View Full Version : The Center of the Earth

Squashed

2006-Aug-28, 02:45 PM

If two large bodies were close together would gravitational time dilation be greatest at the gravitational midpoint** between the two or would it be greater on the opposite side of the larger body?

** - (what is the technical term for this point?)

I guess the root of my question lies in whether gravity cancels itself or if only the effect of gravity is nullified.

Would a person at the center of the Earth experience a slower or faster time than a person on the surface of the Earth?

If gravitons cancelled each other at the center then it would seem like time would flow faster because there is less gravity ...

but if only the collective effect of gravity is nullified then there is more gravity at the center of the Earth than at the surface of the Earth and so time goes slower at the center of the Earth than at the surface of the Earth.

hhEb09'1

2006-Aug-28, 03:12 PM

** - (what is the technical term for this point?)the barycenter

Ken G

2006-Aug-28, 03:28 PM

** - (what is the technical term for this point?)

Or less jargony sounding, the "center of mass" or "center of gravity".

Would a person at the center of the Earth experience a slower or faster time than a person on the surface of the Earth?

The issue is the strength of the gravitational potential. An easy way to think about this is just imagine dropping something from a very great distance. The places where the object would have the greatest speed are the places that are deepest in the gravitational well, and those are also the places where time flows most slowly. So the center of the Earth is the slowest place, even though there's no net gravitational acceleration there.

hhEb09'1

2006-Aug-28, 03:48 PM

Or less jargony sounding, the "center of mass" or "center of gravity".I just realized that I misunderstood the question. It appears that he's asking for the name of the place where the gravitational attraction from each body cancels out, which is not the barycenter (or center of mass).

Squashed

2006-Aug-28, 04:13 PM

I just realized that I misunderstood the question. It appears that he's asking for the name of the place where the gravitational attraction from each body cancels out, which is not the barycenter (or center of mass).

You are correct.

antoniseb

2006-Aug-28, 05:55 PM

It appears that he's asking for the name of the place where the gravitational attraction from each body cancels out, which is not the barycenter (or center of mass).

Are you referring to the L3 point between the Earth and Moon? Or is he talking about the Earth-Sun system? Not clear from the OP.

Squashed

2006-Aug-28, 06:42 PM

Are you referring to the L3 point between the Earth and Moon? Or is he talking about the Earth-Sun system? Not clear from the OP.

The L1 point is what I was thinking, thank you antoniseb.

In my mind I was thinking Earth-Moon, since it is the closest, but for all practical purposes of discussion it could be any 2-body system.

I think there is a difference in saying the gravity cancels out or that the effect of gravity cancels out.

A clarifying example would be taking two flashlights and pointing the beams at each other: there is a tiny force exerted on an object placed between the two flashlights from the photons striking it and there is a certain point where the force of photons from flashlight "A" equals the force from flashlight "B" but there is still photons from both flashlights striking the object.

In the case of gravity between say the Earth and the Moon at the L1 point the effect of both bodies' gravity is zero but the amount of gravity is twice what it would be at a similar altitude from a single body.

Since there is twice as much gravity at the L1 point then is time dilated greater at this point than at another arbitrary point at a similar altitude from either body?

hhEb09'1

2006-Aug-28, 07:05 PM

Are you referring to the L3 point between the Earth and Moon? Or is he talking about the Earth-Sun system? Not clear from the OP.Between, so L1, right? And isn't it called the L1 point whether it's the earth/moon system or sun/earth system?

Of course, the L1 and the other Lagrange points also takes into account the inertial force of the orbital motion--L2 is on the far side of the smaller body, and so is attracted to both, in the same direction, but it's still an equilibrium position.

I think there is a difference in saying the gravity cancels out or that the effect of gravity cancels out.

::snip::

Since there is twice as much gravity at the L1 point then is time dilated greater at this point than at another arbitrary point at a similar altitude from either body?It's all relative. :)

In some formulations of general relativity, you'd see that such a position would be relatively flat, the gravities do "cancel" out just as light photons can interfere and cancel each other out. Plus, it's not the magnitude of the gravity that causes the effect anyway--in a constant gravitational field, where the force is the same everywhere, in the same direction, the objects farther down the potential would experience a greater effect (as KenG mentions above).

