Where is most "gravity", inside or out?

[exchemist]

But your response to my post implied (or it appeared to me) that you are supporting the contention that potential is highest at the centre of the earth.

Now with this post you are implying that you do not agree with this.

Can you please be more specific on this point? That is, is gravity highest at the centre of the earth or not?

I'm not sure why you are continuing to ask this, when I have explained to you, with a diagram, that the potential is a minimum at the centre. It is the gravitational force that is zero.
I am not aware that anybody on this thread has claimed the potential is a maximum at the centre - unless you interpret some of the nebulous ramblings of nebel in this way.

Are you, yourself, still unclear on this issue?

And why are you insisting that NotEinstein reconfirm that your misunderstanding of what he said is wrong?

 

[nebel]

The steepness of the slope, at any given point, is the strength of the gravitational force at that point.

I like that visualization, somehow did not see that at all on my screen yesterday. Am working to draw something like that for the trench that would result if you plotted the strength gs in 3D. of origin's plot. of g /R.
I can see Sisyphus risking life and limb as he tries to tackle the near vertical wall at the surface section, that seem to be where the rings have double spacing. (surface not clearly marked only improvement suggested). Great!, Now,
Coming to the OP question: "where is more gravity, inside or out?", would I be correct to try to find the answer by imagining to fill that container with a measured hardening liquid, up to the surface level, and then add a measured volume of water to fill above that, comparing the two?
The answer, the ratio could be: " it depends on the size of the surface, the central mass, the denser, steeper the inner slope, the more "outside gravity" is generated. or, Having to use different density liquids? and consider comparing weights?
I like the picture of the ball almost freely rolling on level ground in the center well, but needing rocket thrust to climb at the surface. as it does to reach escape velocity, ,keep going.

 

[exchemist]

I like that visualization, somehow did not see that at all on my screen yesterday. Am working to draw something like that for the trench that would result if you plotted the strength gs in 3D. of origin's plot. of g /R.
I can see Sisyphus risking life and limb as he tries to tackle the near vertical wall at the surface section, that seem to be where the rings have double spacing. (surface not clearly marked only improvement suggested). Great!, Now,
Coming to the OP question: "where is more gravity, inside or out?", would I be correct to try to find the answer by imagining to fill that container with a measured hardening liquid, up to the surface level, and then add a measured volume of water to fill above that, comparing the two?
The answer, the ratio could be: " it depends on the size of the surface, the central mass, the denser, steeper the inner slope, the more "outside gravity" is generated. or, Having to use different density liquids? and consider comparing weights?
I like the picture of the ball almost freely rolling on level ground in the center well, but needing rocket thrust to climb at the surface. as it does to reach escape velocity, ,keep going.

No, because your question is a silly one and your analogy is ridiculous, since gravity is not "stuff", as several people have pointed out.

I have now demonstrated why you have to decide whether to graph force or potential and why the two graphs look quite different from one another *. You can do one or the other, but there is no graph you can draw to show "gravity" as if it were a substance that you could measure by the bucketload. This analogy does not work, as I have demonstrated to you in some detail.

If you persist in asking silly questions, you will get silly - and/or increasingly exasperated - answers.

* If you know a bit of maths, you will realise that force is the derivative of potential wrt distance and potential is the integral wrt distance of force.


P.S. Here is a graph, since you seem interested, that show how the gravitational field, that is, the force on a unit mass, varies from the centre, through to the surface, where it is at a peak and then out towards infinity:

 

[origin]

I can not envision the center as the lowest point in the gravity "well"

Then visualize this:
If we send a rocket to the ISS (250 miles above) it will take a certain amount of energy. If we make huge tunnel into the earth 250 miles deep, the acceleration due to gravity will be lower at the bottom but if we launch a rocket from there it would take almost twice the amount of energy to have that rocket reach the ISS.
If there was a tunnel that went to the center of the earth a rocket would have to expend a massive amount of energy to move from the center to the surface of the earth.
So it takes progressively more energy to move the rocket in the tunnel to the surface the deeper into the earth you go, even though the acceleration due to gravity is decreasing as move to the center of the earth.

 

[sweetpea]

I hope I do Origin justice here, the following is what I understood from Origin's post#344...
The gravitational potential tells you how much energy you need to get from point A to point B (radial from the centre) within the field.
If you drop (freefall) a ball from point B back down to point A, you will find the energy of the ball when reaching A is the same as the energy required to get the ball from A to B.
Sorry Origin if I misunderstood, I'm trying to see what nebel can't catch.

 

[nebel]

s no graph you can draw to show "gravity" as if it were a substance that you could measure by the bucketload.

