• #### The center of gravity

From Luigi Fortunati@21:1/5 to All on Sat Oct 29 13:17:53 2022
If we let all the elevators in the world move freely (unhindered), they
would head towards the center of the Earth where they would all meet.

If we rested a body anywhere else, it would invariably accelerate
towards the center of the Earth, and only if we rested it in the center
of the Earth would it remain stationary in its place.

So there is no doubt that the center of the Earth is not the same as
all the other points but it is very special, because it is a center of
gravity (and the other points don't).

Also for General Relativity, is the center of the Earth different from
all other points?

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• From Phillip Helbig (undress to reply@21:1/5 to fortunati.luigi@gmail.com on Mon Oct 31 18:02:13 2022
In article <tjc3cb\$f48\$1@gioia.aioe.org>, Luigi Fortunati <fortunati.luigi@gmail.com> writes:

If we let all the elevators in the world move freely (unhindered), they
would head towards the center of the Earth where they would all meet.

If we rested a body anywhere else, it would invariably accelerate
towards the center of the Earth, and only if we rested it in the center
of the Earth would it remain stationary in its place.

So there is no doubt that the center of the Earth is not the same as
all the other points but it is very special, because it is a center of gravity (and the other points don't).

Also for General Relativity, is the center of the Earth different from
all other points?

Not different from all other points, but different from all other points
on Earth because, as you mentioned, it is the center of gravity. But
there is nothing special about the location per se, as one can change
the center of gravity by, say, digging a hole and piling the dirt into a
hill nearby.

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• From Luigi Fortunati@21:1/5 to All on Tue Nov 1 00:46:21 2022
Phillip Helbigundress to reply luned=EC 31/10/2022 alle ore 12:02:13 ha scritto:
In article <tjc3cb\$f48\$1@gioia.aioe.org>, Luigi Fortunati <fortunati.luigi@gmail.com> writes:

If we let all the elevators in the world move freely (unhindered), they
would head towards the center of the Earth where they would all meet.

If we rested a body anywhere else, it would invariably accelerate
towards the center of the Earth, and only if we rested it in the center
of the Earth would it remain stationary in its place.

So there is no doubt that the center of the Earth is not the same as
all the other points but it is very special, because it is a center of
gravity (and the other points don't).

Also for General Relativity, is the center of the Earth different from
all other points?

Not different from all other points, but different from all other points
on Earth because, as you mentioned, it is the center of gravity. But
there is nothing special about the location per se, as one can change
the center of gravity by, say, digging a hole and piling the dirt into a
hill nearby.

It is not true that "there is nothing special about the location per
se" it is the location itself that is special.

And nothing changes if you move the privileged point by making a hole
and a small hill beyond: the privilege passes from one point to another
but does not disappear.

And what is this privilege?

If you are on Earth and you throw a stone anywhere, the stone does not
come back on its own.

But if you are in the center of the Earth and you throw a stone in any direction, it will come back * by itself *, accelerating towards you.

That's what's special about the center of gravity location, that's its privilege.

[[Mod. note -- I think Phillip Helbig's point is that if you change the
Earth's mass distribution a bit (e.g., by digging a hole and piling the
dirt into a hill nearby), that the center of gravity will change to
a different point. If you are in the original (pre-digging) center
of the Earth-with-hole-and-pile-of-dirt and throw a stone, the stone
does *not* come back to you.
-- jt]]

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• From Luigi Fortunati@21:1/5 to All on Tue Nov 1 08:32:39 2022
Luigi Fortunati lunedÃ¬ 31/10/2022 alle ore 18:46:21 ha scritto:
If we let all the elevators in the world move freely (unhindered), they would head towards the center of the Earth where they would all meet.

If we rested a body anywhere else, it would invariably accelerate towards the center of the Earth, and only if we rested it in the center of the Earth would it remain stationary in its place.

So there is no doubt that the center of the Earth is not the same as all the other points but it is very special, because it is a center of gravity (and the other points don't).

Also for General Relativity, is the center of the Earth different from all other points?

