21 Jan 2015 15:09:49 UTC

Topic 197940

(moderation:

This question has always bugged me, and since I joined E@H I've been itching to ask it.

Please join me for NewGuy 101 this semester.

Disregarding all other factors, such as pressure, temperature, etc., let's travel to the center of the earth and assume we can survive on our nice sight seeing tour.

Since the mass of the earth now surrounds you, wouldn't the gravity of the earth pull you in all directions? Causing you to "float"?

Or is the gravity field more like a well with the center being the bottom of said well?

Phil

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## Null Gravity?

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Aside from the minor detail of how to get there, and how to build a "cave" standing off the pressure at that depth, yes, net gravity on you at the center of mass of the earth (which because of non-uniform mass density won't be quite exactly the center by other means of determination). is zero.

A fun fact from freshman physics: While most folks know that the force of gravity drops off as the square of the distance from the center of mass as you rise above the surface, fewer people know that the force of gravity ALSO drops off as you descend below the surface toward the center. Oddly enough, for the (not quite right) simplifying case of perfectly uniform mass density, I think I remember that the force drops linearly.

As even the deepest gold mines don't get down three miles, and the radius of the earth is near-enough 4000 miles, this drop in the force of gravity is not of much practical importance to most people.

## Wouldn't you know that

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Wouldn't you know that Wikipedia has a nice graph on this point.

Wouldn't you know that it says I am wrong (because I underestimated the degree of impact from non-uniform mass density).

earth gravity below and above surface

In summary--it says that the farther-down bits are so much more dense than are the farther-out bits that for quite a while the gravity rises or stays about equal as you go deeper, not transitioning to a decisive drop until about half an earth radius down.

Getting back to the question originally posed--it does show zero at zero--so I got that bit right.

## @Archae86 Interesting

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@Archae86

Interesting info. I had not even considered the Wiki. I'll have to go look that up.

Some of these type of questions can be confusing to someone like me. I have a deep technical background in electronics but didn't even take physics in high school.

Thanks for the responses, and anyone else please feel free to jump in for us laymen.

Phil

## This is all good. Normally I

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This is all good. Normally I would say Beware Of The Wiki but it's OK on this one. I'll just add that if you want the nett gravitational force upon you to be always directed at the centre of the Earth then you'll want a spherically symmetric density pattern. Fortunately spinning bodies tend to yield that by default. But they found out otherwise at the Moon during Apollo, which wasn't discovered ( obviously ) until they arrived. So called 'mass concentrations' were speeding up and slowing down sections of the close-in orbits - compared to simple Keplerian expectations - sufficiently to cause concern for launch and re-docking timings.

I want to know if there is a trampoline at the centre. Jules Verne had bloody dinosaurs and what not .... and I don't want to come back up via a volcano! :-)

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter ...

... and my other CPU is a Ryzen 5950X :-) Blaise Pascal

## I just love this science

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I just love this science forum. Thanks to everyone. Big plus for Einstein crunchers.

merle

What is freedom of expression? Without the freedom to offend, it ceases to exist.

— Salman Rushdie

## So ..... Is gravity Zero at

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So ..... Is gravity Zero at the center of a Black Hole ?

Not that I'd want to go there )

Bill

## RE: So ..... Is gravity

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Ooooh .... a corker of a question there Bill. :-)

Classical GR says the density is infinite there. Well, Newton also for that matter. That's a hint that we can't legitimately make any genuine interpretive statement from theory. It's best to say "don't know" here rather than give a figure, or even say infinite gravity or whatever. Leave it as a patch of ignorance to be safe.

Such points in the theory are known by the mathematical term 'singularity', a type of naughtiness ( more or less the difficulty produced when you divide a number by zero ) that some functions have at certain points. It's not just gravitational theory that mentions singularities, these are know to occur in the mathematics of many other areas of physics also.

Sometimes it is not an especial problem for a theory overall but rather for the way a physical situation has been modelled in some example to which theory has been applied, and in particular by choice of a coordinate scheme to define a scenario. A good example of that is the event horizon of a black hole which has singularity features only evident with certain choices of reference frame. The difficulty may be 'transformed away' eg. by taking the viewpoint of an object descending into a black hole. Nothing especial happens at the Schwarzschild radius in that case. The central singularity remains with any/all choices of frame and is if you like a more general roadblock to understanding.

It is of great note that quantum mechanics has this blessed ability to prevent some reasons for singularities occurring. The core idea here is that one can't really pin down positions and movement simultaneously for any entity ( and regardless of whether you label said entity a 'particle' or a 'wave' ). The machinery of QM prevents 'one thing sitting atop another', and hence the sort of stacking up and totalling of things without bound. There must be some separation of things. I guess with a quantum theory of gravitation that would enforce an upper limit on densities.

So the Heisenberg Uncertainty Principle, which is usually disdained for it's imprecise undercurrent, can come into play to protect a theory from yielding singularities. Well that's a rough take on it at least.

[aside]There is a trick used often with quantum field theories called 'renormalisation'. This is a tactic that essentially excludes certain infinite sums from being performed ( as a mathematical procedure ), and that reflects back onto the modelling as only assessing quantities above a certain scale size. Very roughly speaking if you don't look too close around the region of some point then you can't manufacture a singularity ...

... Feynman admitted this was 'sweeping infinity under the rug'. He found in quantum electrodynamics that some parts of a calculation would have a sum which totalled to infinity. The very same sum ie. the mathematical expression, appeared in several places. He decided to simply replace that crappy term with a ( finite ) value as measured by experiment. This divided QED calculations into two parts : that which gave sensible results and that which gave the silly ones. Calculate the sensible bits, straight up ignore the bad bits by replacing them with a valid number from the real world. This is not terrible, more to the point it is a recognition that below a certain distance scale we don't know what is happening, but we can accept a 'summary' of behaviour that occurs at that difficult scale.

So that's sort of like producing a profit & loss statement for a company without going into finer details of it's operations. If you own a group of companies then look at said group in toto by manipulating the various profit/loss statements of each. Anyone who has either dealt with an accountant and/or read The Hitch-hikers Guide To The Galaxy series knows that much useful work can come forth from the minds of accountants ... :-)[/aside]

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter ...

... and my other CPU is a Ryzen 5950X :-) Blaise Pascal

## Thanks Mike ! In the latest

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Thanks Mike !

In the latest Star Trek movies with the younger Kirk, Spock etc.

They had some Red Gel-lo stuff that could create what they called 'Singularities'

thus destroying entire planets )

Well, it made for an interesting storyline anyway )

Bill