[Johann Mahne]

I'm thinking of his famous equation where he states:

 

In his own words, “I deduced that the forces which keep the planets in their orbs must [be] reciprocally as the squares of their distances from the centers about which they revolve:

The distance to the sun was not known,even Huygens who lived in Newton's time had inaccurate faults in his distance calculations ( so say the historians)
The distance to the moon was also far from accurate during that time.

[syhprum]

I always heard that Newton had grave doubts about his theory of gravitation due to the inaccurate published figure for the distance of the moon.

[JP]

He had a very big ruler.

Also, he relied heavily on the works of Johannes Kepler, who had compiled a lot of very detailed information on the motion of the planets.  Exact distances might not have been known, but he knew that the orbits were elliptical and how quickly the planets moved around these ellipses.  Most importantly, Kepler worked out from these observations that the planet's motion around the sun varied in a precise mathematical way depending on how far they were from the sun.  Even if the exact distances were wrong, the data was good enough to see a pattern in planetary motion as it related to distance from the sun.  Newton's genius was to look at this and figure out how to express it in terms of gravitational forces.

http://en.wikipedia.org/wiki/Johannes_Kepler

http://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion

[imatfaal]

Johann - you would be interested in one of Feynman's books - I read it many years ago and the title escapes me (I will find it eventually).  Richard Feynman set his grad class a holiday challenge of reproving much of Newtons work using first principles and without modern mathematics!  He was disappointed when none managed it and very surprised when he realised how difficult it was when he tried himself.  It's a great read (as are all of RF's books) and very instructive

[imatfaal]

It was just proving Kepler's Law of Ellipses using inverse square relationship! 

Here is the book
http://www.amazon.co.uk/Feynmans-Lost-Lecture-Motions-Planets/dp/0099736217/ref=sr_1_20?ie=UTF8&qid=1306833075&sr=8-20

Now I will have to dig it out and read it (add it to the huge pile of reading)

[Bored chemist]

It's possible that, while they had an inaccurate measurement of the planets, they had a much better measurement of the relative distances. They could measure the distances by triangulation from the diameter of the Earth's orbit. But they didn't really know what that diameter was (until, iirc, they did some measurements of the transit of Venus)

[Johann Mahne]

It was just proving Kepler's Law of Ellipses using inverse square relationship! 

Here is the book
http://www.amazon.co.uk/Feynmans-Lost-Lecture-Motions-Planets/dp/0099736217/ref=sr_1_20?ie=UTF8&qid=1306833075&sr=8-20

Now I will have to dig it out and read it (add it to the huge pile of reading)

Thanks very much imatfaal.It been has puzzled me for some time.Thanks also to JP.