Ken G

2006-Aug-29, 02:45 AM

Yes, and notice that hhEb09'1 is correcting the idea that the gravities balance at the L1 point-- you have to also include the "centrifugal force" to find the L1 point. In general, this will be a point where the gravity is larger from the more massive object (in the Newtonian sense). Indeed, for an obiting telecommunications satellite, the satellite is in effect at its own L1 point, in the limit that the gravity of the satellite plays no role at all in the balance.

Squashed

2006-Aug-29, 01:31 PM

In some formulations of general relativity, you'd see that such a position would be relatively flat, the gravities do "cancel" out just as light photons can interfere and cancel each other out. Plus, it's not the magnitude of the gravity that causes the effect anyway--in a constant gravitational field, where the force is the same everywhere, in the same direction, the objects farther down the potential would experience a greater effect (as KenG mentions above).

In a constant single-body gravitational field it seems rather plain that farther down into the gravtity potential would experience greater general relativistic time dilation but I would like to understand the 2-body situation (static/motionless would be easiest).

It would seem that the center of gravity would be the deepest down the gravity well but as the distance between the two bodies increases then there is a transition that occurs where the general relativistic time dilation lessens at the center of gravity while it remains the same at the center of gravity of each individual body.

Another example would be an explosion/supernova. Prior to the explosion the center of gravity of the star would be the deepest in the gravity well and the slowest time dilation but afterward since there is less concentrated mass the magnitude of the time dilation is greatly reduced. This all happens even though when viewed from an infinite distance time dilation remains the same - the escape velocity from the remaining star and its explosive debris is still the same, ... or is it?

hhEb09'1

2006-Aug-29, 01:56 PM

It would seem that the center of gravity would be the deepest down the gravity well but as the distance between the two bodies increases then there is a transition that occurs where the general relativistic time dilation lessens at the center of gravity while it remains the same at the center of gravity of each individual body.I'm not sure I follow that.

Let's put it into the context of a concrete example, the earth and moon. The center of gravity of the earth/moon is inside the earth, about a quarter of the way towards the center. The L1 point is closer to the moon than the earth. Can you rephrase your comments in that context?

Ken G

2006-Aug-29, 02:48 PM

This all happens even though when viewed from an infinite distance time dilation remains the same - the escape velocity from the remaining star and its explosive debris is still the same, ... or is it?

It isn't-- the escape speed from an expanding shell drops as the shell expands. So you are right that the depth of the well decreases, but this is what determines the escape speed-- and it also decreases, as does the time dilation. They are directly related.

Squashed

2006-Aug-29, 03:47 PM

I'm not sure I follow that.

Let's put it into the context of a concrete example, the earth and moon. The center of gravity of the earth/moon is inside the earth, about a quarter of the way towards the center. The L1 point is closer to the moon than the earth. Can you rephrase your comments in that context?

In the earth/moon system if the distance between the two bodies were increased then the collective center of gravity for the two bodies would move farther from the earth's individual center of gravity, possibly even outside the earth.

As the distance between the two bodies increases the general relativistic time dilation effects decrease at the collective center of gravity for the two bodies but since no mass is removed from either body then each body's individual general relativistic effect remains the same. Collectively the GR effects decrease but individually the GR effects remain the same.

I don't know if the L1 point is exactly the point I am thinking because what I am referring to when I reference that point is the point between two gravitating bodies where their combined gravitational effects equals zero. The L1 points are more orbital points but maybe the L1 point and the point I refer to are one and the same.

I think Ken G's last post is getting at what I am trying to explore. Although I think it is also feasible to determine whether gravity actually cancels or whether it accumulates, but the accumulated effects equal zero force.

hhEb09'1

2006-Aug-29, 03:53 PM

In the earth/moon system if the distance between the two bodies were increased then the collective center of gravity for the two bodies would move farther from the earth's individual center of gravity, possibly even outside the earth.And, as I've like to point out, that's true even of a baseball, if thrown far enough. :)

But I think what you really may be looking for is potential. Instead of calculating gravitational force, look at the potential function. The GR effects that you are asking about will be essentially constant over constant potential.