Not different from all other points, but different from all other points on Earth because, as you mentioned, it is the center of gravity. But there is nothing special about the location per se, as one can change the center of gravity by, say, digging
a hole and piling the dirt into a hill nearby.

It is not true that "there is nothing special about the location per se" it is the location itself that is special.

And nothing changes if you move the privileged point by making a hole and a small hill beyond: the privilege passes from one point to another but does not disappear.

And what is this privilege?

If you are on Earth and you throw a stone anywhere, the stone does not come back on its own.

But if you are in the center of the Earth and you throw a stone in any direction, it will come back * by itself *, accelerating towards you.

That's what's special about the center of gravity location, that's its privilege.

[[Mod. note -- I think Phillip Helbig's point is that if you change the Earth's mass distribution a bit (e.g., by digging a hole and piling the
dirt into a hill nearby), that the center of gravity will change to
a different point. If you are in the original (pre-digging) center
of the Earth-with-hole-and-pile-of-dirt and throw a stone, the stone
does *not* come back to you.
-- jt]]

He doesn't come back to me because I'm no longer in the center of
gravity.

The stone comes back to me (obviously) only if I am in the center of
gravity.

It is the center of gravity that has these characteristics, not me.

What I wanted to point out is that the center of gravity (wherever it
is) is * unique *, that is, it is the only point where gravity
converges.

And no other point has the same characteristics.

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• From Tom Roberts@21:1/5 to Luigi Fortunati on Tue Nov 1 22:33:27 2022
On 11/1/22 2:46 AM, Luigi Fortunati wrote:
Phillip Helbigundress to reply luned=EC 31/10/2022 alle ore 12:02:13
ha scritto:
In article <tjc3cb\$f48\$1@gioia.aioe.org>, Luigi Fortunati
<fortunati.luigi@gmail.com> writes:
If we let all the elevators in the world move freely
(unhindered), they would head towards the center of the Earth
where they would all meet.

It is not true that "there is nothing special about the location per
se" it is the location itself that is special.

Yes.

And what is this privilege?

It is the (unique) point of spherical symmetry -- here an aspect of the geometry. Note that "all objects falling to the center of mass" is
geometrical, and in this case merely reflects that spherical symmetry.

There is nothing mysterious here, just basic geometry.

Tom Roberts

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• From Luigi Fortunati@21:1/5 to All on Wed Nov 2 08:03:38 2022
Tom Roberts martedÃ¬ 01/11/2022 alle ore 16:33:27 ha scritto:
If we let all the elevators in the world move freely (unhindered), they would head towards the center of the Earth where they would all meet.

It is not true that "there is nothing special about the location per se" it is the location itself that is special.

Yes.

And what is this privilege?

It is the (unique) point of spherical symmetry -- here an aspect of the geometry. Note that "all objects falling to the center of mass" is geometrical, and in this case merely reflects that spherical symmetry.

There is nothing mysterious here, just basic geometry.

Ok.

And also in General Relativity do all objects "fall" radially towards a
single point?

Luigi

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• From xray4abc@21:1/5 to Luigi Fortunati on Fri Nov 4 08:23:14 2022
On Saturday, October 29, 2022 at 9:17:57 AM UTC-4, Luigi Fortunati wrote:
If we let all the elevators in the world move freely (unhindered), they
would head towards the center of the Earth where they would all meet.

If we rested a body anywhere else, it would invariably accelerate
towards the center of the Earth, and only if we rested it in the center
of the Earth would it remain stationary in its place.

So there is no doubt that the center of the Earth is not the same as
all the other points but it is very special, because it is a center of gravity (and the other points don't).

Also for General Relativity, is the center of the Earth different from
all other points?
Realistically ...can one be sure that ....there exists such a thing
..that is a point-like centre of gravity?
That is ...other than...a convenient mathematical abstraction.
I am inclined to believe that even the equivalence principle itself is
..just a statement ..convenient for mathematicians..to play with
..... physics.
As a hint, why do I think this.....well, remembering Einstein's
elevator.....I am quite sure that in any REAL "elevator" ,
an observer CAN without major difficulties, using minimal laboratory equipment, point to the real situation, that is... he could tell apart gravitational field versus accelerated movement.
Where then will this leave..General Relativity?
Now, I would like to consult you guys, about a different subject. some of you may be better informed than I am.
I have tried, unsuccessfully, create magnetic effects by moving
(rotating) electrically charged objects.
Other than Rowland's experiment I could not find on the subject.
Do you have any suggestions on this matter?

