I remember reading that book a while back. It’s a nice historical review of force. Google books has a limited preview version of it.

My experience with history of the concept of force is that reading about it is good to get a historical perspective but does not help solve the question I am interested in. I am looking at a specific question: What is the relation of force to Kepler’s rule?

Kepler’s rule is a simple proportionality that ties the radius and period of an orbit. This rule does not contain a term for force. Therefore, to me, force does not have an observational basis. As you agreed, force is a placeholder. Physicists write it to save Newton’s auhority. If this is true then force has no place in astronomy.

Thanks for the comment. You are right that Newton is usually credited with unification of terrestrial and celestial realms.

The way I see it Kepler’s Rule unifies the two realms not Newton’s force. (By the way, a nitpick: Newton did not use equations, he always worked with proportionalities.)

Cavendish experiment is a terrestrial experiment and it is an application of Kepler’s rule. Newton’s calculation of celestial quantities is also an application of Kepler’s rule. So Kepler’s rule unites the two realms. Newton’s force actually divides them. In Newtonism there are two official realms modelled by terrestrial mechanics and celestial mechanics. Both have their own set of rules.

If we take Kepler’s rule as fundamental then there are no two distinct mechanics but one rule explaining both.

Newton branded the universe on its own image. He designed and marketed a Newtonian world. In this world Newton’s Soul is the cause of all phenomena. This is not unification. This is branding.

Usually Newton’s so-called “Moon test” is given as the proof of his unification of the two realms. But Newton’s Moon test is also a pure application of Kepler’s rule. I would be willing to give Newton credit as the first person to apply Kepler’s rule to show the Moon obeyed Kepler’s rule. He may or may not be the first person to do that, but the point is that Newton claimed to use not Kepler’s rule but an occult quantity he claimed he discovered, namely, his force. Force is a placeholder that does not enter computations. Force has no place in science.

There is some more thoughts on unification of realms on this post.

Thanks again for the comment.

My point is that Newton always uses Kepler’s rule R3/T2=constant to make astronomical calculations. But he always expresses what he does with his own labels. These labels are written and then cancelled. They are not needed and they are not used in calculations.

Newton claims to compute “the action,” that is, Newtonian occult force, of Jupiter upon Saturn. He makes this claim because he writes Kepler’s rule in two parts F=1/R2 and F=R/T2 then combines them to recover the rule by eliminating his placeholder F.

In this proposition Newton applies rules of proportions to combine (or compound) the ratios of distances between Jupiter and Saturn and Sun, then applies Kepler’s rule without explicitly mentioning it.

Newton’s calculations are for Jupiter-Saturn conjuction so we have the alignment Sun, Jupiter, and Saturn.

Newton knows Jupiter-Saturn distance (J = 4) and he also knows Sun-Saturn distance (S = 9). So J/S = 4/9.

Newton computed in a previous proposition that the ratio of 1/R2 for J and S at equal distances was

J/S = 1/1067

Now Newton applies Kepler’s rule for the given distance

S^2/J^2 = 9^2/4^2 * 1/1067 = 1/211

So Newton does nothing more than applying Kepler’s rule. Newton uses Kepler’s rule to compute but he describes what he does with his own labels. There is nothing Newton adds to Kepler’s rule. Except that he labelled “1/R2″ “Force.”

But F on its own is meaningless. Newton cannot compute positions of planets by using F=1/R2 alone. This is not the correct proportionality. He must recover R3/T2 by eliminating F.

Kepler’s rule defines a density continuum. The Sun, Jupiter or Saturn or any “object” is not separate from this continuum. Humans perceive some parts of the continuum as “objects” because we take ourselves to be the measure. (And we can only perceive names or labels.) Anything denser than human body we call an “object.”

Consider the Earth. There is no discontinuity at the “surface” of the Earth. Humans happen to be living at a place in the continuum where the density of water, earth and air meet. There is no Earth.

Newton denies this all pervading density contiuum and imposes his religious doctrine of atomic materialism on the world and paints a picture of “objects” interacting with each other by way of Newton’s occult force. This force is a placeholder and does not even enter the computations. Only radius R and period T are used in computations. F is a placeholder and it cancels.

Thanks once again for the comment.

Newton’s reformulation works for N-bodies. It gives corrections to Kepler’s laws where a 3rd body is involved: Earth around sun modified by Jupiter’s gravity.

So you really can’t say that Newton added nothing to Kepler.