Author Topic: If the center of the earth was hollow what would happen if you stood in it?  (Read 14286 times)

0 Members and 1 Guest are viewing this topic.

Offline Brumby

  • Supporter
  • ****
  • Posts: 12288
  • Country: au
OK the short answer is you could walk around on the walls but the gravity pulling you toward your feet would be very low because you would have all the mass above your head pulling you up.
If we use the ideal spherical model, my understanding is that this is incorrect - as per the shell theorem.  If there is no mass in the void, the gravity at all points of the void will be zero.

Quote
If you jumped you could reach the center and float  because the gravity would be equal in all directions?
If you jumped, you would have a velocity that would carry you to an opposite wall.  To float, you would need to be able to stop yourself - and wherever you stopped is where you would stay.
 

Offline BeaminTopic starter

  • Super Contributor
  • ***
  • Posts: 1567
  • Country: us
  • If you think my Boobs are big you should see my ba
OK the short answer is you could walk around on the walls but the gravity pulling you toward your feet would be very low because you would have all the mass above your head pulling you up.
If we use the ideal spherical model, my understanding is that this is incorrect - as per the shell theorem.  If there is no mass in the void, the gravity at all points of the void will be zero.

Quote
If you jumped you could reach the center and float  because the gravity would be equal in all directions?
If you jumped, you would have a velocity that would carry you to an opposite wall.  To float, you would need to be able to stop yourself - and wherever you stopped is where you would stay.

But you have a huge amount of mass above you that doesn't just go away or are you saying it cancels out?

Plus I think the core has huge iron crystals in it that are some 30 miles long according to science.
Max characters: 300; characters remaining: 191
Images in your signature must be no greater than 500x25 pixels
 

Online Zero999

  • Super Contributor
  • ***
  • Posts: 19345
  • Country: gb
  • 0999
OK the short answer is you could walk around on the walls but the gravity pulling you toward your feet would be very low because you would have all the mass above your head pulling you up.
If we use the ideal spherical model, my understanding is that this is incorrect - as per the shell theorem.  If there is no mass in the void, the gravity at all points of the void will be zero.

Quote
If you jumped you could reach the center and float  because the gravity would be equal in all directions?
If you jumped, you would have a velocity that would carry you to an opposite wall.  To float, you would need to be able to stop yourself - and wherever you stopped is where you would stay.

But you have a huge amount of mass above you that doesn't just go away or are you saying it cancels out?
Well if you're in the gravitational centre, there's an equal amount of mass above you, as below you, pulling you in opposite directions, thus cancelling eacth other out.

Quote
Plus I think the core has huge iron crystals in it that are some 30 miles long according to science.
I thought the centre of the earth was liquid iron? In any case, it's impossible to build a capsule capable of sustaining human life in the centre of the earth.
 

Offline rhb

  • Super Contributor
  • ***
  • Posts: 3476
  • Country: us
I'd like to nominate this for "stupidest thread" although @beamin has started a number of close competitors.   The gravitational forces on a spherical particle contained inside a spherical shell is an advanced undergraduate physics problem.  And not an especially hard one at that.  Real world analogies are meaningless because the real world is far too complex and variable.

Aside from the earth not being a sphere, the gravity varies from point to point throughout the entire earth because the composition is not uniform.   Moreover, it is spinning.  So the gravitational forces in any direction are constantly changing.  That has never been measured and never will be measured because no instrument would survive the conditions even 10 miles below your feet.

How many angels can dance on the head of a pin?  That's as sensible a question.  But neither have anything remotely to do with electronics or even science.

A sensible question would address the forces on the gyros of the Gravity B probe.  But that would require actual work.
 
The following users thanked this post: Beamin

Online Zero999

  • Super Contributor
  • ***
  • Posts: 19345
  • Country: gb
  • 0999
I'd like to nominate this for "stupidest thread" although @beamin has started a number of close competitors.   The gravitational forces on a spherical particle contained inside a spherical shell is an advanced undergraduate physics problem.  And not an especially hard one at that.  Real world analogies are meaningless because the real world is far too complex and variable.

Aside from the earth not being a sphere, the gravity varies from point to point throughout the entire earth because the composition is not uniform.   Moreover, it is spinning.  So the gravitational forces in any direction are constantly changing.  That has never been measured and never will be measured because no instrument would survive the conditions even 10 miles below your feet.

How many angels can dance on the head of a pin?  That's as sensible a question.  But neither have anything remotely to do with electronics or even science.

A sensible question would address the forces on the gyros of the Gravity B probe.  But that would require actual work.
I agree with you, this is a silly question, but don't think there is any ill intent.
 

