# Tag Info

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In this answer we assume a spherically symmetric spacetime and no cosmological constant $\Lambda=0$. I) Birkhoff's theorem (BT) only works for vacuum branches of a spherically symmetric spacetime, i.e. in regions without any matter, cf. e.g. this Phys.SE post. Therefore BT would apply to a hollow planet, cf. e.g. this Phys.SE post. The Newtonian shell ...

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The Guardian article is over dramatising a bit. GPS satellites normally orbit at an approximately fixed altitude and orbital speed so their gravitational time dilation is constant. Because Galileo 5 and 6 are in elliptical orbits their time dilation is constantly varying. The variation is partly due to changes in altitude and partly due to changes in the ...

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Normal force $F_N$ is just the force between two surfaces. It's called "normal" because it acts perpendicular (normal) to the surfaces. Gravitational force is completely unrelated. Gravity always acts with $F_g = -mg$. The minus sign indicates that the force points down. These two forces often oppose each other, which is why $F_N$ OFTEN, BUT NOT ALWAYS, ...

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Normal Force arises due to the Newton's Third law. Normal Force will be always acting opposite to the force falling on the surface. Normal Force is a reaction force. Remember Normal force is equal to mg only when the object is placed horizontally, and the force is acting in the direction of the gravitational field. Now your second question Here you ...

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Briefly, the normal force is $F_N=mg$ when the surface that mass $m$ is resting on is horizontal (when the surface is inclined by an angle $\theta$ to the horizontal, then it's just $F_N=mg\cos\theta$). Friction has nothing to do with $F_N$, per se. But the frictional force experienced by $m$ sliding down an inclined plane is the coefficient of (kinetic) ...

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I am looking for the name of a theory positing that "empty" space itself is not empty Rather surprisingly, it's called General Relativity. See the Einstein digital papers where in his 1920 Leyden Address Einstein said this: "This space-time variability of the reciprocal relations of the standards of space and time, or, perhaps, the recognition of the ...

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I think many people here just too intelligent to see this point: because you do not have a better choice. It is simply not practical and not feasible to teach kids in high school about General Relativity. (um... expecting they know some tensor already? and understand space-time?) Besides, as mentioned by many others, the Newton approach is not so bad. In ...

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you could do that by replacing gravity (that is ultra-weak) by another similar force (i.e. attraction in $\frac 1 {d^2}$ ), like electrostatic. It's easy to act on small charged objects. (but if you want a liquid to be attracted, it's more difficult :-) )

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I know of two reasons for why we should consider gravity to be a force. The first is purely classical and Newtonian: tidal forces. Gravity is solely responsible for producing tidal forces, and they cannot be considered a fictitious force, whereas the usual acceleration due to gravity in some sense can always be thought of as fictitious. The way you know ...

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The geometry of spacetime is described by a function called the metric tensor. If you're starting to learn GR then any moment you'll encounter the Schwarzschild metric that describes the geometry outside a sphrically symmetric body. When you go inside the body the geometry is described by the (less well known) Schwarzschild interior metric. The exact form ...

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If gravity isn't a force, then why do we learn in school that it is? Because it is a force. It's just not a force in the Newtonian sense, wherein work = force x distance. When you drop a brick the "force" of gravity doesn't add any energy to the brick. Instead it converts potential energy into kinetic energy. This is different to what you do if you ...

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I gather that the large source of error you are worried about is the ability of the experimenter to accurately hit the start/stop button on the stopwatch at the start/stop of the ball's journey down the ramp. What is the approximate magnitude of error we'd expect? Before I directly answer your question, let's estimate how bad the experimental error will be ...

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What is the general relativity explanation for why objects at the center of the earth are weightless? At that location spacetime is locally flat. See the Wikipedia Riemann curvature tensor article and look at the schematic on the right: CCASA image by Johnstone, see Wikipedia Let's imagine we could take away the Earth and look more closely. ...

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The explanation is Birkhoff's theorem, which states that the Schwarzschild solution is the unique spherically symmetric vacuum solution in general relativity. An immediate result of this is that, just as in Newtonian gravity, a spherical shell does not contribute to the gravity experienced by an object within it. If this were otherwise it would suggest the ...

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Gravity as a field theory shows that particles move because of the curvature of spacetime - the field here is spacetime itself. Electromagnetism is a field theory and light are just waves in the EM field which is cocontiguous with space that bears it. Both the above are classical descriptions. QM, and then QFT showed that we should quantise fields. This ...

