[Phractality]

I'm seeing notes that the center of gravity of the Earth is about 4600 km from the middle...  And, since the Earth is spinning, it would be essentially be moving around all the time.

The point you are referring to, 4641 km from the center of the Earth is the location of the Earth-moon system's barycenter. If you were orbiting the Earth-moon system at a point far beyond the moon you would orbit around that barycenter, with wobbles as you pass near the line between the Earth and moon. In low Earth orbit, you orbit the center of Earth, but the Earth happens to be orbiting the barycenter. In low lunar orbit, you orbit the center of the moon, which is also orbiting the barycenter. So your choice of reference frame is important. Near Earth, we usually name the center of Earth as the origin; near the moon, we name the center of the moon as the origin.

If you droped something inside a bubble at the barycenter, it would accelerate toward the center of the Earth. The barycenter is roughly 3/4 of the way out from the center to the surface, but the denser parts are in the middle, so your dropped object would accelerate toward the center at roughly 1/2 g. That's if your reference frame is centered on the Earth and rotating with the Earth.

[CliffordK]

Thanks,
So, if you had two objects of equal mass, then the center of mass of the two object system would be between them.

But, on either one object, the majority of the gravity would be towards the center of the object...

But, can one entirely ignore the second object?  The tides, of course. are about 6 feet, but are rather symmetrical around the center of the planet.

Or, is the symmetry of the tides the answer.  So, the gravitational center is offset by a few feet, but well balanced by centrifugal force.

[yor_on]

Not as I think Clifford. Mass and gravity goes together, when you're at the 'center' Earths mass is surrounding you, negating its 'pull outwards'. But if we magically cut away three quarters of the earth you would find 'gravity' again, pointing to where you came from, and no weightlessness. It doesn't matter which side of the earth you are, the direction of gravity is approximately inwards to the center but the deeper you get, the more mass you leave behind (above, and around) you.
==

Pressure will point inwards in a perfect non rotating sphere, undisturbed by other heavenly objects gravity. But pressure will also 'line itself up' relative gravity's direction, assuming kinetic energy to define a pressure. So if we cut away 3/4 of the Earth (starting at that center) you would find yourself on a top instead of a center, and the pressure would act the other way, following gravity's new direction. And from that we can see that energy obey gravity

[Phractality]

This is all covered by Newton's shell theorem. Given uniform distribution of mass in a hollow shell, the gravity inside the shell is zero. The mass outside of the shell doesn't pull things apart; the gravity from opposite direction merely cancels out. It doesn't pull different directions on different parts of an object; instead, it doesn't pull at all on any part of the object.

Outside the shell, gravity is the same as if all the mass of the shell were concentrated at the center. So outside of the shell, gravity is proportional to the inverse square of distance from the center.

Inside a solid sphere, at distance r from the center, you can divide the problem into two parts. The part closer than r to the center acts like all of its mass is concentrated at the center. The part farther than r from the center is just a hollow shell, so it contributes nothing to the gravity at radius r.

As r increases, the mass inside r increases as r³, so the gravity at r increases in direct proportion to r³/r² = r.



That graph assumes uniform density. In fact the interior is denser, so the slope is steeper near the center.

[yor_on]

Da*, you're right

It was me getting confused thinking about it. Gravity could be treated as a pressure of a 'density' I guess and then you just have to imagine something moving inside that. The direction is inwards everywhere, so my spaghettifcation can only come to be due to tidal forces as something (neutronstar) rotates. It was me misleading meself here
==

Reminder to myself: Have to stop playing wow, it influences my physics I sort of forgot to count that other side of the sphere counteracting my 'possible' pull. But the rest, I insist, is correct, ahem...

[yor_on]

Or can it?

Can gravity be treated as a pressure?
What type of pressure if so, a pressure in a classically empty 'space' or as a pressure inside a fluid?
And I'm still stuck on why that balloon need to burst in space.

Pressure can be counted on, but as with everything else, that relies on the history of how a pressure behaves as I see it. It does not answer why there is pressure, and the reason for that balloon bursting. And that brings me back to my 'rest space' for particles?

[Phractality]

Yor_on,

Pressure at radius R from the center of a gaseous planet is the weight (mass times gravity) of everything above radius R, spread over the area 4πR². The gas inside R pushes outward against the weight of what's outside R.

When integrating mass times gravity over the volume outside of R, you can simplify the problem by dividing the atmosphere into hollow shells. Each shell must support the weight of everything above it. The weight of each shell is due to the mass of what's below it.

