The Moon's Gravitation

Proposition 5 Theorem 5

The circumjovial planets gravitate towards Jupiter. The circnntsaturnal gravitate towards Saturn. The circumsolar gravitate towards the sun.

By their gravity, they are maintained in curvilinear orbits.

Scholium

We shall call the centripetal force which retains the celestial bodies in their orbits as gravity since it is a gravitating force.

The cause of that centripetal force which retains the moon in its orbit will extend itself to all the planets, by Rule 1, 2, and 4

Proposition 6 Theorem 6

All bodies gravitate towards every planet. The weights of bodies towards any the same planet, at equal distances from the centre of the planet, are proportional to the quantities of matter which they contain.

Heavy bodies fall from equal heights at equal times. This is proven by pendulums. I have tried gold, silver, lead, glass, sand, eommpn salt, wood, water, and wheat.

I took two equal round wooden boxes.

• I filled one with

Corollary 1: Hence the weights of bodies do not depend on their forms and textures.

This is because if the weights were changed with the forms, they would change according to the variety of forms while their mass staying the same. This is against experience.

Corollary 2: Universally, all bodies around the earth gravitate towards the earth. The weights of all gravitate at equal distances from the earth s centre depending on the quantities of matter in them.

If the aether were void of gravity, or were to gravitate less in proportion to its quantity of matter, then, because (according to Aris totle, Des Carles, and others) there is no difference between that and other bodies but in mere form of matter, by a successive change from form to form, it might be changed at last into a body of the same condition with those which gravitate most in proportion to their quantity of matter.

On the other hand, the heaviest bodies, acquiring the first form of that body, might gradually lose their gravity. Therefore the weights would depend on the shapes of bodies, and with those shapes might be changed. This is contrary to what was proved in Corollary 2.

Corollary 3: All spaces are not equally full.

If all spaces were equal, then the specific gravity of the fluid which fills the region of the air, on account of the extreme density of the matter, would fall nothing short of the specific gravity of quicksilver, or gold, or any other the most dense body.

Therefore, neither gold, nor any other body, could descend in air.

Bodies do not descend in fluids, unless they are specifically heavier than the fluids.

If the quantity of matter in a given space can, by any rarefaction, be diminished, what should hinder a diminution to infinity ?

Corollary 4: If all the solid particles of all bodies are of the same density, nor can be rarefied without pores, a void, space, or vacuum must be granted.

Bodies of the same density means bodies whose inertia are proportional to their sizes.

Corollary 5: The power of gravity is of a different nature from the power of magnetism

Magnetic attraction does not depend on matter. Some bodies are attracted by magnets, some are not.

Magnetism in a body can be increased or reduced, sometimes stronger than gravity.

Going away from the magnet does not reduce the magnetism by half.

Proposition 7 Theorem 7

A power of gravity tends to all bodies, proportional to the quantities of matter which they contain.

All the planets mutually gravitate one towards another. This gravity is the square of the distance of places from the centre of the planet. It follows (by Prop. 69, Book 1) that gravity in all the planets is proportional to the matter which they contain.

All the parts of any planet A gravitate towards planet B, just as planet B gravitates towards A.

Corollary 1

Total attraction in gravity and electromagnetism is made up of all of the partial attractions.

Corollary 2

The force of gravity towards the several equal particles of any reciprocally as the square of the distance of places from the particles, as appears from Book 1 Cor. 3, Prop. 69