What's happened here is we've seen a sequence of proposals. There are 11 stages of this that form the theory of universal gravity that Newton's gonna defend in the Principia. It's bad enough that he's gotta deal with all the uneven motions. He's now gonna be proposing something that actually is totally implausible.
So let me sell it. You notice what it says, increasingly implausible. Orbiting bodies are retained in orbit rather than moving forward uniformly in a straight line by forces directed toward central bodies. Hooke had said that. These forces, and hence the resulting centripetal accelerations, vary inversely with the square of the distance from the central body.
Hooke had said that. These forces act not only on the principal bodies orbiting the central bodies, but on other bodies as well. Okay, in the case of the Moon, the force in question is simply terrestrial gravity. That's the Moon test. In all celestial cases, the force in question is one in kind with terrestrial gravity.
What makes it one in kind? This peculiar feature that it is always proportional to the quantity of matter in the body. No other force is like that. That's why Einstein quit calling gravity force. Because it's different from all other forces. There is a force of the same kind on the central body directed toward each body orbiting it.
So that the central and orbiting bodies, the Sun and Jupiter, interact. That's what we saw to begin with in the augmented version of De Motu. There are mutual forces of this kind between all celestial bodies. Jupiter and Saturn interact. The forces in question vary in accord with the law of gravity.
The mode of force on a body directed toward another body Is proportional to the product of the masses of the two bodies and inversely proportional to the square of the distance between them. Nine, the gravitational forces between bodies are composed out of inverse square gravitational forces between each pair of individual particles of matter respectively comprising the two bodies.
The force of gravity is universal. The law of gravity holds not merely between bodies, but between all particles of matter in the universe. And this is then, you'll read this in the preface to the Principia for the next reading. The force of gravity is one of the fundamental forces of nature.
That is, it's not composed out of forces of other known kinds. Every step down there is more preposterous on its face than the one before, and the last ones are really quite extraordinary. So Newton's problem in the Principia ends up being to give empirical evidence for all of these from the motion of the planets.
Because you can't get it on the Earth because of forces of gravity are too small, from the motions of the planets, which are beyond calculations. That's the problem he faces. And that's the problem the Principia shows a way of solving that then led, over the next two centuries, to the highest quality evidence.