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Frank,

> "Kepler's laws are obeyed exactly by a system of two bodies which attract 
each other by the inverse square law."
> Of course, and we owe that understanding to Isaac Newton. Horrocks certainly didn't know that.

That's correct. Horrocks considered Kepler laws as primary, fundamental laws.
But he had the great insight that ay deviation from them is due to gravitation.

So Newton's contribution to the subject was two-fold:
a) He proved that gravitation implies Kepler laws, and
b) Realized that the law of gravitation has universal characters, and claimed
that a complete explanation of all movements of celestial bodies can be derived from the
law of gravitation. In the proof of this claim he made only partial success.

> What did Horrocks actually say on this matter? 

I have not read Horrocks himself, 
but I know that he made the only progress in the description of Moon's motion
between the times of Kepler and Newton, and that Newton, despite his enormous 
efforts could not improve much on Horrocks's theory.

Influneced by this discussion, I found a paper by Curtis Wilson, On the origin 
of the Horrocks's Lunar theory,
Journal of History of astronomy, 18 (1987), but have not read it yet.

> He didn't speak of gravitational influence obviously. 

Apparently he did, at least in the case of Saturn and tides.
I am not sure about Lunar theory, still have to read the paper.

Alex.

   

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