Offline Brumby

  • Supporter
  • ****
  • Posts: 12288
  • Country: au
It is not a silly question at all.  It is a thought experiment - and has been stated as such many times.

It has never been intended as a practical problem in itself, but more to evoke an understanding of the physics behind it.  That understanding allows further thinking to expand on the principles identified with the possibility of an analogous situation being understood.  It also holds true for considering the gravitational effects on the material that does exist at the centre of the Earth - for whatever reason you might want to know that.

As for the minutiae of irregular mass distribution, that is a distraction from the fundamental concept being discussed.  Certainly is is not an invalid component, but it's effect needs to be referenced against the whole body being assessed, based on some identifiable properties.  Such properties can only be determined by the use of assumptions which give us a starting point.  Then each assumption is addressed in turn and the model refined.  For example, we may start out with the assumption that the density throughout the whole body is the same.  After investigating this, we refine the model to allow a spherically symmetric distribution of mass.  We can then go on and look at other details.

The important point, though, is that we had to start somewhere - which is where this thought experiment holds perfect validity.
« Last Edit: May 20, 2018, 04:03:53 am by Brumby »
 
The following users thanked this post: Beamin

Offline GlennSprigg

  • Super Contributor
  • ***
  • Posts: 1259
  • Country: au
  • Medically retired Tech. Old School / re-learning !
One thing that seems to be 'assumed' in  regards to this concept of 'Walking' inside such a Sphere...
is the relative 'scale', which I do not think was originally considered/spoken-of in the original Hypothesis.
If a 'Man' was 6' tall, walking inside a "very massive" 20' shell, then obviously we would be talking
about the obvious difference between "Head & Shoulders" attraction above, compared to "Feet" attraction
below....  as the 'Man' has no specified 'Centre' for calculations or in thought of the 'Real World' hypothesis.

I would LIKE TO THINK that the 'Man' is but a DOT in 'space', and that the 'Hollow Sphere' was the size of
Earth !!!, so that RELATIVELY speaking, his 'head' & 'feet' are considered the same, in relative scale.
That being the case, there is COUNTLESS thousands of sites/refs that agree that INSIDE of a hollow 'Mass',
(and interestingly it does NOT have to be Spherical !!) there is a 100% balance of equilibrium within !!
Diagonal of 1x1 square = Root-2. Ok.
Diagonal of 1x1x1 cube = Root-3 !!!  Beautiful !!
 

Offline CatalinaWOW

  • Super Contributor
  • ***
  • Posts: 5170
  • Country: us
One thing that seems to be 'assumed' in  regards to this concept of 'Walking' inside such a Sphere...
is the relative 'scale', which I do not think was originally considered/spoken-of in the original Hypothesis.
If a 'Man' was 6' tall, walking inside a "very massive" 20' shell, then obviously we would be talking
about the obvious difference between "Head & Shoulders" attraction above, compared to "Feet" attraction
below....  as the 'Man' has no specified 'Centre' for calculations or in thought of the 'Real World' hypothesis.

I would LIKE TO THINK that the 'Man' is but a DOT in 'space', and that the 'Hollow Sphere' was the size of
Earth !!!, so that RELATIVELY speaking, his 'head' & 'feet' are considered the same, in relative scale.
That being the case, there is COUNTLESS thousands of sites/refs that agree that INSIDE of a hollow 'Mass',
(and interestingly it does NOT have to be Spherical !!) there is a 100% balance of equilibrium within !!

A little thought shows that the last statement is not generically true.  As I sit in my totally enclosed region of space (my house) I am not floating off of my chair.  The symmetry of the matter outside the hollow does matter.
 

Offline ez24

  • Super Contributor
  • ***
  • Posts: 3082
  • Country: us
  • L.D.A.
Plus I think the core has huge iron crystals in it that are some 30 miles long according to science.

But I thought you carved out a hollow area which would include the crystals.   My theory is that it would look like the inside of the space station.  With little energy you could float to the other side.
YouTube and Website Electronic Resources ------>  https://www.eevblog.com/forum/other-blog-specific/a/msg1341166/#msg1341166
 

Offline Brumby

  • Supporter
  • ****
  • Posts: 12288
  • Country: au
(and interestingly it does NOT have to be Spherical !!)

Be careful with that.  I have not looked closely at the maths, but I would consider it essential to at least qualify it with the mass of the body having point symmetry about its centre.

One thing that seems to be 'assumed' in  regards to this concept of 'Walking' inside such a Sphere...
is the relative 'scale', which I do not think was originally considered/spoken-of in the original Hypothesis.
If a 'Man' was 6' tall, walking inside a "very massive" 20' shell, then obviously we would be talking
about the obvious difference between "Head & Shoulders" attraction above, compared to "Feet" attraction
below....  as the 'Man' has no specified 'Centre' for calculations or in thought of the 'Real World' hypothesis.

