Shouldn't planets have no core (just shell?)

[mcpng]

Hi,

 

New here, just needed to fire off some burning questions. Been watching some vids on cosmology and here are few things I really don't get and can't find internet data about:

 

1) Shouldn't gravitational pull be strongest at the surface of a planet (assume uniform density for sake of simplicity). The gravitational pull inside the planet should have some cancelling effects on one another, and in the core will be net zero. This is validated by some google searches. But then, why do we believe the planets have a core? Isn't it more sensible to think we're just a spherical shell, perhaps many kilometers thick, held toward a center of gravity?

 

2) Following up on question one, how does gravity explain the theory that massive objects exert a force so powerful in the center due to gravity, that it overcomes electromagnetic forces and begins the process of fusion? If fusion takes place, shouldn't it be where gravity is strongest, ie. at some radius away from the center of gravity?

 

3) If gravitational force is directly related to mass and indirectly to distance from the center of mass, then hypothetically, 2 tiniest particles in terms of size touching each other would have a gravitational pull of infinity (as r approaches 0). This is provided the r can approach 0 more than mass m can approach 0. However, if this were true, then these 2 tiniest particles can be hypothetically broken down to think about the smaller exact point of contact between the 2 particles. This makes the gravitational effect further approach infinity, upon which, an infinite gravitational field should not just be a black hole, but should instantaneously suck in the entire universe. Since this didn't happen, would it be accurate to say that hypothetically, in 2 tiniest particles, mass m approaches 0 faster than r approaches 0?

[Schrödinger's hat]

Hi,

 

New here, just needed to fire off some burning questions. Been watching some vids on cosmology and here are few things I really don't get and can't find internet data about:

 

1) Shouldn't gravitational pull be strongest at the surface of a planet (assume uniform density for sake of simplicity). The gravitational pull inside the planet should have some cancelling effects on one another, and in the core will be net zero. This is validated by some google searches. But then, why do we believe the planets have a core? Isn't it more sensible to think we're just a spherical shell, perhaps many kilometers thick, held toward a center of gravity?

The inside of the earth isn't pulled up by the outside.

You're right to think that the stuff on the crust will exert a gravitational force pulling the stuff below up, but it turns out that it's exactly cancelled by the gravitational force of the crust on the opposite side of the planet. So anything at a higher altitude contributes nothing

 

You're also right to think that the gravitational force does get weaker and weaker as you go down (you only need to consider what is deeper than you to work out the force). However, the stuff above you needs to be held up by something, and that something is the pressure it exerts on stuff below it.

This compresses it into a super dense state, not because of the strong gravitational field (the field is in fact weaker as you thought), but because there is so much stuff above it.

2) Following up on question one, how does gravity explain the theory that massive objects exert a force so powerful in the center due to gravity, that it overcomes electromagnetic forces and begins the process of fusion? If fusion takes place, shouldn't it be where gravity is strongest, ie. at some radius away from the center of gravity?

Again, it's the pressure due to the gravity on everything above it.

3) If gravitational force is directly related to mass and indirectly to distance from the center of mass, then hypothetically, 2 tiniest particles in terms of size touching each other would have a gravitational pull of infinity (as r approaches 0). This is provided the r can approach 0 more than mass m can approach 0. However, if this were true, then these 2 tiniest particles can be hypothetically broken down to think about the smaller exact point of contact between the 2 particles. This makes the gravitational effect further approach infinity, upon which, an infinite gravitational field should not just be a black hole, but should instantaneously suck in the entire universe. Since this didn't happen, would it be accurate to say that hypothetically, in 2 tiniest particles, mass m approaches 0 faster than r approaches 0?

 

Uhmm, that'd only be the attraction between those two particles, not their attraction to other stuff.

 

Not only that but talking about gravity on a very small scale is difficult. We don't have a good quantum theory of gravity.

On top of this things like electrons have no known minimum size, but they spend most of their time somewhat de-localised, so thinking about their mass all being at a point is a bit misleading.

Maybe someone more knowledgable about GR or progress on quantum gravity than I could answer your question a bit better.

