Newton Calculates Mass of Sun and Planets

If the peculiar genius of Newton has been displayed in his investigation of the law of universal gravitation, it shines with no less luster in the patience and sagacity with which he traced the consequences of this fertile principle.

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

By taking a more general view of the subject Newton demonstrated that a conic section was the only curve in which a body could move when acted upon by a force varying inversely as the square of the distance; and he established the conditions depending on the velocity and the primitive position of the body, which were requisite to make it describe a circular, an elliptical, a parabolic, or a hyperbolic orbit.

Notwithstanding the generality and importance of these results, it still remained to be determined whether the forces resided in the centers of the planets or belonged to each individual particle of which they were composed. Newton removed this uncertainty by demonstrating that if a spherical body acts upon a distant body with a force varying as the distance of this body from the center of the sphere, the same effect will be produced as if each of its particles acted upon the distant body according to the same law. And hence it follows that the spheres, whether they are of uniform density or consist of concentric layers, with densities varying according to any law whatever, will act upon each other in the same manner as if their force resided in their centers alone.

But as the bodies of the solar system are very nearly spherical they will all act upon one another, and upon bodies placed on their surfaces, as if they were so many centers of attraction; and therefore we obtain the law of gravity which subsists between spherical bodies, namely, that one sphere will act upon another with a force directly proportional to the quantity of matter, and inversely as the square of the distance between the centers of the spheres. From the equality of action and reaction, to which no exception can be found, Newton concluded that the sun gravitated to the planets, and the planets to their satellites; and the earth itself to the stone which falls upon its surface, and, consequently, that the two mutually gravitating bodies approached to one another with velocities inversely proportional to their quantities of matter.

Having established this universal law, Newton was enabled not only to determine the weight which the same body would have at the surface of the sun and the planets, but even to calculate the quantity of matter in the sun, and in all the planets that had satellites, and even to determine the density or specific gravity of the matter of which they were composed. In this way he found that the weight of the same body would be twenty-three times greater at the surface of the sun than at the surface of the earth, and that the density of the earth was four times greater than that of the sun, the planets increasing in density as they receded from the center of the system.

If the peculiar genius of Newton has been displayed in his investigation of the law of universal gravitation, it shines with no less luster in the patience and sagacity with which he traced the consequences of this fertile principle. The discovery of the spheroidal form of Jupiter by Cassini had probably directed the attention of Newton to the determination of its cause, and consequently to the investigation of the true figure of the earth. The next subject to which Newton applied the principle of gravity was the tides of the ocean.

The philosophers of all ages had recognized the connection between the phenomena of the tides and the position of the moon. The College of Jesuits at Coimbra, and subsequently Antonio de Dominis and Kepler, distinctly referred the tides to the attraction of the waters of the earth by the moon; but so imperfect was the explanation which was thus given of the phenomena that Galileo ridiculed the idea of lunar attraction, and substituted for it a fallacious explanation of his own. That the moon is the principal cause of the tides is obvious from the well-known fact that it is high water at any given place about the time when she is in the meridian of that place; and that the sun performs a secondary part in their production may be proved from the circumstance that the highest tides take place when the sun, the moon, and the earth are in the same straight line; that is, when the force of the sun conspires with that of the moon; and that the lowest tides take place when the lines drawn from the sun and moon to the earth are at right angles to each other; that is, when the force of the sun acts in opposition to that of the moon.

By comparing the spring and neap tides Newton found that the force with which the moon acted upon the waters of the earth was to that with which the sun acted upon them as 4.48 to 1; that the force of the moon produced a tide of 8.63 feet; that of the sun, one of 1.93 feet; and both of them combined, one of 10-1/2 French feet, a result which in the open sea does not deviate much from observation. Having thus ascertained the force of the moon on the waters of our globe, he found that the quantity of matter in the moon was to that in the earth as 1 to 40, and the density of the moon to that of the earth as 11 to 9.

The motions of the moon, so much within the reach of our own observation, presented a fine field for the application of the theory of universal gravitation. The irregularities exhibited in the lunar motions had been known in the time of Hipparchus and Ptolemy. Tycho had discovered the great inequality, called the “variation,” amounting to 37′, and depending on the alternate acceleration and retardation of the moon in every quarter of a revolution, and he had also ascertained the existence of the annual equation. Of these two inequalities Newton gave a most satisfactory explanation.

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