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Newtonsstudent
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Is the value of g at the center of the Earth zero or infinite ?
Which direction would it point to, if it wasn't zero?Newtonsstudent said:Is the value of g at the center of the Earth zero or infinite ?
It's only valid for point masses and outside of spherical masses. For the inside see this:Newtonsstudent said:Intuitively I know it's zero, but when I applied that to the gravitational law, I got confused.
Delta² said:Though the gravitational field can become as big as we want as we get closer and closer to the point particle (due to the law of inverse square), at exactly the point of the particle it would be zero. And the reason again is symmetry.
UltrafastPED said:Didn't Isaac Newton already work this problem?
RyanXXVI said:If one were to gradually did down towards the center of the earth, would the force of gravity gradually increase or decrease? Intuition tells me the force would decrease, but the science says otherwise.
The mass between one and the Earth's center would decrease, decreasing the force, but the distance between one ant the Earth's center would also decrease, increasing the force of gravity in total because the radius is squared.
You have to show how you applied the gravitational law.Newtonsstudent said:Intuitively I know it's zero, but when I applied that to the gravitational law, I got confused.
TumblingDice said:As an interesting aside, did you know that (with a perfect sphere and uniform density), if you drilled a hole between any two locations, you could jump in and gravity would accelerate you the first half, decelerate the second half, and you arrive at the other end. Perhaps more interesting is that the hole needn't pass through the center of the Earth (sphere), and also that every trip, no matter what locations the hole connects, take the SAME TIME to complete.
Gerinski said:Now that's funny, because once you have arrived at the other end, the process should work the other way around, taking you back to the initial end just by the force of gravity, and then back to the other end and so endlessly. Does not this sound like a perpetual motion machine moving you constantly to and fro without any energy being spent?
carrz said:Speaking of which, what is it that makes inner core more dense than the outer layers, is it its own attraction towards the center, or is it pressure from the layers above, or maybe both?
Thanks, so if I understand correctly you would be a sort of "underground pendulum, ideally without friction", right.UltrafastPED said:The hole need not go through the Earth - the same goes for low Earth orbit.
It is perpetual in the sense of any perfect machine, capable of perpetual motion of the first kind; it is the action of additional forces such as air friction which requires adjustments, and hence the continual decay of the orbit.
For a more perfect example, consider the earth-moon system. How long has it been going? Why is it slowing down? Something always goes wrong over the long term; it is a fun physics project to figure out where the energy losses are in each such system.
UltrafastPED said:You can start here: https://en.wikipedia.org/wiki/Inner_core
You're making it overly complicated. Do you know why hot air goes up and cold goes down? It's the same reason.carrz said:I'm afraid I don't see the answer there. I'll try to answer it then. It kind of looks like two faces of the same coin. I'm not sure if north upper layers are really pressuring north lower layers, but lower north layers are surely attracted to south upper layers. Therefore, outer layers are definitively required, that much I can say.
Bandersnatch said:You're making it overly complicated. Do you know why hot air goes up and cold goes down? It's the same reason.
Below is a plot of density as a function of distance from the center of the Earth, based on the Preliminary Reference Earth Model:carrz said:Speaking of which, what is it that makes inner core more dense than the outer layers, is it its own attraction towards the center, or is it pressure from the layers above, or maybe both?
D H said:Note that density generally decreases gradually with increasing distance from the center but is punctuated by some marked step changes. The gradual decreases in density result from decreasing pressure. The step changes represent physical differences in the constituent matter at those step change boundaries. The largest step change is at the core-mantle boundary. The Earth's core is primarily iron and nickel, which are rather dense even at the surface, and are significantly more dense at the immense pressures inside the Earth. The mantle and everything above is "rock".
That different materials differentiate by density is critical to understanding the makeup of a planet. All of the terrestrial planets have a differentiated core, and the gas giants most likely have one as well.carrz said:That's really interesting graph, but different materials make the question less clear.