I would LIKE TO THINK that the 'Man' is but a DOT in 'space', and that the 'Hollow Sphere' was the size of
Earth !!!, so that RELATIVELY speaking, his 'head' & 'feet' are considered the same, in relative scale.

That, actually, is irrelevant.

Consider each part of a person's body in isolation.  Each of those will be subject to the same mathematical process to assess the gravitational effects - and each of those calculations will result in a zero net result.  You can continue this analysis to infinitely small divisions, so the scale of the human isn't really a factor at all.
 

Offline CatalinaWOW

  • Super Contributor
  • ***
  • Posts: 5170
  • Country: us
Some of the confusion about this may come from comparison with electrostatic fields - which I contributed to with my earlier statement on the proper approach to this problem on this forum.  The fundamental difference is that the electric field parallel to a conductor is nominally zero, and is indeed zero at the surface of a perfect conductor.  There is no such thing as a gravitational conductor (as far as we know today) which makes it a fundamentally different situation.

While I am still not sure what the fundamental idea Brumby is aiming for in his thought experiment, the basic answer is that the net gravitational pull at the center of an ideal spherical assembly of mass is zero.  Once the symmetry of that ideal case is lost the devil is in the details.  There will be a point near the center of any assembly of mass where the net gravitational pull from that mass is zero.  The exact location becomes computationally difficult for anything other than homogeneous simple geometric solids (a cube for example is also easy) but exists none the less.  As another aside, you can mix shapes.  Put a cubical cavity in a spherical mass.  As long as their centers match the pull at the center will be zero.

The same kind of symmetry applies to objects placed at the center of the cavity.  A sphere centered in the cavity would stay put.  Any shape with it's gravitational center placed at the spheres center would stay put.  But a human whose center of gravity was placed at the center would have to remain absolutely motionless to maintain that point.  Any position changes that changed the persons center of gravity would spoil the balance.

Finally, the equilibrium is unstable, in the same way that a pin balanced on it's point is unstable.  Any displacement results in further motion away from the balance point.   The forces will be quite small for small displacements, but they are there.
 

Offline Brumby

  • Supporter
  • ****
  • Posts: 12288
  • Country: au
While I am still not sure what the fundamental idea Brumby is aiming for in his thought experiment
Keep reading....

Quote
the basic answer is that the net gravitational pull at the center of an ideal spherical assembly of mass is zero.
That is the obvious - but there's more ...

Quote
  Once the symmetry of that ideal case is lost the devil is in the details.
The only symmetry that is important is that of the spherical body (which goes a bit deeper as well)

Quote
The exact location becomes computationally difficult for anything other than homogeneous simple geometric solids (a cube for example is also easy) but exists none the less.
You would think.  However, if we stick with the spherical, the answers are surprisingly simple.

The thing that seems mysterious is covered by the Shell Theorem - specifically this point: If the body is a spherically symmetric shell (i.e., a hollow ball), no net gravitational force is exerted by the shell on any object inside, regardless of the object's location within the shell.
It's that last phrase that is not intuitive - but I had reservations that such might be possible, which is why I said this earlier:
It has also been an observation of mine that circular and spherical geometry often have some surprisingly simple formulae drop out of analytical efforts - so the idea of a net zero-G environment throughout the void is not something I could dismiss through casual inspection....
« Last Edit: May 22, 2018, 12:47:32 pm by Brumby »
 

Offline CatalinaWOW

  • Super Contributor
  • ***
  • Posts: 5170
  • Country: us
OK, it finally broke through to me - sorry about my slow mind, but need to keep the details of the theorem in mind.  Easy to go astray as above with the idea that gravity is zero inside any spherical void.  Only true if the mass is spherically arranged around the void, which is only true for the special case of a void centered in the earth.  Also the tidal effects due to orbiting the sun still apply.
 

Offline Brumby

  • Supporter
  • ****
  • Posts: 12288
  • Country: au
Not to worry - we've all had moments like that ... and, yes, I agree with your other comments.

What I like to take from this is the extension of this into more realistic scenarios...

For starters, the requirements for a shell are that it is spherical, of constant thickness and constant density.  There are no constraints on the actual diameter nor the actual thickness.  If you had a shell with an outer diameter of 12,000km and a thickness of 1,000km, then the 10,000km diameter void within would present zero gravity at any point within.  You could also take another shell with an outer diameter of 10,000km and a thickness of 500km, then the 9,000km diameter void within would also present zero gravity at any point within.  The density of these two shells does not have to be the same for this to hold true.  What's more, you could place the smaller shell inside the larger one and the 9,000km diameter void within would still present zero gravity.