[michel123456]

(...)an infinite gravitational field should not just be a black hole, but should instantaneously suck in the entire universe. Since this didn't happen, would it be accurate to say that hypothetically, in 2 tiniest particles, mass m approaches 0 faster than r approaches 0?

Bolded mine in order to answer.

1. Nothing happens instantaneously, you have to consider C (speed of light) as a limit. IOW you need a certain amount of time for anything to happen. It may not be really clear why, but it is what we are observing.

2. "Since this didn't happen" is the obvious answer. The non-obvious answer is to consider that indeed it was happening and that it is still happening right now: that we are living inside a collapsing universe, or because we are inside the phenomena and thus looking from the other side, in an expanding universe. This is speculation of course but there are some theories about this point of vue, at least one of my knowledge.

[baric]

3) If gravitational force is directly related to mass and indirectly to distance from the center of mass, then hypothetically, 2 tiniest particles in terms of size touching each other would have a gravitational pull of infinity (as r approaches 0).

 

R does not reach zero. At some point, you get down to the Planck length and quantum effects take over. In other words, it is not possible for two particles to ever "touch".

 

In addition, gravity waves propagate at the speed of light, so nothing ever happens instantaneously.

 

Finally, gravity is a curvature of space, not a pulling force, and is a result of mass. A black hole with one solar mass exerts the same exact gravitational pull as our Sun.

[mcpng]

Regarding the comments about nothing moving faster than the speed of light, isn't a black hole sucking things in faster than light? My terminology may not be right, but the idea being that "movement" is inward toward the centre of the black hole even for light. Otherwise, any reaction that sparks either on or inside the event horizon would have at least one beam of light moving in the exact opposite direction from the black hole's center, and this photon would effectively be static in space, absolutely no movement in or out the black hole? Plus, I know light is somewhat special, but considering the balloon analogy of the universe expanding, wouldn't a light particle be moving faster than the speed of light relative to something else in the opposite direction?

 

The inside of the earth isn't pulled up by the outside.

You're right to think that the stuff on the crust will exert a gravitational force pulling the stuff below up, but it turns out that it's exactly cancelled by the gravitational force of the crust on the opposite side of the planet. So anything at a higher altitude contributes nothing

 

You're also right to think that the gravitational force does get weaker and weaker as you go down (you only need to consider what is deeper than you to work out the force). However, the stuff above you needs to be held up by something, and that something is the pressure it exerts on stuff below it.

This compresses it into a super dense state, not because of the strong gravitational field (the field is in fact weaker as you thought), but because there is so much stuff above it.

 

If the stuff inside the crust has gravitational forces cancelling one another out, then shouldn't it just be free floating, net zero gravity? This still means that the crust should be the point of highest gravitational force. Like a doughnut being held together toward the center, even though the centre is hollow for example. The compression because there's stuff above it still requires some force to make sense of why anything above should exert pressure on anything below. If it's not gravity (and assumedly not the other 3 forces), then what is it?

[Schrödinger's hat]

If the stuff inside the crust has gravitational forces cancelling one another out, then shouldn't it just be free floating, net zero gravity? This still means that the crust should be the point of highest gravitational force. Like a doughnut being held together toward the center, even though the centre is hollow for example. The compression because there's stuff above it still requires some force to make sense of why anything above should exert pressure on anything below. If it's not gravity (and assumedly not the other 3 forces), then what is it?

 

There's no gravity from the stuff above it, but the stuff below still acts (until you get really near the centre, then the stuff below has insignificant gravity).

 

Re. the compression. The stuff at the surface is resting on the stuff below that.

And that stuff (along with the stuff above if) is resting on the stuff below that.

And so on.

Think of resting a table on your foot. Doesn't hurt too much.

But if someone sits on the table, you're in trouble.

Because, even though the table is holding up the person, you're holding up the table and the person. Then the floor is holding up you the table and the person.

The ground is holding all that up

The rocks below... and so on.

 

So the stuff at the bottom isn't contributing much to the force, but it has to support everything above it. So the pressure is massive.

[baric]

Regarding the comments about nothing moving faster than the speed of light, isn't a black hole sucking things in faster than light? My terminology may not be right, but the idea being that "movement" is inward toward the centre of the black hole even for light.

