679–1680 had reawakened his dormant interest in astronomical matters but that did not mean, according to Newton, Hooke had told Newton anything new or original. Newton wrote:

Yet am I not beholden to him for any light into that business... but only for the diversion he gave me from my other studies to think on these things & for his dogmaticalness in writing as if he had found the motion in the Ellipsis, which inclined me to try it.

Whilst Newton was primarily a pioneer in mathematical analysis and its applications, and optical experimentation, Hooke was a creative experimenter of such great range who left some of his ideas, such as those about gravitation, undeveloped. In 1759, decades after the deaths of both Newton and Hooke, Alexis Clairaut, mathematical astronomer eminent in his own right in the field of gravitational studies, reviewed Hooke's published work on gravitation. According to Stephen Peter Rigaud, Clairaut wrote: "The example of Hooke and that of Kepler to show what a distance there is between a truth that is glimpsed and a truth that is demonstrated". I. Bernard Cohen said: "Hooke's claim to the inverse-square law has masked Newton's far more fundamental debt to him, the analysis of curvilinear orbital motion. In asking for too much credit, Hooke effectively denied to himself the credit due him for a seminal idea".