Early Life of Isaac Newton - Universal Law of Gravitation

Universal Law of Gravitation

It is supposed that it was at Woolsthorpe in the summer of 1666 that Newton's thoughts were directed to the subject of gravity. They are said to be inspired by Newton's seeing an apple fall from a tree on his mothers farm, a version for which there is reasonable historical evidence. In one version of the story, the apple is supposed to have fallen on Newton's head; this version appears to be invented by Isaac D'Israeli. Voltaire is the authority for the former version of the story. He had his information from Newton's favourite niece Catherine Barton, who married John Conduitt, a fellow of the Royal Society, and one of Newton's intimate friends. How much truth there is in what is a plausible and a favourite story can never be known, but it is certain that tradition marked a tree as that from which the apple fell, till 1860, when, owing to decay, the tree was cut down and its wood carefully preserved.

Johannes Kepler had proved by an elaborate series of measurements that each planet revolves in an elliptical orbit around the Sun, whose centre occupies one of the foci of the orbit, that the radius vector of each planet drawn from the sun sweeps out equal areas in equal times, and that the squares of the periodic times of the planets are in the same proportion as the cubes of their mean distances from the sun. The fact that heavy bodies have always a tendency to fall to the earth, no matter at what height they are placed above the Earth's surface, seems to have led Newton to conjecture that it was possible that the same tendency to fall to the earth was the cause by which the moon was retained in its orbit round the earth.

Newton, by calculating from Kepler's laws, and supposing the orbits of the planets to be circles round the sun in the centre, had already proved that the force of the sun acting upon the different planets must vary as the inverse square of the distances of the planets from the sun. He therefore was led to inquire whether, if the Earth's attraction extended to the moon, the force at that distance would be of the exact magnitude necessary to retain the moon in its orbit. He found that the moon by her motion in her orbit was deflected from the tangent in every minute of time through a space of thirteen feet. But by observing the distance through which a body would fall in one second of time at the Earth's surface, and by calculating from that on the supposition of the force diminishing in the ratio of the inverse square of the distance, he found that the Earth's attraction at the distance of the moon would draw a body through 15 ft. (4.57 metres) in one minute. Newton regarded the discrepancy between the results as a proof of the inaccuracy of his conjecture, and "laid aside at that time any further thoughts of this matter." (See Newton's cannonball.)

In November 1679, Hooke (after his appointment to manage the Royal Society's correspondence) began an exchange of letters with Newton: he wished to hear from members about their researches, or their views about the researches of others. The correspondence later led to controversy. Hooke and Newton disagreed about the form of the path of a body falling from a height, taking the motion of the earth round its axis into consideration. Newton later acknowledged that the exchanges of 1679-80 had reawakened his dormant interest in astronomy. It led Newton to revert to his former conjectures on the moon. The estimate Newton had used for the radius of the earth, which had been accepted by geographers and navigators, was based on the very rough estimate that the length of a degree of latitude of the Earth's surface measured along a meridian was 60 nautical miles. At a meeting of the Royal Society on 11 January 1672, Oldenburg, the secretary, read a letter from Paris describing the procedure followed by Jean Picard in measuring a degree, and specifically stating the precise length that he calculated it to be. It is probable that Newton had become acquainted with this measurement of Picard's, and that he was therefore led to make use of it when his thoughts were redirected to the subject. This estimate of the Earth's magnitude, giving 691 miles (1112 km) to 10°, made the two results, the discrepancy between which Newton had regarded as a disproof of his conjecture, to agree so exactly that he now regarded his conjecture as fully established.

In January 1684, Sir Christopher Wren, Halley and Hooke were led to discuss the law of gravity, and although probably they all agreed in the truth of the law of the inverse square, yet this truth was not looked upon as established. It appears that Hooke professed to have a solution of the problem of the path of a body moving round a centre of force attracting as the inverse square of the distance, but Halley declared after a delay of some months that Hooke "had not been so good as his word" in showing his solution to Wren, and started for Cambridge, in the month of August 1684, to consult Newton on the subject. Without mentioning the speculations which had been made, he asked Newton what would be the curve described by a planet round the sun on the assumption that the sun's force diminished as the square of the distance. Newton replied promptly, "an ellipse", and on being questioned by Halley as to the reason for his answer he replied, "Why, I have calculated it." He could not, however, put his hand upon his calculation, but he promised to send it to Halley. After the latter had left Cambridge, Newton set to work to reproduce the calculation. After making a mistake and producing a different result he corrected his work and obtained his former result.

In the following November Newton redeemed his promise to Halley by sending him, by the hand of Mr Paget, one of the fellows of his own college, and at that time mathematical master of Christ's Hospital, a copy of his demonstration; and very soon afterwards Halley paid another visit to Cambridge to confer with Newton about the problem. On his return to London on 10 December 1684, he informed the Royal Society "that he had lately seen Mr Newton at Cambridge, who had showed him a curious treatise De Motu", which at Halley's desire he promised to send to the Society to be entered upon their register. "Mr Halley was desired to put Mr Newton in mind of his promise for the securing this invention to himself, till such time as he could be at leisure to publish it", and Paget was desired to join with Halley in urging Newton to do so. By the middle of February Newton had sent his paper to Aston, one of the secretaries of the Society, and in a letter to Aston dated 23 February 1685, Newton thanked him for "having entered on the register his notions about motion." This treatise De Motu was the starting point of the Principia, and was meant to be a short account of what that work was intended to embrace. It occupies twenty-four octavo pages, and consists of four theorems and seven problems, some of which are identical with some of the most important propositions of the second and third sections of the first book of the Principia.