In laws, universal gravitation law, aka “Newton’s law of universal gravitation”, is []

In c.1645, Ismael Bullialdus (1605-1694) wrote, without proof, that there was a force on the earth towards the sun.

In 1666, Giovanni Borelli, in his Theory of the Motion of the Medicean planets [Moons of Jupiter] deduced from Physical Causes, argued that the planets were revolving as a result of three forces. The first force involved the planets' desire to approach the sun. The second force dictated that the planets were propelled to the side by impulses from sunlight, which is corporeal. Finally, the third force impelled the planets outward due to the sun’s revolution. The result of these forces is similar to a stone’s orbit when tied on a string.

In Jan 1684, Edmond Halley, Christopher Wren, and Robert Hooke were engaged in an animated conversation, either over drinks before a roaring fire (Christianson, 1988), or at a coffee house in London (Ѻ), on the topic of why planets traveled in ellipses, according to which, either Hooke or Halley, or both, depending on story, claimed to have solved the problem, via the theory that the inward force of attraction between planets and the sun must decrease in inverse proportion to the square of the distance between them. Wren, to settle the matter, offered them either a large sum or money or book worth forty shillings to whoever could come up with the mathematical means of proving their theory. Hooke, supposedly, claimed to have solved the problem, “but would conceal the solution for some time so that others trying and failing might know how to value it, when he should make it public.”

In Aug 1684, Wren went to Cambridge to see if Newton had the solution, the event of which, as recounted by French mathematician Abraham de Moivre, to whom Newton related the event in his later years, is as follows:

“In 1684, Halley came to visit Newton at Cambridge, after they had been some time together, Halley asked him what he thought the curve would be that would be described by the planets supposing the force of attraction towards the sun be reciprocal to the square of their distance from it. Newton replied immediately that it would be an ellipsis; Hooke, struck with hoy and amazement, asked him how he knew it, to which Newton said that he had calculated it, whereupon Halley asked him for his calculation. Without any further delay, Newton looked among his papers, but could not find it, but he promised him to renew it, and send it.”

In 1686, Newton, in his Principia, citing Bullialdus and Borelli, the latter of whom whose book he had, stated that every point mass attracts every single other point mass by a force pointing along the line intersecting both points, wherein the force is proportional to the product of the two masses and inversely proportional to the square of the distance between them; stated formulaically as such:

universal gravitation law

where F is the force between the two masses, G is the gravitational constant, m1 is the first mass, m2 is the second mass, and r is the distance between the centers of the two bodies.

Quotes | Related
The following are related quotes:

“One must not think that this idea of Hooke diminishes Newton’s glory. The example of Hooke serves to show what a distance there is between a truth that is glimpsed and a truth that is demonstrated.”
— Alexis Clairaut (1727), comment (Ѻ) on review of what Hooke published

See also
Laws of motion

1. Borelli, Giovanni. (1666). Theory of the Motion of the Medicean planets [Moons of Jupiter] deduced from Physical Causes (Theoricae Mediceorum Planetarum ex Causius Physicis Deductae). Florence.

External links
Newton’s law of universal gravitation – Wikipedia.

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