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Post by Progenitor A on Apr 2, 2011 9:17:56 GMT 1
We all know that inside a hollow sphere we have a resultant zero gravitational field. So imagine that you are floating aound in such a hollow sphere and someone cuts a thin slice out of the sphere - just like the thin slice from a melon. What would happen? Would you now be attracted toward the inner wall of the sphere opposite the open slice?
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Post by carnyx on Apr 2, 2011 9:52:16 GMT 1
A fascinating question! It's keep me going for a few days ...
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Post by Progenitor A on Apr 4, 2011 7:20:24 GMT 1
Not much interest in this thread I fear cranyx, so let's try spicing it up a little We all know that inside a hollow sphere there is a cancellation of gravitational fields so that at every point inside the (perfect) sphere there is no gravitation. Now imagine a ball bearing floating around inside such a sphere (there is also no external gravitational field to confuse things [just as in the 2nd Law of thermodynamics we specify a closed system for clarity {it is not the case as some portentous Bozo said, that the 2nd Law applies only to closed systems - but I digress}]) So this ball bearing is floating around - presumably with some Brownian-type motion Now along comes someone and drills a hole in the shell of the sphere What will happen to th ball bearing? Will it 1. Be attracted to the wall of the shell opposite the hole? 2. Will it gravitate toward the centre of the sphere? To add a little spice, on the outside of the shell live a highly civilized community - no homophobes, no racists no xenophobes (how I hate that percussion musical instrument!), a Lesbian-Feminist Alliance in Parliament (free tattoos for all and a subsidy on Doc Martin boots) no Daily Mail, and a benefit system that allows everyone to afford a Filipino servant - yes you have guessed it they are very civilized and quite, quite dim! Any way at the centre of the hollow sphere is a proximity detector that will detect if the ball bearing comes near and explode a nuclear bomb, destroying the Guardian reading glo'al sto'ers that live above. Imagine the ball bearing is offset from where the hole appears when the hole appears (so that if it is attracted to th far wall it will not pass through the centre of the sphere) Would you advise your friends above to evacuate their planet?
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Post by eamonnshute on Apr 4, 2011 8:53:45 GMT 1
Now along comes someone and drills a hole in the shell of the sphere What will happen to th ball bearing? Suppose the disc of material removed form the shell has mass m. This is actually the same as having the whole sphere with a small disc of mass -m attached to the surface, so that the total mass at the position of the disc is zero. So the resulting gravity is that of the whole sphere, plus a small negative mass on the surface. (probably impossible in practice, but a negative mass is a useful mathematical fiction in this problem.)
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Post by Progenitor A on Apr 4, 2011 9:10:42 GMT 1
Now along comes someone and drills a hole in the shell of the sphere What will happen to th ball bearing? Suppose the disc of material removed form the shell has mass m. This is actually the same as having the whole sphere with a small disc of mass -m attached to the surface, so that the total mass at the position of the disc is zero. So the resulting gravity is that of the whole sphere, plus a small negative mass on the surface. (probably impossible in practice, but a negative mass is a useful mathematical fiction in this problem.) Good start What happens to the floating ball bearing?
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Post by eamonnshute on Apr 4, 2011 9:15:18 GMT 1
What happens to the floating ball bearing? Isn't that obvious? It is repelled from the hole with a force inversely proportional to the square of the distance (if the distance is large compared to the size of the hole).
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Post by Progenitor A on Apr 4, 2011 9:23:19 GMT 1
What happens to the floating ball bearing? Isn't that obvious? It is repelled from the hole with a force inversely proportional to the square of the distance (if the distance is large compared to the size of the hole). Perhaps that is 'obvious' But in which direction is it impelled to travel and where will it finish, will it come to rest??
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Post by abacus9900 on Apr 4, 2011 10:19:58 GMT 1
I would have thought so naymissus, yes, because in drilling a hole on one side you have removed a certain amount of mass thereby making the opposite side gain more gravitational pull.
