Despite what Lahev and Calder say, it is not simply possible but highly probable that Newton was investigating Hooke's spring law formulation of celestial force in the passage outlined.

The big difference in the laws is that when we look at the force holding the Moon in orbit, if we think of it in terms of Newtonian gravity, it gives a measurement of the force of gravity that is almost exactly equal to that of measurements done on the surface of the Earth. If we think of the force holding the Moon in orbit as Hooke's force, then we get a measurement of a force that thas nothing to do, physically or numerically, with the force of Gravity on Earth. It is the measurement unity that is demonstrable from investigation that Newton uses in almost all of his arguments from investigation in Book III of the *Principia*.

Given Newton's reasoning, he could be quite happy in using the Moon test (or other tests) as an approximate measure of the force of what we call Newtonian gravity, and using deviations from what it might predict to measure the influence of the Hooke term. This is essentially what Einstein did in using the perihelion advance of Mercury as evidence for General Relativity.

I think that it is anachronistic to consider Hooke's force to be something like dark energy in concept, even though it shares some mathematical characteristics.

Other than this, the history in that article seems pretty good.