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On 2002-08-23 20:51, Richard J. Hanak wrote:
It is surprising that Mach did not realize that if the Earth rotated around the bucket, let alone the whole universe, no mere meniscus would have been formed. The strongest tidal force imaginable would have emptied the bucket.
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The ocean tides on Earth are caused by the gravitational effects of the Moon,....
... 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.
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Hold it right there R.J.!
The earth radius is
FAAAR greater than the bucket! AND the tidal force is proportional to THE RADIUS of the object acted upon. Since the earth's radius is 3.5 x 10^7 times that of a 1/3 meter bucket, the bucket experience 35,000,000 times
less tidal force, (all other things being equal). Small radii experience little tidal forces.
Since the tidal force is also proportional to the mass acting on the bucket, even if we replace the mass of the moon with that of the earth (leaving distance the same), then it would only increase the T.F. by a factor of about 81.
Remember those things called
equations?
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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.
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Hold on now; you're still not thinking things thru......
The original question was whether an
orbiting earth could replicate the spinning water. Obviously if you could get the Earth orbiting at the same rate that the water was formerly spinning in the bucket (say, once per second or so), the water would be unable to leap out in one direction in so short a time before being pulled from the other direction, and the force would circulate quickly around the bucket continuously, keeping the water inside the bucket. (of course, we aren't talking tidal force here, but just plain ol' gravitation).
I'm not saying that this proceedure shows the grav. field to be the source of inertia, but only that it is faulty logic to say the water must exit the bucket. [img]/phpBB/images/smiles/icon_biggrin.gif[/img]
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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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Not so, as I showed previously; you are forgetting about the orbital rate required to replicate the rotation rate of the spinning water.
I suppose you posted these things without having read my last post but...
Sorry, I just can let these things slide.
G^2
** footnote: Tidal force = 2GMr/d^3 where M is the mass producing the T.F. acting upon a body of radius,r; and d is the distance between the
centers of the 2 bodies.
So, even though decreasing the distance increases tidal force by the inverse cube; in our bucket example, the centers would have to get closer than about 10 km. just to approach unity, 1 nt. But the earth's radius is 6300 km., meaning that d can get no smaller than 6300 km. before collision of the surfaces; so the tidal force remains exceedingly small.
<font size=-1>[ This Message was edited by: Gsquare on 2002-08-24 17:23 ]</font>