 

The effect if gravity is based solely on mass and distance. The radius of the Earth is about 4000 miles, meaning you are about that far from its center. If you were within 4000 miles of a black hole with the mass of Earth, you would feel exactly the same gravitational force. The "escape velocity" from the surface of the Earth is about 7 miles/second, which means rockets have to be able to reach that speed to escape Earth's gravitational attraction.

 

The key difference is that the black hole is much, much smaller than the Earth because of its incredible density. This means that objects, including you and photons, can get much closer to the center of the black hole's mass than you can for the Earth.

 

As you fall closer to the black hole, the gravitational force and escape velocity increases because the distance decreases. Soon, the escape velocity becomes so great that no man-made rocket could ever accelerate away from it.

 

Black holes are unique in that they are so dense (and therefore tiny), that any object can get so close to it that it can't get away no matter how fast it can travel. In other words, you can get so close to a black hole that its escape velocity exceeds the speed of light! And since this is the fastest possible speed, nothing can get away if it HAPPENS to get that close.

 

But it is easy enough to keep your distance from a black hole, just as it is easy to keep from colliding into the Moon, the Sun, or any other body.

Edited October 7, 2011 by baric

[mcpng]

There's no gravity from the stuff above it, but the stuff below still acts (until you get really near the centre, then the stuff below has insignificant gravity).

 

Re. the compression. The stuff at the surface is resting on the stuff below that.

And that stuff (along with the stuff above if) is resting on the stuff below that.

And so on.

Think of resting a table on your foot. Doesn't hurt too much.

But if someone sits on the table, you're in trouble.

Because, even though the table is holding up the person, you're holding up the table and the person. Then the floor is holding up you the table and the person.

The ground is holding all that up

The rocks below... and so on.

 

So the stuff at the bottom isn't contributing much to the force, but it has to support everything above it. So the pressure is massive.

 

So you're saying that everything inside and the planet has a gravitational pull toward the centre. Within the planet, the net force is still toward the centre even though not as strong as the surface.

And because it just so happens that there are tons of stuff stuck between the crust and the centre of gravity, the strongest gravitational forces at the crust pulling the crust inward squeezes everything in between. This gravitational force of the crust is stronger than the opposing force the rocks would give to protest being squeezed. Net effect, squeezed rocks, resulting ultimately in high temp. and core?

 

The effect if gravity is based solely on mass and distance. The radius of the Earth is about 4000 miles, meaning you are about that far from its center. If you were within 4000 miles of a black hole with the mass of Earth, you would feel exactly the same gravitational force. The "escape velocity" from the surface of the Earth is about 7 miles/second, which means rockets have to be able to reach that speed to escape Earth's gravitational attraction.

 

The key difference is that the black hole is much, much smaller than the Earth because of its incredible density. This means that objects, including you and photons, can get much closer to the center of the black hole's mass than you can for the Earth.

 

As you fall closer to the black hole, the gravitational force and escape velocity increases because the distance decreases. Soon, the escape velocity becomes so great that no man-made rocket could ever accelerate away from it.

 

Black holes are unique in that they are so dense (and therefore tiny), that any object can get so close to it that it can't get away no matter how fast it can travel. In other words, you can get so close to a black hole that its escape velocity exceeds the speed of light! And since this is the fastest possible speed, nothing can get away if it HAPPENS to get that close.

 

But it is easy enough to keep your distance from a black hole, just as it is easy to keep from colliding into the Moon, the Sun, or any other body.

 

If gravity is based solely on distance and mass, then the photon must have a mass, right? Let's say we give it the smallest possible mass, x.

How does this work out using F = ma, and F = GMm/R^2 ?

This may be straying off topic, but first thing I notice is...does a photon have acceleration? Considering the speed of light is constant in a vacuum, I supposed not. In that case, the force of light is 0 (which so far makes sense since i'm not being pushed away from my monitor). But, since gravity works on mass, GMm/R^2 is definitely >0. This means any gravitational pull should change the direction of the photon completely to head toward the centre of gravity. Since net gravitational force on earth is toward the ground, all light should just hit ground now. You wouldn't need a black hole.

[DrRocket]

If gravity is based solely on distance and mass, then the photon must have a mass, right? Let's say we give it the smallest possible mass, x.

