Having thus obtained a law, he next tried to ascertain if it applied to the moon and the earth, to determine if the force emanating from the earth was sufficient, if diminished in the duplicate ratio of the moon’s distance, to retain the moon in its orbit.  For this purpose it was necessary to compare the space through which heavy bodies fall in a second at the surface of the earth with the space through which the moon, as it were, falls to the earth in a second of time, while revolving in a circular orbit.  Owing to an erroneous estimate of the earth’s diameter, he found the facts not quite in accordance with the supposed law; he found that the force which on this assumption would act upon the moon would be one-sixth more than required to retain it in its orbit.

Because of this incongruity he let the matter drop for a time.  But, in 1679, his mind again reverted to the subject; and in 1682, having obtained a correct measurement of the diameter of the earth, he repeated his calculations of 1666.  In the progress of his calculations he saw that the result which he had formerly expected was likely to be produced, and he was thrown into such a state of nervous irritability that he was unable to carry on the calculation.  In this state of mind he entrusted it to one of his friends, and he had the high satisfaction of finding his former views amply realised.  The force of gravity which regulated the fall of bodies at the earth’s surface, when diminished as the square of the moon’s distance from the earth, was found to be exactly equal to the centrifugal force of the moon as deduced from her observed distance and velocity.

The influence of such a result upon such a mind may be more easily conceived than described.  The whole material universe was opened out before him; the sun with all his attending planets; the planets with all their satellites; the comets wheeling in every direction in their eccentric orbits; and the system of the fixed stars stretching to the remotest limits of space.  All the varied and complicated movements of the heavens, in short, must have been at once presented to his mind as the necessary result of that law which he had established in reference to the earth and the moon.

After extending this law to the other bodies of the system, he composed a series of propositions on the motion of the primary planets about the sun, which was sent to London about the end of 1683, and was soon afterwards communicated to the Royal Society.

Newton’s discovery was claimed by Hooke, who certainly aided Newton to reach the truth, and was certainly also on the track of the same law.

Between 1686 and 1687 appeared the three books of Newton’s immortal work, known as the “Principia.”  The first and second book are entitled “On the Motion of Bodies,” and the third “On the System of the World.”