I'm reading Peter Collier's book on relativity and was on the chapter where he describes how Newton figured out the law for universal gravitation. This is the cannonball referred to in the following context. He writes
By careful observation Newton determined that the Moon actually ‘falls’ not 5 m, but 1.37 mm (0.00137 m or about one sixteenth of an inch) below a straight line trajectory in 1 second.
Assuming that both the cannonball and the Moon are accelerating towards the centre of the Earth, the ratio of the Moon’s acceleration to the cannonball’s is 1.37/5000, which is approximately equal to 1/3600.
My Question is: How was Newton able to determine how much the Moon "fell" below the straight line trajectory?