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On 2002-08-23 20:51, Richard J. Hanak wrote, addressing me:
If the moon were at half the distance, 115,000 miles, a place that might otherwise experience a 10-foot tide would experience a 40-foot tide.
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The lunar tide is not even that high. There are such large tides, but they are the result of coastal configuration, and the size of the tide--if the moon were closer--would not necessarily follow that relationship.
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The moon at 57,500 miles would create a 160-foot tide, and at 28,750 miles a 640-foot tide, at 14,375 miles a 2,560-foot tide. Keep going with the series and by the time the Moon’s surface is 457 miles from Earth’s surface, the tide will be 496 miles high. Not only would the Moon get a bath, but the Moon’s gravitational force would make lots of water leave the Earth and go to the Moon.
The Earth is larger and heavier than the moon. The bucket, being very small and insignificant compared to the Earth, would not have enough gravitational force to keep any of its water. Perhaps you can now understand that if the Earth orbited even a couple of miles away from (let alone right next to) a stationary bucket containing water, the Earth would suck that bucket dry to the last drop.
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Actually, the Earth would be spinning beneath the bucket, would it not? If the bucket were motionless, but the relationship between the Earth and bucket was the same? So, in Mach's thought experiment, the Earth would
not orbit the bucket.
That is a misunderstanding on your part.
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If Mach meant that only the really far parts of the universe should rotate around the bucket, he should have said so. If you think about that similarly to the Moon-Earth example we just went through, you should find all kinds of disruptive phenomena, including tides, all over again. I still say I’m surprised that a really brilliant physicist like Mach didn’t think of the implications of his impossible-to-do experiment
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As I said before, it wasn't Mach who misunderstood.