What acceleration? A planet or star is more or less in a state of hydrostatic equilibrium, where the gravitational force and the gradient in pressure are in balance. There is no acceleration. Understanding hydrostatic equilibrium is easiest for a star or the atmosphere of a planet, where there are no phase changes. With regard to your hypothetical planet that is pure water (which can't happen!), hydrostatic equilibrium explains why pressure and density increase with increasing depth.Suppose a whole planet is made of water. We now look at three molecules of water half-way to the center, they are right on top of each other. How much the distance between the bottom and the middle molecule depends on acceleration of the middle molecule itself, and how much it depends on acceleration of the molecule above it?
D H said:What acceleration?
A planet or star is more or less in a state of hydrostatic equilibrium, where the gravitational force and the gradient in pressure are in balance. There is no acceleration. Understanding hydrostatic equilibrium is easiest for a star or the atmosphere of a planet, where there are no phase changes. With regard to your hypothetical planet that is pure water (which can't happen!), hydrostatic equilibrium explains why pressure and density increase with increasing depth.
What hydrostatic equilibrium by itself cannot explain is why even your pure water planet would have step changes in density. At some depth, that liquid water will become solid, and it won't be the kind of ice that floats. It will instead be ice VII, ice X, or ice XI. In fact, you will see multiple step changes in pressure as liquid water transitions to ice VII, then ice X, and then ice XI.
You realize that your question has been answered by post #5 right?carrz said:I'm afraid I don't see the answer [in wikipedia]. I'll try to answer it then.
"acceleraton" is fine. "acceleration of gravity" is better. "free-fall acceleration of gravity" is best.carrz said:Gravity acceleration. I should have said "force" I guess.
Only for a uniform hollow spherical shell. Only inside the hollow part.So since every molecule is static, that means acceleration vectors cancel at every point inside a planet, not just the center?
No. In order to be a machine it has to do useful work. A perpetual motion machine, therefore, must do useful work in perpetuity with no energy input.Gerinski said:Now that's funny, because once you have arrived at the other end, the process should work the other way around, taking you back to the initial end just by the force of gravity, and then back to the other end and so endlessly. Does not this sound like a perpetual motion machine moving you constantly to and fro without any energy being spent?
The end location has to be at equal or lower radial distance than the start location.Gerinski said:That was very interesting, thanks!
Something else though, the original quote said:
"if you drilled a hole between any two locations, you could jump in and gravity would accelerate you the first half, decelerate the second half, and you arrive at the other end. Perhaps more interesting is that the hole needn't pass through the center of the Earth (sphere), and also that every trip, no matter what locations the hole connects, take the SAME TIME to complete."
I guess that this would only happen if the starting location is farther from the center than the end location.
Conservation of energy would have you pop up no farther from the center than you started - assuming uniform mass distributions of course. This is correct.And so, my consideration of you getting transported continuously to and fro would only happen when the two locations are at equal distance from the center, otherwise you will just stop at the location closest to the center, right?
The value of g at the center of the earth is zero. This is because at the center of the earth, all the mass of the earth is pulling equally in all directions, resulting in a net gravitational force of zero.
The value of g at the center of the earth is affected by the distribution of mass within the earth. If the earth had a uniform density, the value of g at the center would still be zero. However, if the density is not uniform, the value of g may be slightly different from zero.
No, we cannot directly measure the value of g at the center of the earth. This is because it is impossible for humans to reach the center of the earth, and even if we could, the extreme pressure and temperature would make it impossible to take accurate measurements.
Yes, the value of g at the center of the earth is different from the surface of the earth. On the surface, g is approximately 9.8 m/s², while at the center it is zero. This is because the distance from the center of the earth affects the strength of the gravitational force.
The value of g at the center of the earth is important for understanding the structure and composition of the earth. It also helps us to better understand the effects of gravity on different parts of the earth, such as the surface and the atmosphere.