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I would like to take a slightly different angle on this question and point out that most physicists believe that gravity is in fact a force. The great triumph of modern particle physics, the standard model, contains the strong, weak, and electromagnetic forces. These forces are represented in the standard model by the presence of force carriers (spin 1 gauge ...

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I like this question: I understand you are asking what are the consequences and the opportunities if this is true. If gravity is not a constant then perhaps we can control this by either increasing or decreasing gravity. If gravity is not a constant and gravity can be greater this may be a method of putting out forest fires. The fire may have to expend ...

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gravity, it's positive or negative? The most convenient reference systems, the ones having the origin a point on the surface of the earth or in the center of our planet, work with a negative force of gravity because g points to the origin.

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You are correct that the gravity of everythig in the Unuverse should have contracted the universe from everything we know, but the fact is we don't have all the answers. For example, what caused the big bang? What cause the sudden inflation? what is dark energy? String theory has some potential answers for the initial inflation but string theory has run ...

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Your question assumes that the universe started out as a point at the Big Bang and then expanded outwards, however this is not the case. Have a look at my answer to Did the Big Bang happen at a point? for more on this. However your main point remains, that is shouldn't gravity be slowing the expansion, and indeed it did until a few billion years ago. The ...

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No, the straight beam will not magically turn into a curved beam. I suspect you have a slightly confused idea of what the curvature of spacetime means physically. Basically it means that a freely moving body will appear to accelerate relative to some distant observer. Conversely if we want stop the body from accelerating then we have to apply a force (i.e. ...

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Goutham is quite correct in some ways but overlooks something. Look at the diagram below: We known the centre of gravity (COG) of the empty cylinder is $z_1=10\:\mathrm{cm}$ and the mass of the empty cylinder is $100\:\mathrm{g}$. If we fill the cylinder up with water to height $2z_2$ then the COG of the water is $z_2$ and the mass of water is (assuming ...

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Tim B. takes the position that this an example of lying to children. I completely disagree; in my view, what this is an example of is idealization, which is something that every model must do, in every branch of science. As George E.P.Box once wrote: Essentially, all models are wrong, but some are useful. It isn't lying, it's called doing science. ...

1

The flask become most stable when its centre of gravity is at the smallest height. If you start pouring water, you will notice that the effective centre of gravity gets down to a lower postion. As you keep on filling, it would be at the lowest height for some level of water and rises again, afterwards. You will have to find that point of minimum height. Just ...

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I don't agree with the previous answer. Firstly, the OP's question isn't about the lagrangian formulation, it's about the Einstein equation : $$\tag{1} G_{\mu \nu} + \Lambda \, g_{\mu \nu} = -\; \kappa \, T_{\mu \nu}.$$ Secondly, there are stress-tensors that can't be derived from an action : fluids tensors (especially with ...

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Even if we restrict ourselves to a Newtonian conception of the world, forces do not exist. An essential thing that is not emphasized enough when teaching physics, is that physics (in all its wonder) is nothing but a mathematical model of the reality we perceive. Whether you are considering Newtonian mechanics, relativity, or quantum mechanics. There are ...

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There's a very real phenomenon called 'Gravitational Lensing', in which light is bent from its original trajectory by a massive enough cluster of matter (which curves the space-time around it). Moreover, it's bent by a different amount than predicted by a simply application of Newtonian ideas, as kindly pointed out by Rob Jeffries. Is this evidence enough? ...

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If we observe our school syllabus, almost all the physics that we learn is Newtonian physics. Everything from force to the laws of motion are all based on Newtonian ideas. And the general theory of relativity is a modern concept which in fact is more true. But you know the GTR is a difficult concept to understand for a child. So to make the course simple ...

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It's an example of "lie to children". https://en.wikipedia.org/wiki/Lie-to-children Because some topics can be extremely difficult to understand without experience, introducing a full level of complexity to a student or child all at once can be overwhelming. Hence elementary explanations are simplified in a way that makes the lesson more understandable, ...

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We know that is not regular energy nor is regular matter. Dark energy must clump as per space is distorted from its flat symetry (space is dragged like a blanked would be so more cubic space dragged by a massive object than by one less massive) in places where you have concentrated mass like neutron stars and blackholes. There seems to be the posibility ...

