Projectile force demonstrable.
102. We find the Moon moves round the Earth in an Orbit nearly circular. The Moon therefore must be acted on by two powers or forces; one which would cause her to move in a right line, another bending her motion from that line into a curve. This attractive power must be seated in the Earth; for there is no other body within the Moon’s Orbit to draw her. The attractive power of the Earth therefore extends to the Moon; and, in combination with her projectile force, causes her to move round the Earth in the same manner as the circulating body above supposed.
The Sun and Planets attract each other.
103. The Moons of Jupiter and Saturn are observed to move round their primary Planets: therefore there is such a power as gravity in these Planets. All the Planets move round the Sun, and respect it for their centre of motion: therefore the Sun must be endowed with attracting force, as well as the Earth and Planets. The like may be proved of the Comets. So that all the bodies or matter in the Solar System are possessed of this power; and perhaps so is all matter whatsoever.
104. As the Sun attracts the Planets with their Satellites, and the Earth the Moon, so the Planets and Satellites re-attract the Sun, and the Moon the Earth: action and re-action being always equal. This is also confirmed by observation; for the Moon raises tides in the ocean, the Satellites and Planets disturb one another’s motions.
105. Every particle of matter being possessed of an attracting power, the effect of the whole must be in proportion to the number of attracting particles: that is, to the quantity of matter in the body. This is demonstrated from experiments on pendulums: for, if they are of equal lengths, whatever their weights be, they always vibrate in equal times. Now, if one be double the weight of another, the force of gravity or attraction must be double to make it oscillate with the same celerity: if one is thrice the weight or quantity of matter of another, it requires thrice the force of gravity to make it move with the same celerity. Hence it is certain, that the power of gravity is always proportional to the quantity of matter in bodies, whatever their bulks or figures are.
106. Gravity also, like all other virtues or emanations issuing from a centre, decreases as the square of the distance increases: that is, a body at twice the distance attracts another with only a fourth part of the force; at four times the distance, with a sixteenth part of the force. This too is confirmed from observation, by comparing the distance which the Moon falls in a minute from a right line touching her Orbit, with the space which bodies near the Earth fall in the same time: and also by comparing the forces which retain Jupiter’s Moons in their Orbits. This will be more fully explained in the [seventh Chapter].
Gravitation and projection exemplified.
107. The mutual attraction of bodies may be exemplified by a boat and a ship on the Water, tied by a rope. Let a man either in ship or boat pull the rope (it is the same in effect at which end he pulls, for the rope will be equally stretched throughout,) the ship and boat will be drawn towards one another; but with this difference, that the boat will move as much faster than the ship as the ship is heavier than the boat. Suppose the boat as heavy as the ship, and they will draw one another equally (setting aside the greater resistance of the Water on the bigger body) and meet in the middle of the first distance between them. If the ship is a thousand or ten thousand times heavier than the boat, the boat will be drawn a thousand or ten thousand times faster than the ship; and meet proportionably nearer the place from which the ship set out. Now, whilst one man pulls the rope, endeavouring to bring the ship and boat together, let another man, in the boat, endeavour to row her off sidewise, or at right Angles to the rope; and the former, instead of being able to draw the boat to the ship, will find it enough for him to keep the boat from going further off; whilst the latter, endeavouring to row off the boat in a straight line, will, by means of the other’s pulling it towards the ship, row the boat round the ship at the rope’s length from her. Here, the power employed to draw the ship and boat to one another represents the mutual attraction of the Sun and Planets, by which the Planets would fall freely towards the Sun with a quick motion; and would also in falling attract the Sun towards them. And the power employed to row off the boat represents the projectile force impressed on the Planets at right Angles, or nearly so, to the Sun’s attraction; by which means the Planets move round the Sun, and are kept from falling to it. On the other hand, if it be attempted to make a heavy ship go round a light boat, they will meet sooner than the ship can get round; or the ship will drag the boat after it.
108. Let the above principles be applied to the Sun and Earth; and they will evince, beyond a possibility of doubt, that the Sun, not the Earth, is the center of the System; and that the Earth moves round the Sun as the other Planets do.