If I would not be so handicapped I would try, so,
take your graph of the [strength of?] field on the unit mass (which is different than origins's I suppose?), and add a factor that shows that the diminishing strength acts through an increasingly greater total area, -- how would that quantify gravity to fit in the OP question? thank you

 

[nebel]

a rocket would have to expend a massive amount of energy to move from the center to the surface of the earth.

yea, it would be smart to store the energy that could be ideally harvested (and re-use with 100% efficiency) as the stuff gets down there. good point, To restate the OP, though:
Would there more gravity have to be overcome on the way up to the surface, then to give it escape velocity out of the galaxy, to the edge, area of zero G? Hate to be around at launch time, (had a house within eyesight of the shuttle launches, and even going to Mars rattled your teeth) thank you.

 

[exchemist]

If I would not be so handicapped I would try, so,
take your graph of the [strength of?] field on the unit mass (which is different than origins's I suppose?), and add a factor that shows that the diminishing strength acts through an increasingly greater total area, -- how would that quantify gravity to fit in the OP question? thank you

I've already quantified gravity (in the Newtonian model) for you, in terms of both force and potential, which are the only two ways of expressing it that are of any use, and I've given you pictures of both. Any further futzing around is really a waste of everybody's time. Just use force and potential and you can do anything you need to.

P.S. If you like, you can draw yourself field lines, as one can do for a magnetic or electric field, radiating from the centre of the mass and convince yourself that, at double the distance, the density of the lines has fallen by a factor of 4. This is the same factor as the factor by which the surface area of a sphere at that radius has grown. (F proportional to 1/r², but Area proportional to r²).

So gravitational force behaves like an influence radiating from the centre in the same way as light radiates from a point source.

 

[DaveC426913]

I'm not sure why you are continuing to ask this, when I have explained to you, with a diagram, that the potential is a minimum at the centre. It is the gravitational force that is zero.

OK, now I'm getting confused.

If both the gravitational force and the gravitational potential are at the minimum at the centre of the Earth, then what is the property that results in time dilation being greatest at the centre?

 

[exchemist]

OK, now I'm getting confused.

If both the gravitational force and the gravitational potential are at the minimum at the centre of the Earth, then what is the property that results in time dilation being greatest at the centre?

You'll need to consult Wiki for how gravitational time dilation works - as I say, I am not an expert on GR.

But, regarding potential, one needs to recognise that in free space, in the absence of matter, the potential is zero, whereas under the influence of mass it becomes increasingly -ve. So a minimum, in this context, refers to a significant -ve value, by comparison with the zero of free space. That -ve value is the source of the time dilation. Apparently.

 

[DaveC426913]

OK:

"According to the general theory of relativity, gravitational time dilation is copresent with the existence of an accelerated reference frame. An exception is the center of a concentric distribution of matter, where there is no accelerated reference frame, yet clocks are still supposed to tick slowly. "

So, left side of green line:

 

[nebel]

If both the gravitational force and the gravitational potential are at the minimum at the centre of the Earth, then what is the property that results in time dilation being greatest at the

I think the potential is not at the minimum but maximum, I have learned. it still begs the question why a zero gravity reading on an instrument at the center would trigger relativity and clocks to slow down rather speed up.

So gravitational force behaves like an influence radiating from the centre in the same way as light radiates from a point source.

which would mean that there is always the same "sum" of gravity, no matter where you measure the total. thank you. or?

 

[nebel]

An exception is the center of a concentric distribution of matter, where there is no accelerated reference frame, yet clocks are still supposed to tick slowly. "

so how can I understand that exception, the cause of no acceleration, but drag on the clock?

 

[exchemist]

I think the potential is not at the minimum but maximum, I have learned. it still begs the question why a zero gravity reading on an instrument at the center would trigger relativity and clocks to slow down rather speed up.

which would mean that there is always the same "sum" of gravity, no matter where you measure the total. thank you. or?

Christ Almighty. I have told you several times it is a minimum. Can't you read?

 

[exchemist]

OK:

"According to the general theory of relativity, gravitational time dilation is copresent with the existence of an accelerated reference frame. An exception is the center of a concentric distribution of matter, where there is no accelerated reference frame, yet clocks are still supposed to tick slowly. "

So, left side of green line:

Yes so the reduction in clock speed is the green line, which resembles very closely the graph of gravitational potential I provided in post 319, the only difference being that this graph takes the surface of the Earth as the zero point, i.e. it shows deviation in clock speed relative to our everyday experience on the Earth's surface. Nice graph.