When a balloon is deflated, it has equal pressure inside and out. Pumping more air in increases the pressure on the inside; greater pressure inside than out pushes the skin of the balloon out; that stretches the balloon making the volume inside greater. The skin stops stretching when the tension in the skin plus the outside air pressure balances the the inside pressure.

When you put the balloon in a sealed chamber and put out the air, that removes the air pressure outside the balloon, so the skin must stretch more and push in harder to keep the inside gas from escaping. The tension in the skin is roughly proportional to the pressure difference between inside and out. The inside pressure is the sum of outside pressure and tension in the skin.

The tension in the skin is tangential, while the gas pressure is radial. The difficult way to reconcile that difference is to look at the radial component of tension from a small section of the curved surface and integrate that over the entire area. The easy way is to divide the balloon in half with an imaginary plane surface. The pressure times area on opposite sides of the surface is equal and opposite. So each half of the balloon applies an inward force equal to the cross section area times the pressure.

[graham.d]

Don't forget if you had a "hollow" planet that was a perfect spherical shell, you would not experience any gravitational force if you were floating about inside it.

[CliffordK]

The direction is inwards everywhere

Yes,
Although, you can think of gravity as the sum of the interaction of any one particle with any other particle in the system. 

So, you could think of every molecule in your body interacting with the approximately 10⁵⁰ atoms in the earth.

As you descend towards the center of the planet, your molecules are being pulled in all directions.  However, one thinks of GRAVITY as the vector sum of all of those interactions that will pull you towards the center of the planet.

Or, once in the middle, the vector sum is equal to ZERO!  (with the exception of tides and density variations).

[yor_on]

Yep. that's the way I think of it too Clifford, as every rest mass interacting with every rest mass gravitationally.

Do you mean that you can't equate a gravity with a pressure Graham? You're probably right if so. What I was thinking was that if gravity could be seen as a 'pressure', then it should have to be a fluid, it should behave as fluids. But, as usual, I'm not sure And a quite nice and understandable explanation of the mathematics behind Phractality, but, why does pressure exist? Can there be a 'ground state' for pressure?
==

Gravity 'bends' all space, somehow. But, how does it do it? How can it 'bend' what is 'not there'? A fluid in dynamical (relative) motion/change? I know, it do sound as me discussing some sort of aether, but I'm only looking at it, trying to compare it to pressure. Because pressure is seriously weird to me, although I don't really know why I'm thinking of it

[yor_on]

And then we have those particles bursting the balloon due to 'pressure' differences. Without particles of rest mass inside there would be no pressure. But then we have massless photons, that both have a momentum and, according to Lightarrow, can beget a rest mass (mathematically and theoretically) following certain constrictions. Although that one is hard to proof practically, as far as I know?

But a photon, does it have a pressure? It do have a momentum?

[Phractality]

Yep. that's the way I think of it too Clifford, as every rest mass interacting with every rest mass gravitationally.

Do you mean that you can't equate a gravity with a pressure Graham? You're probably right if so. What I was thinking was that if gravity could be seen as a 'pressure', then it should have to be a fluid, it should behave as fluids. But, as usual, I'm not sure And a quite nice and understandable explanation of the mathematics behind Phractality, but, why does pressure exist? Can there be a 'ground state' for pressure? []

At macroscopic scales, pressure is force/area. At microscopic scales, pressure is many tiny exchanges of momentum. Each time a molecule bounces off of another molecule, there is exchange of momentum between them. Averaging those exchanges over time, you get a force. Averaging the force over an area, you get pressure.

Gravity is not pressure; it doesn't have the same dimensions as pressure. But gravity times mass is force; and force divided by area is pressure. The downward force of gravity acting on quintillions of gas molecules pulls all those molecules together into a gas planet. The force of gravity pulling outer molecules in is balanced by the force of the inner molecules trying to push each other out (because they are moving fast and bouncing off one another, exchanging momentum). The pressure is just the many tiny exchanges of momentum averaged over time and area.

Gravity 'bends' all space, somehow. But, how does it do it? How can it 'bend' what is 'not there'? A fluid in dynamical (relative) motion/change? I know, it do sound as me discussing some sort of aether, but I'm only looking at it, trying to compare it to pressure. Because pressure is seriously weird to me, although I don't really know why I'm thinking of it

Gravity bends (warps) Minkowski space-time because of how that space-time is defined. Each hypercube of Minkowski space-time is one meter on each side and one second in duration. The meter and second are defined in terms of a particular light emission from a cesium atom; by definition, that emission has the same frequency and wavelength, regardless of where the cesium atom is. The cesium atom can be in the middle of an empty cosmic void or at the event horizon of a black hole, and still its emission has the same frequency and wavelength, by definition.

