- #1
A_B
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Hi,
This question is about a discussion in the two chief world systems, the second day about p 230 in the modern science library edition (around figures 10 and 11). I haven't found the excerpt online so I hope someone has the book.
As an objection to a rotating earth, the claim that any object on its surface must experience a centripetal acceleration and thus be projected from the surface of the Earth is considered.
Galileo argues that the downward motion of anybody is always sufficient to overcome its tendency to to be projected from the rotating sphere.
I don't understand the argument at all, for example in his discussions relating to figure 11 he seems to be comparing distances (the arc) with velocities (the perpendiculars).
Furthermore, Nowhere in the argument is there used anything such that it could not be applied to a rotating wheel with objects loosely attached to its circumference. Galileo knows full well that by spinning the wheel fast enough, the loosely attached objects would break free, but to me it seems that the argument would exclude this possibility as well.
(PS I am aware of the Newtonian description for this problem. It can be easily derives from the radius and period of revolution of the Earth that the centripetal acceleration of any object is about 0.036ms-2 and its acceleration due to gravity is about 10ms-2, so that objects stay on the surface of the earth. The question is more about understanding Galileo's line of though then about understanding the phenomenon)
Thanks,
A_B
This question is about a discussion in the two chief world systems, the second day about p 230 in the modern science library edition (around figures 10 and 11). I haven't found the excerpt online so I hope someone has the book.
As an objection to a rotating earth, the claim that any object on its surface must experience a centripetal acceleration and thus be projected from the surface of the Earth is considered.
Galileo argues that the downward motion of anybody is always sufficient to overcome its tendency to to be projected from the rotating sphere.
I don't understand the argument at all, for example in his discussions relating to figure 11 he seems to be comparing distances (the arc) with velocities (the perpendiculars).
Furthermore, Nowhere in the argument is there used anything such that it could not be applied to a rotating wheel with objects loosely attached to its circumference. Galileo knows full well that by spinning the wheel fast enough, the loosely attached objects would break free, but to me it seems that the argument would exclude this possibility as well.
(PS I am aware of the Newtonian description for this problem. It can be easily derives from the radius and period of revolution of the Earth that the centripetal acceleration of any object is about 0.036ms-2 and its acceleration due to gravity is about 10ms-2, so that objects stay on the surface of the earth. The question is more about understanding Galileo's line of though then about understanding the phenomenon)
Thanks,
A_B