Extending this idea even further and you could have thousands of concentric shells and the void within the smallest of them would still present zero gravity.  This provides us with a model which offers characteristics that are more closely related to a real world example.  Yes, the concept of a real, physical void is absurd, but the layered structure will better reflect planetary construction.

At this point, I would like to address the "finer details" that have been mentioned such as irregular mass distribution.  While I don't argue against their existence, I have to question their relevance to the discussion.  It is like debating relativistic effects in a discussion on Newtonian mechanics where those effects can be ignored and the discussion can still yield functionally valid results.  I would say: Let's make a note of these things as they may be useful if we want to delve deeper, but let's not try and build such a detailed model at the outset where the basic observations are being explored.

As a last point, let us consider the above example with multiple shells and a 9,000km diameter (4,500km radius) void - and we set our observation point on the inner surface of the smallest shell, some 4,500km from the centre of our body.  As I have said before, if that void has no mass then the gravity at our observation point will be zero ... but what if that void did have mass?  The answer is, there would be gravity.  In my previous mention of this, I used an example where the void was rather small in diameter and was filled with air.  This resulted in very low gravity, but it was non-zero.

Now, instead of air, what would happen if we placed the Moon within the void?  It could float about in an essentially weightless state - yet it would exert it's own gravity.  The gravitational effect on the observation point set above would be a simple calculation based on Newton's Law of Gravity in relation to the Moon and the observation point ... the shell structure they are within does not even come into it.

Up to this point, we have explored "impossible" scenarios - just to explore the maths - but here we can step into a real world example that uses these explorations to give a useful start.....

Let us revisit the above example with the 9,000km diameter void, remove the Moon and fill the void with a 9,000km diameter ball of matter (the sort of thing you might find at the centre of the Earth) and for whatever reason, you need the calculation for the gravitational effects at a point 4,500km from the centre.  You can now do it and the answer is delightfully simple - it is Newton's Law of Gravity applied to the 9,000km diameter ball of matter.  Everything outside that distance can be considered as having zero effect (from the Shell Theorem) and everything inside it can be considered just the same as any other planet, with the observation point being on its surface.

Simples.
« Last Edit: May 23, 2018, 01:37:15 am by Brumby »
 

Offline Rerouter

  • Super Contributor
  • ***
  • Posts: 4694
  • Country: au
  • Question Everything... Except This Statement
Re: Nerd Sniping - If the center of the earth was hollow
« Reply #114 on: May 25, 2018, 12:56:53 pm »
As someone who enjoys physics, There is fun in starting with the spherical cow in a vacuum, then adding back in real world effects to build a better understanding piece by piece, And those small effects are what make the difference between no net acceleration and more interesting interactions,

To put some numbers to the non uniformity of the distribution of mass around the earth, we have gravitational anomaly maps, this one also gives number for the acceleration due to the sun and moon.

https://earthscience.stackexchange.com/questions/7449/does-gravity-differ-from-place-to-place-on-earth

The real fun in this situation happens when you ask what happens when you jump off the inside the shell, the larger the shell, the more the anomalies and the sun and moons influence add up, leading to weirder and weirder paths as the shell radius gets bigger, not to mention the earth is spinning, so unless the shell is very small, your interaction may not be very pleasent when you reach another side.
 

Offline Brumby

  • Supporter
  • ****
  • Posts: 12288
  • Country: au
Re: Nerd Sniping - If the center of the earth was hollow
« Reply #115 on: May 25, 2018, 02:12:29 pm »
As someone who enjoys physics, There is fun in starting with the spherical cow in a vacuum, then adding back in real world effects to build a better understanding piece by piece, And those small effects are what make the difference between no net acceleration and more interesting interactions,

Exactly why starting off with an ideal situation allows such progression and thought experiments on impossible scenarios can deliver useful models - which, without such simplistic origins, may never have been developed.

It is fun.
 

Offline BeaminTopic starter

  • Super Contributor
  • ***
  • Posts: 1567
  • Country: us
  • If you think my Boobs are big you should see my ba
It is not a silly question at all.  It is a thought experiment - and has been stated as such many times.

It has never been intended as a practical problem in itself, but more to evoke an understanding of the physics behind it.  That understanding allows further thinking to expand on the principles identified with the possibility of an analogous situation being understood.  It also holds true for considering the gravitational effects on the material that does exist at the centre of the Earth - for whatever reason you might want to know that.