In a different kind of space-time that is flat by definition, the units of distance and time would have to be defined differently; it might also be necessary to allow the speed of light to be variable (when expressed in those units of distance and time). Instead of hypercubes defined by meters and seconds, the grid of this space-time would be hypercubes defined by some other units of distance and time. Measured in those units, the emission from a cesium atom would have different frequencies and wavelengths, depending on where the cesium atom is.

Minkowski space-time is a mathematical entity, not a substance. If physical space is a substance, that substance is probably uniform when mapped on a space-time grid which is defined as flat. Mapping it with Minkowski space-time probably would make it appear lumpy. I believe physical space does have a substance, but that is ontology, and ontology is frowned upon by today's mainstream scientists. It is anathema in this mainstream board.

[Phractality]

And then we have those particles bursting the balloon due to 'pressure' differences. Without particles of rest mass inside there would be no pressure. But then we have massless photons, that both have a momentum and, according to Lightarrow, can beget a rest mass (mathematically and theoretically) following certain constrictions. Although that one is hard to proof practically, as far as I know?

But a photon, does it have a pressure? It do have a momentum?

Yes; photons have momentum. When a photon is reflected off of a mirror, its momentum reverses direction. Momentum is conserved because the mirror receives an equal and opposite change of momentum. This has been demonstrated by using a powerful laser beam to accelerate a thin mirror. I don't think this type of propulsion will ever put a satellite into orbit, but it might be practical, some day, for sending a vehicle to neighboring stars, like Alpha Centauri.

A laser source imparts momentum to the laser beam. Momentum = energy / speed of light. The laser source receives equal and opposite momentum or recoil. The recoil force is power / speed of light. To get one Newton (3.6 ounce) of recoil, you need a 300,000,000 watt laser. Hey; watch where you're pointing that thing!!!!

Pressure is force / area. The interior area of a sphere of radius 1 meter is 12.566 m². So a 300 watt light source inside a real mirror globe would exert outward pressure of (2 x 10^-6 newton / 12.566 m²) times the average number of times a photon is reflected before being absorbed. Reflectivity varies with wavelength; silver reflects roughly 90 of visible light. (I did the math once upon a time, but today my brain is on strike. I'll let yooze guys figure out the average number of times a photon would be reflected.) Anyway, the pressure would be extremely small.

However, if you imagine a sphere whose inner surface is a perfect reflector, the light intensity from a constant power light source would build steadily. With each photon reflecting something like 300,000,000 times per second the pressure from one Joule of light would be about 2 newton / 12.566 m². A 300 watt light source would increase the pressure by roughly 50 n/m²/s until the sphere exploded with a blinding flash of light.

[yor_on]

So we can in a way define a momentum as a pressure. Now, photons do not interact, as far as i know, what a photon interacts with is matter, or 'rest mass' if we're talking particles. Do the pressure exist if there is only photons?

[yor_on]

That came out weird. Imagine a 'photon sea'. We do not care about what limit that sea, only about the 'photons' themselves. Maybe you can put it this way too. What gives them a pressure?

[JP]

So we can in a way define a momentum as a pressure.

No we can't, since they're two different things.  Momentum is a conserved property of physical systems having to do with their motion.  Pressure is force applied divided by area over which it is applied.  More precisely, momentum has units of (length x mass) / time, whereas pressure has units of                    mass / (length x time²) so they represent two completely different physical things. 

Photons flying around without hitting anything do not impart force on anything, so they exert no pressure.  If they're absorbed or reflected off a surface, they do impart a force (as Phractality pointed out), so you can define a pressure over that surface.  There's a concept called radiation pressure that calculates the pressure on a hypothetical, perfectly absorbing surface placed in a radiation field.

[yor_on]

So pressure is a interaction solely JP? Whereas momentum is a description of intrinsic 'force' due to the propagation of photons? So the 'pressure' in 'space' is what? And then we have the opposite description, a 'tension'. A tension must come to be if we in some way can define walls to a system, or am I being simplistic there?

[yor_on]

Te pressure in space, and the tension are described in the stress energy tensor, so it as that one I was thinking of there btw Classically, and macroscopically, speaking space has no pressure, that I know of that is? But pressure is a strange word as is tension.They both come from matter it seems to me, but has later become used for all sorts of things.