Jeff Root

2006-Aug-29, 04:36 PM

These two questions may already have been answered in this

thread, but I think they're essential to what Squashed is asking:

1) On what does gravitational time dilation (or perhaps more

accurately, spacetime distortion) depend? Is it gravitational

potential? Gravitational field strength? Or what?

2) What is the measure of depth in a "gravity well"? Is it

gravitational potential? Gravitational field strength? Or what?

I think those two questions have the same answer, because

they are asking the same thing, but I'm not sure.

-- Jeff, in Minneapolis

Ken G

2006-Aug-29, 06:19 PM

Yes, and the answer to both is gravitational potential. A potential is globally determined, whereas field strength can be monkeyed with in an arbitrarily small region with no effect on time dilation.

Squashed

2006-Aug-29, 07:43 PM

Yes, and the answer to both is gravitational potential. A potential is globally determined, whereas field strength can be monkeyed with in an arbitrarily small region with no effect on time dilation.

Thanks Jeff Root & Ken G.

So if I understand correctly then at the L1 point, even though an atomic clock present there experiences zero gravitational force, there would still be GR time dilation because the escape velocity from that point is a value greater than zero?

Then if there are two atomic clocks, one at L1 and another at an arbitrary point at the same altitude, from either body, then no time discrepancy due to GR should be registered?

This also leads me to believe that if an astronaut were on a very massive star then he would see distant starlight blueshifted but as the astronaut rocketed off the star the distant starlight would transition from blueshift to redshift.

hhEb09'1

2006-Aug-29, 08:07 PM

So if I understand correctly then at the L1 point, even though an atomic clock present there experiences zero gravitational force, there would still be GR time dilation because the escape velocity from that point is a value greater than zero?At L1, the gravitational forces don't balance to zero, because they have to compensate for the centrifictional forces as well. But the time dilation is not absolute, it is relative--so everywhere experiences time dilation, but how much depends upon where you are comparing it to.

Then if there are two atomic clocks, one at L1 and another at an arbitrary point at the same altitude, from either body, then no time discrepancy due to GR should be registered?No, the equipotential surfaces will not generally be constant altitudes, in this case.

Ken G

2006-Aug-31, 03:56 AM

So if I understand correctly then at the L1 point, even though an atomic clock present there experiences zero gravitational force, there would still be GR time dilation because the escape velocity from that point is a value greater than zero?

Yes that's right, and to hhEb09'1's correct answers, I would add that if you include the centrifugal force as a type of gravity (it acts just the same way, and is connected to gravity via the equivalence principle, even though it is not a real Newtonian force), then the forces do balance at L1, yet there is still a slowing of time relative to infinity, because of the nonzero escape speed.

This also leads me to believe that if an astronaut were on a very massive star then he would see distant starlight blueshifted but as the astronaut rocketed off the star the distant starlight would transition from blueshift to redshift.

He would see distant starlight blueshifted, expressly due to the time dilation effect. How you are picturing the redshift is unclear-- it would have to be a motion that created a "normal" Doppler redshift.

Squashed

2006-Aug-31, 12:28 PM

How you are picturing the redshift is unclear-- it would have to be a motion that created a "normal" Doppler redshift.

I was thinking along the lines that the redshift was caused by GR due to the universe arising out of the initial intense gravitational well. So as the astronaut departed from the local blueshifting gravitational well of the star then the distant stars would exhibit only the "old" signature from the earlier gravitational period.

In the supernova example I gave earlier in this thread it seems that a gravitational well can be destroyed by explosive separation of the original constituents of the mass that created the gravitational well - is this true?

Ken G

2006-Aug-31, 01:15 PM

I was thinking along the lines that the redshift was caused by GR due to the universe arising out of the initial intense gravitational well.

Oh I see, you were talking about cosmological distances. Those kinds of redshifts are generally quite large, much more so than the blueshift from a star's gravity.

In the supernova example I gave earlier in this thread it seems that a gravitational well can be destroyed by explosive separation of the original constituents of the mass that created the gravitational well - is this true?Yes.

Squashed

2006-Aug-31, 01:31 PM

Oh I see, you were talking about cosmological distances. Those kinds of redshifts are generally quite large, much more so than the blueshift from a star's gravity.

