I Understanding of gravity in the Middle Ages

[sophiecentaur]

Stand at the edge of a high precipice, Mark the spot directly beneath a ball that you hold in your hand.

I wonder how you would determine where that spot is and the accuracy of your chosen method. I would suggest that dropping the ball would be a probable way - or a plumb line. Did you calculate the likely difference between the answers from the two methods. Latitude would affect things, too.

 

[Mark Harder]

I wonder how you would determine where that spot is and the accuracy of your chosen method. I would suggest that dropping the ball would be a probable way - or a plumb line. Did you calculate the likely difference between the answers from the two methods. Latitude would affect things, too.

Dropping a ball to mark the spot would be a circular argument. I imagine they had plumb bobs in those days. I think they would consider the line to the weight moves with the earth. If you move the top of the line by exerting an unnatural force on it, it moves in the direction of motion of the suspension point.
I 'm afraid I can't answer your question about the precision of the measurement. I don't know if they took that into consideration. They were capable of measuring the relative angular motion of the stars and moon, but I believe they would need trigonometry to convert angular to linear measurements, unless they used Euclid and similar triangles. Still, that would require knowing the distance to the reference object in space. By the middle ages, Euclid was known and the diameter of the Earth was known. However, the discipline of mathematical physics took a while. I believe Galileo is generally considered the founder of math phys. because he derived laws governing falling objects, for instance, from experimental measurements - inclined planes in this case. It's possible that earlier experiments were strictly qualitative, not quantitative. In which case, experiments like the falling ball are subject to experimental error and lack of precision, as you point out.

 

[sophiecentaur]

Dropping a ball to mark the spot would be a circular argument.

That's why I queried what you wrote. A falling ball will be subject to the fictional Coriolis force, which will take it Eastwards as its height reduces. The amount of movement will be small - by a factor of height / Earth's radius. What you say about astronomical measurements could be relevant; the Maths would have been no problem for them. I am always stunned at how Keppler and others worked to such accuracy but angles between point sources are probably a lot easier to measure reliably (averaging out atmospheric disturbances etc.) than the equivalent on Earth. I would expect air currents to produce errors which are greater than what's being measured unless the ball is very massive.