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Because Newtonian gravity, where it indeed is considered a force, is a good enough approximation to the situations you consider in middle school (and beyond). General relativistic effects are very weak at the ordinary scales we humans look at, and it would be overkill to introduce the full-blown machinery of general relativity (which demands a considerably ...

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There is no %100 proof in science; at least not for good science. It's always a question of being the most accurate / descriptive / useful theory. For example, Newtonian gravity is 'true' to the extent that it is very effective in a huge diversity of situations. General Relativity (GR) includes all of the accuracies of Newtonian Gravity, and then also ...

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I found the Weinberg passage, but to quote it I need to do it in an answer (too long). So here it goes. We have seen in this chapter that the nonvanishing of the tensor $R_{\lambda \mu \nu \kappa}$ is the true expression of the presence of a gravitational field. We also saw in Chapter 1 that Gauss was led to introduce the Gaussian curvature $K = -R/2$ as ...

1

Its not that tough. You can work it out by using just two equations. But the one thing you should keep in mind is that when the comet is at the minimum distance from the sun, its velocity must be perpendicular to the radial vector (sun to comet). So the minimum distance is itself the minimum perpendicular distance used in the angular momentum formula at ...

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Rather than starting with the object-surface interaction and adding a lift force, start with the object-lift interaction and add the surface later. If you have an object that weighs 10 Newtons and pull up on it with a force of 8 Newtons, then there's an imbalance: there's a net downward 2 Newton force and thus a net downward acceleration. Your object ...

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What would happen here is that the object would not be lifted off of the surface. Instead, you would be relieving some of the normal force that is exerted by the table. Instead of $\vec{R} = -M\vec{g}$, you'd have $\vec{R} = \vec{F}-M\vec{g}$, where $|\vec{F}| < Mg$. The net force would still be zero. Imagine the following: If you put a block on ...

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Gravitational waves do cause fluctuations in clock rate. However, a gravitational wave as strong as you request would very strongly self-gravitate. It might even collapse into a black hole. By comparison, this is the level of time dilation one would experience hovering above a black hole at a distance about 1% of its radius.

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To give a qualitative answer, the equivalence of gravitational and inertial mass is not a coincidence. Mass has inertia and this resists its motion through space-time (we're moving into the future at the speed of light!). The resistance leads to a bending of space-time and it is this that we interpret as gravity. Sort of...

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I have finally got a answer from a professor Ulf Danielsson. http://katalog.uu.se/empinfo?languageId=1&id=N94-1558_2&q=Ulf+Danielsson He say that time fluctuate around the time of the position where the gravitational wave pass. So now the question remain. Can the general relativity theory mathematically describe a gravitational wave that make the ...

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When the neutron binds gravitationally to the neutron star, it loses a significant fraction of its mass. Not immediately. When things falls they don't gain or lose energy. What really happens is more space is created above them and this makes them look (to people far away) a bit similar to falling. But the people far away don't think they are more ...

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Time appears to slow down as light passes a strong object of gravity. Time is not really a physical property, time is simply a unit of measure invented by earthlings. Time appears to change because gravity bends light and it actually travels further to get to the observer so it takes longer to get there. Time is actually distance travelled. The light that ...

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We could try this one: People down on that planet got few hours older while people on the ship got twenty years older. So, lets do this. Put a telescope on the surface on that planet and observe motion of people and such in the ship. If you could somehow do this, you should be able to see everything on the ship happening faster. Also, if people from the ...

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Let me answer the question with another question. Would they be able to live long enough to tolerate the high pressure of the highly densed air around the black hole? Alright, now if they somehow tolerate that pressure and speed, they would never reach the speed of light atleast in their life. So the time passing for them will not be infinite. That's why, ...

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If you're thinking in terms of waves, yes the mathematical formalism used in both cases are quite similar. Gravity does rid itself from the black hole, because the kind of wave (gravitational one) yielding gravitational radiation, what can be measured outside the event horizon. This gravitational irradiation moves on the speed of light.

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You're on the right track. "How do we know that the space shuttle passes throught the point P after losing speed ?" The assumption (in these types of problems) is that the thruster is applied for a very short time compared to the duration of the orbit. In that way, we can assume that applying the thruster is effectively instantaneous. So if the ...

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It is assumed that the spacecraft fires changes its velocity in an instant, not over a period of time. Its velocity is decreased exactly at the point in time it passes through P. It is true that spaceships in lower circular orbits have greater orbital velocities, but in elliptical orbits the velocity changes with the distance between the two masses (since ...

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