How does this work out using F = ma, and F = GMm/R^2 ?

This may be straying off topic, but first thing I notice is...does a photon have acceleration? Considering the speed of light is constant in a vacuum, I supposed not. In that case, the force of light is 0 (which so far makes sense since i'm not being pushed away from my monitor). But, since gravity works on mass, GMm/R^2 is definitely >0. This means any gravitational pull should change the direction of the photon completely to head toward the centre of gravity. Since net gravitational force on earth is toward the ground, all light should just hit ground now. You wouldn't need a black hole.

 

Gravity is NOT based solely on distance and mass. That is true for the Newtonian model, and in a Newtonian model photons do not feel the gravitational force (though there are some rather ad hoc caalculations that pretend to the contrary).

 

In general relativity spacetime curvature, which is the manifestation of gravity, is determined by the stress-energy tensor, which includes mass/energy, momentum and pressure (all forms of energy except gravitational energy). Electromagnetic energy,i.e. photons, are included. But photons have no rest mass and Newton's gravitational law does not apply.

 

Light follows null geodfesics in spacetime, and the Earth has insuffficient mass to significantly affect light at all. Light does not just it the ground, as you can see since your flashlight works as designed. Bumblebees continue to fly.

 

Photons do not accelerate. Their speed is always c, and their direction is always along a null geodesic.

Edited October 8, 2011 by DrRocket

[Schrödinger's hat]

So you're saying that everything inside and the planet has a gravitational pull toward the centre. Within the planet, the net force is still toward the centre even though not as strong as the surface.

And because it just so happens that there are tons of stuff stuck between the crust and the centre of gravity, the strongest gravitational forces at the crust pulling the crust inward squeezes everything in between. This gravitational force of the crust is stronger than the opposing force the rocks would give to protest being squeezed. Net effect, squeezed rocks, resulting ultimately in high temp. and core?

Yeah, that's a good way of wording it. The stuff in the very middle has very little or no gravitational force on it, but everything outside is squeezing it.

If you want a good idea of how much force is involved in pressure there's a few things you can do:

Lie on the bottom of a swimming pool and try and breathe through a hose. You'll find that when you try to breathe in it feels like a large weight is crushing your chest. This is because you have to lift all the water above you a little bit to make room for the air.

Magdeburg hemispheres are another good one. Two hemispheres are put together, and all the air is removed, even very small hemispheres are impossible to pull apart by hand, even with a large group of people acting together. The only thing holding them together is the weight of the atmosphere above pressing down.

You can do a similar thing by heating a glass bottle with boiling water, then putting your hand over the mouth while it cools. Be very careful here, as you can get your fingers stuck or damage hand if the difference in pressure is too much. In this case you can think of it as the atmosphere is still pushing your hand down, but the little section over the mouth has ever so slightly less force below it pushing it up.

 

 

If gravity is based solely on distance and mass, then the photon must have a mass, right? Let's say we give it the smallest possible mass, x.

How does this work out using F = ma, and F = GMm/R^2 ?

This may be straying off topic, but first thing I notice is...does a photon have acceleration? Considering the speed of light is constant in a vacuum, I supposed not. In that case, the force of light is 0 (which so far makes sense since i'm not being pushed away from my monitor). But, since gravity works on mass, GMm/R^2 is definitely >0. This means any gravitational pull should change the direction of the photon completely to head toward the centre of gravity. Since net gravitational force on earth is toward the ground, all light should just hit ground now. You wouldn't need a black hole.

 

Photons carry momentum, but have no rest mass. Also as DrRocket said you have to be very careful as to where you try to apply Newtonian formulas. They only really apply to massive particles moving at slow speed in relatively weak¹ gravity..

Pretending that photons will undergo an acceleration of [math] \frac{GM}{r^2}[/math] will calculate an angle for gravitational lensing that is very approximately correct in weak fields;I can't remember exactly how far off, but I think it's within an order of magnitude. However, you run into paradoxes (ie. if the light accelerated it's not moving at light speed) unless you take other factors into account.

 

 

¹Weak depends on the context, for most uses, even fields around stars are weak. Although if you want high precision (see precession of mercury) you need to include some general relativistic effects.