More than two decades would elapse from Newton’s awakening to his remarkable learning phase in the mid-1660s, culminating in his writing the Principia. This particular period in his life is rife with myths and legends in popular history.
The entire era begins with a web of myths. One such myth suggests that Newton possessed the idea of universal gravitation, the core component of his Principia, by the mid-1660s. Prominent aspects of this include the apple tale, both mythic and legendary, as well as the Annus mirabilis myth. As described in depth, the Annus mirabilis is the claim that in one year during the plague in 1665, the young Newton, who turned twenty-three that year, essentially uncovered everything—calculus, optics, universal gravity—for which he would later gain fame. In this account, Newton himself is accountable due to assertions he made fifty years later:
At the start of 1665, I made claims regarding mathematics and optics, and in the same year, I began contemplating gravity extending to the Moon’s orbit. Upon discovering how to calculate the force with which a globe revolving within a sphere presses against the sphere’s surface based on Kepler’s rule of the periodic times of the planets being in sesquialterate proportion to their distances from the center of their orbits, I concluded that the forces keeping the planets in their orbits must be inversely proportional to the squares of their distances from their centers of revolution. In doing so, I compared the force needed to maintain the Moon in her orbit with gravity’s force at Earth’s surface, finding them to be quite similar.
In his Waste Book, a sizable notebook bequeathed from his stepfather, during this time, Newton, influenced by Descartes, formulated three geometrical principles of circular motion, none of which hold particular significance. Notably, he did not accept the law of inertia at that time. Nonetheless, these principles led him to compare the “endeavor of the Moon to move away from the center of Earth” with the gravitational pull at Earth’s surface. He determined that gravity was slightly over 4,000 times greater. He also substituted Kepler’s third law (which states that the cubes of the mean radii of planets vary as the squares of their periods) into his centrifugal force formula [derived from Huygens]: “the tendencies to recede from the Sun will be inversely proportional to the squares of their distances from the Sun.” Here lay the inverse-square relationship firmly grounded in Kepler’s third law and the principles of circular motion.
Newton’s reflections, in later years, regarding what he had truly accomplished in the 1660s were aimed at silencing his adversaries and asserting his precedence, especially due to his contention with Leibniz over calculus. His remarks on gravity were later aimed at Robert Hooke (1635–1703), who claimed that Newton derived the concept of universal gravity from him. This ties back to a correspondence from 1679, during which Newton was preoccupied with teaching, mathematics, alchemy, and theology, having made no further advancements on the gravity inquiry.
After their contentious disagreement over optics, in which Hooke had rudely dismissed Newton’s initial paper from 1672, the two had not communicated. However, in 1679, Hooke, now the Royal Society’s secretary, reached out to Newton to reestablish communication. He inquired if Newton was aware of his hypothesis regarding planetary motions as a combination of tangential motion and “an attractive motion towards the central body…”
Hooke was referencing a notable paragraph that ended his Attempt to prove the Motion of the Earth (1647, reissued in 1679 in his Lectiones Cutlerianae). In that work, he alluded to a cosmological system he intended to illustrate.
This rests on three suppositions. First, that all celestial bodies possess an attraction or gravitating power towards their centers, enabling them to not only attract their own parts and prevent them from dispersing, as we observe with Earth, but also to draw in all other celestial bodies within their sphere of influence. The second supposition is that all bodies, once set in a direct and unimpeded motion, will continue to move forward in a straight line until acted upon by some other effective forces that redirect them into a circular, elliptical, or other composite curved paths. The third supposition asserts that these attractive forces operate with greater effectiveness the closer the affected body is to their respective centers. The specific degrees of these effects remain experimentally unverified on my part.
Hooke is en route.