 

[exchemist]

so how can I understand that exception, the cause of no acceleration, but drag on the clock?

You can't, because you cannot even grasp what a potential is. This is General Relativity you are talking about here. You have zero chance of understanding that.

I think the potential is not at the minimum but maximum, I have learned. it still begs the question why a zero gravity reading on an instrument at the center would trigger relativity and clocks to slow down rather speed up.

which would mean that there is always the same "sum" of gravity, no matter where you measure the total. thank you. or?

In a way, yes, just as for a light bulb if you add up the total power of the light energy crossing a spherical shell at one radius it is the same as at any other radius.

But the difference is that light is "stuff"(EM radiation with properties such as energy, wavelength etc) in a way that a gravitational field is not. So do not grab hold of this idea and try to do silly things with it. Please.

 

[nebel]

This is General Relativity you are talking about here. You have zero chance of understanding that.

, well, I still like to hear why a zero gravity reading at the center would be overruled, to show a clock slow- down (green line in minus field) vey nice graph!.
Just for fun, have the lines figured in, that the surface is in rotational equatorial speed, same direction like the orbiting timekeeping satellites.? **
Even if I dont understand right away, many viewer might, or appreciate a refresher course.
PS ** seriously, why do clocks slow in the center, the gravity field/ gravity potential explanation,-- because difference in speeds between surface and center does already, a little.

 

[nebel]

so, here is a graph showing the line of gravity doing a reverse back to zero, supposedly a place of fast clocks

here is the original from origin, setting the pace for the turnaround, from high gravity at the surface,= slow clocks, to where in the zero gravity field clocks should run as fast as they can, so,
why does the green line in Dave's graph, below the surface not follow suite. not take an upturn too?

We can read it should, because that slowdown is the exception, but how and why does it happen.? exceptions are not granted lightly. so, because
The gravity potential has been falling since starting at the center, continued to fall in orbit? whereas the gravity field strength has been falling only outside, into orbit heights? but.
why is time dilation so attached to gravity potential and not to the strength of the gravitational field alone?
Is there something to the idea that overlapping gravity fields add up, even if their "pulls" are in opposite directions?
I meant this observation from Jams R in post# 303:
"It's vector addition. If I have two vectors of equal magnitude and opposite directions and I add them together, I get a zero vector as a result. Call this "cancellation" if you want to use that word, but it's just basic addition, really. An overlap of fields (addition) and cancellation are the same in this case. If you add two fields of equal magnitude and opposite directions, you get zero field, not twice the gravity. Twice the gravity would require adding fields that point in the same direction." thank you.

 

[exchemist]

, well, I still like to hear why a zero gravity reading at the center would be overruled, to show a clock slow- down (green line in minus field) vey nice graph!.
Just for fun, have the lines figured in, that the surface is in rotational equatorial speed, same direction like the orbiting timekeeping satellites.? **
Even if I dont understand right away, many viewer might, or appreciate a refresher course.
PS ** seriously, why do clocks slow in the center, the gravity field/ gravity potential explanation,-- because difference in speeds between surface and center does already, a little.

Well I'm certainly not going anywhere near all that with you, seeing as you still can't get it into your head that gravitational potential continues down to a minimum at the centre of the Earth, in spite of having had this explained to you several times now.

 

[exchemist]

so, here is a graph showing the line of gravity doing a reverse back to zero, supposedly a place of fast clocks

here is the original from origin, setting the pace for the turnaround, from high gravity at the surface,= slow clocks, to where in the zero gravity field clocks should run as fast as they can, so,
why does the green line in Dave's graph, below the surface not follow suite. not take an upturn too?

We can read it should, because that slowdown is the exception, but how and why does it happen.? exceptions are not granted lightly. so, because
The gravity potential has been falling since starting at the center, continued to fall in orbit? whereas the gravity field strength has been falling only outside, into orbit heights? but.
why is time dilation so attached to gravity potential and not to the strength of the gravitational field alone?
Is there something to the idea that overlapping gravity fields add up, even if their "pulls" are in opposite directions?
I meant this observation from Jams R in post# 303:
"It's vector addition. If I have two vectors of equal magnitude and opposite directions and I add them together, I get a zero vector as a result. Call this "cancellation" if you want to use that word, but it's just basic addition, really. An overlap of fields (addition) and cancellation are the same in this case. If you add two fields of equal magnitude and opposite directions, you get zero field, not twice the gravity. Twice the gravity would require adding fields that point in the same direction." thank you.

Because, you steaming halfwit, the first graph shows force and second - the green line - shows clock speed which, as we have been saying for a long time now, follows potential.