The Importance of Elliptical Orbits

But though Newton had thus discovered the true cause of all the celestial motions, he did not yet possess any evidence that such a force actually resided in the sun and planets.

Continuing Discovery of Gravity,
our selection from Memoirs of the Life, Writings and Discoveries of Sir Isaac Newton by Sir David Brewster published in 1855. The selection is presented in six easy 5 minute installments. For works benefiting from the latest research see the “More information” section at the bottom of these pages.

Previously in Discovery of Gravity.

Time: 1666
Place: Woolsthrope, England

After his return to Cambridge in 1666 his attention was occupied with optical discoveries; but he had no sooner brought them to a close than his mind reverted to the great subject of the planetary motions. Upon the death of Oldenburg in August, 1678, Dr. Hooke was appointed secretary to the Royal Society; and as this learned body had requested the opinion of Newton about a system of physical astronomy, he addressed a letter to Dr. Hooke on November 28, 1679. In this letter he proposed a direct experiment for verifying the motion of the earth, viz., by observing whether or not bodies that fall from a considerable height descend in a vertical direction; for if the earth were at rest the body would describe exactly a vertical line; whereas if it revolved round its axis, the falling body must deviate from the vertical line toward the east.

The Royal Society attached great value to the idea thus casually suggested, and Dr. Hooke was appointed to put it to the test of experiment. Being thus led to consider the subject more attentively, he wrote to Newton that wherever the direction of gravity was oblique to the axis on which the earth revolved, that is, in every part of the earth except the equator, falling bodies should approach to the equator, and the deviation from the vertical, in place of being exactly to the east, as Newton maintained, should be to the southeast of the point from which the body began to move.

Newton acknowledged that this conclusion was correct in theory, and Dr. Hooke is said to have given an experimental demonstration of it before the Royal Society in December, 1679. Newton had erroneously concluded that the path of the falling body would be a spiral; but Dr. Hooke, on the same occasion on which he made the preceding experiment, read a paper to the society in which he proved that the path of the body would be an eccentric ellipse in vacuo, and an ellipti-spiral if the body moved in a resisting medium.

This correction of Newton’s error, and the discovery that a projectile would move in an elliptical orbit when under the influence of a force varying in the inverse ratio of the square of the distance, led Newton, as he himself informs us in his letter to Halley, to discover “the theorem by which he afterward examined the ellipsis,” and to demonstrate the celebrated proposition that a planet acted upon by an attractive force varying inversely as the squares of the distances, will describe an elliptical orbit in one of whose foci the attractive force resides.

But though Newton had thus discovered the true cause of all the celestial motions, he did not yet possess any evidence that such a force actually resided in the sun and planets. The failure of his former attempt to identify the law of falling bodies at the earth’s surface with that which guided the moon in her orbit, threw a doubt over all his speculations, and prevented him from giving any account of them to the public.

An accident, however, of a very interesting nature induced him to resume his former inquiries, and enabled him to bring them to a close. In June, 1682, when he was attending a meeting of the Royal Society of London, the measurement of a degree of the meridian, executed by M. Picard in 1679, became the subject of conversation. Newton took a memorandum of the result obtained by the French astronomer, and having deduced from it the diameter of the earth, he immediately resumed his calculation of 1665, and began to repeat it with these new data. In the progress of the calculation 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 realized. 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 almost 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 spread 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 systems 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 were sent to London about the end of 1683, and were soon afterward communicated to the Royal Society.

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