Sorry, Ken G, but by blueshifting I meant the light was shifted towards the blue from that which we view now (without a large gravitational field to affect our view). Although, if the star were massive enough it could undo all of the redshift currently viewed and actually blueshift the light - couldn't it?

Ken G

2006-Aug-31, 03:59 PM

Yes, if you are talking about something really dense like a neutron star. Normal stars would induce only a tiny blueshift.

Squashed

2006-Sep-01, 01:05 PM

... Although I think it is also feasible to determine whether gravity actually cancels or whether it accumulates, but the accumulated effects equal zero force.

As far as being able to distinguish whether gravity cancels or the effects of gravity cancels I propose that two atomic clocks be placed on opposite sides of the moon (since it rotates slower than the earth) and then, while a clock is on the face towards the earth, if gravity cancels then it should run at a faster rate (since there is less gravity due to gravity canceling) than the far-side clock but if gravity accumulates then the near-side clock should run slower (since there is more gravity due to gravity accumulation) than the far-side clock.

gravity cancels - on the lunar surface, part of the gravity from the moon is canceled by the gravity from the earth

gravity accumulates - on the lunar surface, the gravity from both the earth and the moon are present but part of the effect of the moon gravity is canceled by earth gravity

Jeff Root

2006-Sep-01, 03:20 PM

Squashed,

You're trying to figure out Mach's principle -- right?

-- Jeff, in Minneapolis

Ken G

2006-Sep-01, 03:26 PM

As far as being able to distinguish whether gravity cancels or the effects of gravity cancels

If you want to know the clock rate, all you need is the escape speed to infinity. Call it what you like, "canceling" or "accumulating", this is already known.

Squashed

2006-Sep-01, 03:50 PM

If you want to know the clock rate, all you need is the escape speed to infinity. Call it what you like, "canceling" or "accumulating", this is already known.

Your statement is true according to General Relativity but if the two clocks determine otherwise then something is amiss either in the application of the theory or the theory itself.

It has been stated that GR treats gravity as canceling in certain situations and so I would like to find out if it really cancels or if only the effects of gravity cancel without influencing the time dilation of gravity.

You're trying to figure out Mach's principle -- right?

Mach's principle - "mass there influences inertia here". (http://en.wikipedia.org/wiki/Mach's_principle)

I guess that I am, somewhat, because if gravity does accumulate, or cancel, then other celestial bodies do affect the the earth's gravity (or any other body's) which would be evident in time dilation discrepancies.

Although I really only want to know if gravity from one body cancels the gravity from another body.

Ken G

2006-Sep-01, 04:21 PM

Your statement is true according to General Relativity but if the two clocks determine otherwise then something is amiss either in the application of the theory or the theory itself.

Yes but this has already been tested, you are reinventing the wheel. NASA constantly detects general relativistic time corrections, as do GPS satellites for that matter. The only general relativistic effects that remain uncertain are high-order corrections like what happens during rotation and are there gravitational waves, and nobody is betting their money against GR on those counts.

It has been stated that GR treats gravity as canceling in certain situations and so I would like to find out if it really cancels or if only the effects of gravity cancel without influencing the time dilation of gravity.

The time dilation of gravity is an effect of gravity, so anything that affects the gravitational potential affects time dilation. Still, it is true that the gravitational potential is itself a simplified entity that doesn't always work even in GR, and issues like "Mach's principle" get quite dicey. But that is not what you are asking when you talk about time dilation on the Moon, for example.

Squashed

2006-Sep-01, 07:03 PM

Over on the thread about tidal locking of moons it has been noted that centrifugal force is equivalent to gravity - does this mean that centrifugal force can cause GR time dilation?

hhEb09'1

2006-Sep-01, 10:41 PM

Over on the thread about tidal locking of moons it has been noted that centrifugal force is equivalent to gravity - does this mean that centrifugal force can cause GR time dilation?Relatively, yes. But remember that the centrifugal force would disappear in some other reference frame--and a different "cause" would appear.

As has been said before, the magnitude of the gravitational force is not the issue--two separated objects can experience identical gravitational forces, yet experience different general relativity effect.

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