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We know that the earth has seen several Ice Ages.

And we know the Earth's magnetic poles seem to flip once in a while.

Could all of this be explained by a once every 250 Million Years or so the Earth actually rotates head over heels, so to speak?

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For a flip over with angular momentum conservation, very drastic things would have to happen.The angular momentum of the earth about an axis vertical to the current axis is very small ( there exists precession of the axis). Let suppose it zero. For the north pole to become the south pole and vice verso the liquid core of the earth would have to take up that angular momentum and as Rod says the geological upheavals would be great. Also whence would come the original impetus for this flip? –  anna v Jan 7 at 9:54
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Is the Earth a Tippe top? (˙ou :ɹǝʍsuɐ) –  RedGrittyBrick Jan 7 at 12:10
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The answer, although I am not a geophysicist, is a definitive no. The main way we can tell that pole reversal happens is with the direction of magnetisation of ferrous ores. One looks at the magnetisation versus age in the ferrous ores and then dates the ore by standard techniques. From this we can deduce where the poles were relative to the particular bit of iron bearing stone in question. If the whole Earth flipped over, the relative orientation of the magnetic field and stone would not change, and we would not see the geomagnetic record we see today.

According to the Geomagnetic Reversal Wikipedia Page there was a complete reversal called the Laschamp Event 41 000 years ago such that the length of reversal- the time for the magnetic field to reverse then switch back - was only 440 years. Such a swift flipping over of the whole planet would be bound to have had whopping ecological effects which would be evident in fossil and atmospheric records (in ice). There are no such effects evident at that time. Indeed, in contrast, it seems that the ecological effect of pole reversal is mild: even species who find their way from the Earth's magnetic field direction (migratory birds and such like) are known to have lived through several reversals.

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Wikipedia states that the 440 was the time the polarity was reversed. And states that the transition took 250 years. I read that as 250+440+250=940 years. Not that this invalidates your point. –  Taemyr Jan 7 at 15:00
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