Propositions 9-12

Proposition 9 Theorem 9

Gravity, as a downward pull of a planet, decreases nearly in the proportion of the distances from their centres.

If the matter of the planet were of an uniform density, this Proposition would be accurately true (by Prop. LXXIII. Book I).

The error no greater than what therefore, can be may arise from the inequality of the density.

Proposition 10 Theorem 10

The motions of the planets in the heavens may subsist an exceedingly long time.

Scholium 40 Book 2 shewed that a globe of and moving freely in our air, in the time that it would describe the length of its semi-diameter, would lose by the resistance of the air 3 \6 part of its motion; and the same proportion holds nearly in all water frozen into globes, ice, how great soever, and moved with whatever

But velocity.

that our density than it would be if the whole consisted of water only, I thus make out. If the whole consisted of water only, whatever was of less density than water, because of its Ivss globe of earth specific gravity, is of greater would emerge and float above.

And upon this account, if a globe of terrestrial matter, covered on all sides with water, was less dense than water, it would emerge somewhere and, the subsiding water falling ; back, would be gathered to the opposite side. And such is the condition of our earth, which in a great measure is covered with seas. The earth, if it was not would emerge from the seas, and, accord would be raised more or less above their surface, for its greater density, ing to its degree of levity, the water of the seas flowing backward to the opposite side. By the same of the which float the the lucid matter thereof. sun, spots argument, upon are lighter than that matter and, however the planets have been formed while they were yet in fluid masses, all the heavier matter subsided to the centre. Since, therefore, the common matter of our earth on the surface ; about twice as heavy as water, and a little lower, in mines, is three, or four, or even five times more heavy, it is probable that the quantity of the whole matter of the earth may be five or six times thereof is found about greater than if it consisted all of water shewed that the earth is about four times ; especially since I more dense than have before Jupiter. If, more dense than water, in the space of thirty of 459 of its semi-diame the that describes which in length planet days, ters, it would, in a medium of the same density Avith our air, lose almost a therefore, Jupiter is a little tenth part of its motion. But since the resistance of mediums decreases in proportion to their weight or density, so that water, which is 13| times and air, which is in that proportion lighter than quicksilver, resists less 860 times lighter than water, resists less in the same proportion therefore ; ; in the heavens, where the weight of the medium in which the planets move immensely diminished, the resistance will almost vanish. It is shewn in the Scholium of Prop. XXII, Book II, that at the height of 200 miles above the earth the air is more rare than it is at the super ficies of the earth in the ratio of 30 to 0,0000000000003999, or as is 75000000000000 to 1 nearly. And hence the planet Jupiter, revolving in a medium of the same density with that superior air, would not lose by the resistance of the medium the 1000000th part of its motion in 1000000 In the spaces near the earth the resistance is produced only by the When these are carefully exhausted by the exhalations, and vapours. years. air, air-pump from under the receiver, heavy bodies fall within the receiver with perfect freedom, and without the le.ist sensible resistance= gold itself, and the lightest down, let fall together, will descend with equal velocity; and though they fall through a space of four, six, and eight feet, they will come to the bottom at the same time; as appears from experiments. And therefore the celestial regions being perfectly void of air and exhalations, the planets and comets meeting no sensible resistance in those spaces will con tinue their motions through them for an immense tract of time.

Hypothesis 1: The centre of universe is immovable

Proposition 11 Theorem 11

The common centre of gravity of the earth, the sun, and all the planets are immovable.

Corollary 4 of the Laws shows that centre is either:

• at rest, or
• moves uniformly forward

But if that centre moved, the centre of the world would move also, against the Hypothesis.

Proposition 12 Theorem 12

The sun is agitated by a perpetual motion, but never recedes far from the common, centre of gravity of all the planets

By Cor. 2, Prop. 8, the quantity of matter in the sun is to the quantity of matter in Jupiter as 1067 = 1.

Based on the distance of Jupiter from the sun, the common center of Jupiter and the sun is at a point a little outside the sun’s surface.

The quantity of matter in the sun is to the quantity of matter in Saturn as 3021 = 1.

Based on the distance of Saturn from the sun, the common center of Saturn and the sun is at a point a little within the sun’s surface.

We extend this to all the planets to find that their common centre of gravity would be within 1 diameter of the sun.

Hence the common centre of gravity of the earth, the sun, and all the planets, is the centre of the universe. This is because the sun, and all the planets, mutually gravitate one towards another, and are therefore, according to their powers of gravity, in perpetual agitation, as the Laws of Motion require, it is plain that their moveable centres can not be taken for the immovable centre of the world.

If that body were to be placed in the centre, towards which other bodies gravitate most, that privilege ought to be allowed to the sun; but since the sun itself is moved, a fixed point is to be chosen from which the be placed centre and from which it would recede yet least, and greater, and therefore less apt denser of the were sun body sun recedes of the less if the to be in moved.