As for the minutiae of irregular mass distribution, that is a distraction from the fundamental concept being discussed.  Certainly is is not an invalid component, but it's effect needs to be referenced against the whole body being assessed, based on some identifiable properties.  Such properties can only be determined by the use of assumptions which give us a starting point.  Then each assumption is addressed in turn and the model refined.  For example, we may start out with the assumption that the density throughout the whole body is the same.  After investigating this, we refine the model to allow a spherically symmetric distribution of mass.  We can then go on and look at other details.

The important point, though, is that we had to start somewhere - which is where this thought experiment holds perfect validity.

100% spot on. My only fault was making this thread before I was warned not to make off topic science threads which I have stopped and stopped replying to except for this one since people seem to like answering it. The purpose of many of my questions is invoke deeper thought and discussion of that which you can't get by "googling" it, plus there are some very smart people on this board who have got me to look at things differently. I should have called this thread "what kind of technology would be needed to measure this effect and how to build it?" But saying this is a "stupid question" is like saying Schrodinger's cat is just dead or it doesn't matter. His cat may have seemed stupid to those who couldn't think outside the radio active cat containing box. Most people in life who told me I had stupid simple questions often didn't understand what I was talking about and I rarely clue them in rather having them come up with it on their own. I have figured out many hard problems with thought experiments.

I wonder if you could measure this by sending a perfect crystal down and recording its distortion through EM disturbances like a harmonic oscillator in RFID cards.
Max characters: 300; characters remaining: 191
Images in your signature must be no greater than 500x25 pixels
 

Offline GlennSprigg

  • Super Contributor
  • ***
  • Posts: 1259
  • Country: au
  • Medically retired Tech. Old School / re-learning !
Although I 'Think' I know, I will quote nothing more, before producing a calculable 'model'.
"I'll be back" !!!!  xox
Diagonal of 1x1 square = Root-2. Ok.
Diagonal of 1x1x1 cube = Root-3 !!!  Beautiful !!
 
The following users thanked this post: Beamin

Offline BeaminTopic starter

  • Super Contributor
  • ***
  • Posts: 1567
  • Country: us
  • If you think my Boobs are big you should see my ba
Although I 'Think' I know, I will quote nothing more, before producing a calculable 'model'.
"I'll be back" !!!!  xox

Please hurry I'm setting up a company that gives tours of the center of the earth and need to see if we need to bring chairs or ropes to keep people from floating away. Some tritanium alloy should work.
Max characters: 300; characters remaining: 191
Images in your signature must be no greater than 500x25 pixels
 
The following users thanked this post: GlennSprigg

Offline GlennSprigg

  • Super Contributor
  • ***
  • Posts: 1259
  • Country: au
  • Medically retired Tech. Old School / re-learning !
Ha !!  :),   It's still in the 'pipeline'.... 
My 'old' work on this was on another old laptop, using real-time 2D physics, which I just recently found !
I had coded the Java/Javascript to take into account various physical size/shape & Mass bodies in space,
with both Gravitational &/or Magnetic properties, involving real time forces both from surface to surface,
as well as between centres of such masses.  (Graphically demonstrated in real time).
This also applies for a shape 'inside' of a shape. However...

Awhile back, 'CatalinaWOW' said in answer to me....
A little thought shows that the last statement is not generically true.  As I sit in my totally enclosed region of space (my house) I am not floating off of my chair.  The symmetry of the matter outside the hollow does matter.
Well...Obviously the scale/masses of a person in a chair reacting to his 'house', and while 'ON' the Earth's
surface, has NO bearing on the original question what so ever xxx, but one thing I realized I should clarify,
is that MY comments about being inside a 'hollow shell', should state, (as that's what I mean), that the WALLS of
such a 'shell' should be of EVEN thickness/mass, be it a circle or an ellipse etc !!!
(NOT obviously (for example) like an 'egg' shaped Hollow, inside a 'cube' outer shape !!)

That put me off, but if interested, I will re-create the scenarios/info, with a real time video-clip of the action.
P.S.
I know you are 'stirring', however in regard to your proposed new 'travel Company'.....  :)....
The Earth, as it is not hollow, is 'different' than the scenarios talked about, and so the 'Gravitational-Pull'
on you as you 'descended', would only 'gradually' decrease, until at the 'centre' where the 'balance' of the
gravitational 'pull', is now 'equal' in all directions !, (although 'effectively' now zero) .
Have a great day !  ;D
Diagonal of 1x1 square = Root-2. Ok.
Diagonal of 1x1x1 cube = Root-3 !!!  Beautiful !!
 


Share me

Digg  Facebook  SlashDot  Delicious  Technorati  Twitter  Google  Yahoo
Smf