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Post by Progenitor A on Apr 4, 2011 11:44:41 GMT 1
Good to see you back Abacus! Lets see how eamonshute develops his ideas (that seem to be consonant with yours) first
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Post by abacus9900 on Apr 4, 2011 12:18:34 GMT 1
Good to see you back Abacus! Lets see how eamonshute develops his ideas (that seem to be consonant with yours) first Thanks, nay, I've had a bit of a rest so I feel a bit more up to it. Perhaps STA should follow suit!
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Post by buckleymanor1 on Apr 4, 2011 16:14:18 GMT 1
I would have thought so naymissus, yes, because in drilling a hole on one side you have removed a certain amount of mass thereby making the opposite side gain more gravitational pull. Yep if you drew a line from the centre of the hole through the centre of the shell to the wall opposite the hole, that would be where the centre of mass of the shell is located. So the ball bearing would roll to it.
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Post by Progenitor A on Apr 4, 2011 16:30:16 GMT 1
I would have thought so naymissus, yes, because in drilling a hole on one side you have removed a certain amount of mass thereby making the opposite side gain more gravitational pull. Yep if you drew a line from the centre of the hole through the centre of the shell to the wall opposite the hole, that would be where the centre of mass of the shell is located. So the ball bearing would roll to it. Centre of what mass Buckley? Do you mean that the centre of mass of the hollow sphere will shift from the centre of the sphere to the far wall? Why would the ball bearing roll?
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Post by speakertoanimals on Apr 4, 2011 16:46:17 GMT 1
I think there is a confusion here! things are only attracted towards the centr eof mass when FAR from the object, NOT when inside it!
Hence drilling a hole in a sphere, as someone already said, can be considered the SAME as removing the sphere entirely (since net gravitational effect zero inside anyway!), and just adding a small NEGATIVE mass on the point where you drilled the hole. Hence you'd be repelled from that point until you just hit the inner surface opposite. You wouldn't orbit about the centre of mass, that particular approximation does not apply when you are INSIDE the set of gravitating masses.
Its easy to see why -- the bit you removed provided a gravitational force that was balanced by the rest of the sphere. Hence by removing it, net effect is MINUS the gravitational force of the bit of removed mass. Hence just have a single negative mass at that position, and forget about the rest of the sphere until you hit it.................
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Post by Progenitor A on Apr 4, 2011 17:06:05 GMT 1
I think there is a confusion here! things are only attracted towards the centr eof mass when FAR from the object, NOT when inside it! Yes you are confused. No-one has said that it wil be attracted to the CofG - it was just a question Hence drilling a hole in a sphere, as someone already said, can be considered the SAME as removing the sphere entirely (since net gravitational effect zero inside anyway!) No-one has said that either, probably because it is nonsense! ... because , and just adding a small NEGATIVE mass on the point where you drilled the hole. That also is nonsense Hence you'd be repelled from that point A repulsive force of gravity! New concept! until you just hit the inner surface opposite. Opposite the ball bearing or the hole? You wouldn't orbit about the centre of mass, that particular approximation does not apply when you are INSIDE the set of gravitating masses. Approximation? Either its wrong or right! Its easy to see why -- the bit you removed provided a gravitational force that was balanced by the rest of the sphere. Hence by removing it, net effect is MINUS the gravitational force of the bit of removed mass. Hence just have a single negative mass at that position, and forget about the rest of the sphere until you hit it................. Negative mass now too! Abacus used just one short sentence to impart the the same but ungarbled information as has taken you to present in about 20 lines of garbled text, and without nonsensicval new cocepts of negative gravity and mass!
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Post by speakertoanimals on Apr 4, 2011 17:29:03 GMT 1
Well, its WRONG then! Except as Newton understood, the difference from a spherically-symmetric inverse square gravitational field when far from a body like the earth is good enough.
Nice to know that you think Newton was wrong in the Principia, or that useful approximations should just be tagged as WRONG.................
Not at all! Not actual repulsive gravity, just easiest to compute net effect by starting froms somehting you do know (zero field inside uniform sphere), and working from that. Hence net effect or removing mass is the same as replacing that removed mass by negative mass, which gives the correct sign for net gravitational effect.
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