Best regards, LL

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• From Edward Prochak@21:1/5 to Luigi Fortunati on Mon Nov 7 08:14:59 2022
On Saturday, October 29, 2022 at 9:17:57 AM UTC-4, Luigi Fortunati wrote:
If we let all the elevators in the world move freely (unhindered), they
would head towards the center of the Earth where they would all meet.

If we rested a body anywhere else, it would invariably accelerate
towards the center of the Earth, and only if we rested it in the center
of the Earth would it remain stationary in its place.

So there is no doubt that the center of the Earth is not the same as
all the other points but it is very special, because it is a center of gravity (and the other points don't).

Your question is unclear. What exactly do you mean by
"not the same as all the other points"

If I assume you mean "all the other points" in the universe,
then consider:
"anywhere else then would include points near Mars for example.
A body rested near Mars would accelerate toward the center of Mars, not Earth. Similar results would be obtained for any large body in the universe.
So "all other points" is not true for the universe of points.

If I assume you mean "all the other points" relative to the earth,
then consider
Lagrange points that exist in the earth moon system. Ideally,
if you rest a body at one of these points, then the object
"would it remain stationary in its place" and is not accelerated
toward the center of the earth.

So I'm am merely trying to determine what you mean by saying
that the center of the Earth is "very special". The phrase just isn't
well defined as a physical property.

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• From Luigi Fortunati@21:1/5 to All on Mon Nov 7 10:55:03 2022
Edward Prochak luned=EC 07/11/2022 alle ore 09:14:59 ha scritto:
If we let all the elevators in the world move freely (unhindered), they
would head towards the center of the Earth where they would all meet.

If we rested a body anywhere else, it would invariably accelerate
towards the center of the Earth, and only if we rested it in the center
of the Earth would it remain stationary in its place.

So there is no doubt that the center of the Earth is not the same as
all the other points but it is very special, because it is a center of
gravity (and the other points don't).

Your question is unclear. What exactly do you mean by
"not the same as all the other points"

If I assume you mean "all the other points" in the universe,
then consider:
"anywhere else then would include points near Mars for example.
A body rested near Mars would accelerate toward the center of Mars, not Earth. Similar results would be obtained for any large body in the universe. So "all other points" is not true for the universe of points.

If I assume you mean "all the other points" relative to the earth,
then consider
Lagrange points that exist in the earth moon system. Ideally,
if you rest a body at one of these points, then the object
"would it remain stationary in its place" and is not accelerated
toward the center of the earth.

So I'm am merely trying to determine what you mean by saying
that the center of the Earth is "very special". The phrase just isn't
well defined as a physical property.

I mean that the center of the Earth is a particular (unique) point with
respect to all other points on the Earth (and not those of the Moon or
Mars).

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• From Edward Prochak@21:1/5 to Luigi Fortunati on Tue Nov 8 22:33:08 2022
On Monday, November 7, 2022 at 1:55:08 PM UTC-5, Luigi Fortunati wrote:
Edward Prochak luned=EC 07/11/2022 alle ore 09:14:59 ha scritto:
[]
If I assume you mean "all the other points" relative to the earth,
then consider
Lagrange points that exist in the earth moon system. Ideally,
if you rest a body at one of these points, then the object
"would it remain stationary in its place" and is not accelerated
toward the center of the earth.

So I'm am merely trying to determine what you mean by saying
that the center of the Earth is "very special". The phrase just isn't
well defined as a physical property.
I mean that the center of the Earth is a particular (unique) point with respect to all other points on the Earth (and not those of the Moon or
Mars).

Did you consider the Lagrange points?
ed

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