# Tag Info

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Generically, if I have a particle which has potential energy $\phi(x,y,z)$, then the force on that particle will be given by ${\vec F} = - {\vec \nabla}\phi$. So, generically, the motion of particles will "try" to minimze the potential energy. In particular, the only points where the particle will not move will be those points where $\nabla \phi = 0$, or, ...

9

The source of gravity is not mass, but stress-energy-momentum, so you are correct that the energy converted in this process already has gravity and that that gravity is only rearranged The change in the gravitational field needs time to propagate, though, and this does indeed happen at the speed of light.

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$H$ tells us how fast the universe is expanding, relative to how much it has already expanded. It has units of inverse time. For example, if $H=0.1\ \mathrm{s}^{-1}$, then the universe is expanding by 10% every second. Suppose that the density of mass-energy in the universe was so small that deceleration was negligible, and suppose that at $t=1$ s, we have ...

9

The key to answering this question is the Goldschmidt classification of elements. Thirteen of the long-lived elements are siderophilic; they preferentially bind to iron. Those thirteen elements are significantly depleted in the Earth's crust compared to their prevalence on meteors, asteroids, and the Sun. This list of thirteen does includes rhenium to gold, ...

3

Actually, they are still currently sinking to the core. Earth's internal heat comes from a number of sources, and one of these is the release of gravitational energy from the heavy elements migrating further toward the center. A similar statement holds for other planets. This isn't the majority of the source of heat. Other sources are the original thermal ...

1

The core-collapse phase of a supernova commences once the final stages of nuclear burning are complete. This final phase of fusion reactions involving silicon, produce a core composed of iron-peak elements (not just iron). The cessation of nuclear burning leads to the contraction of the core. This happens relatively slowly at first, on a timescale given by ...

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Here is one take on how to understand the relation between force and potential energy, which I think is the closest modern version of how it would have been seen originally. Let's take as the conditions for a force to be conservative $$\nabla \times \mathbf{F} = 0$$ and $\mathbf{F}$ is a function of position only (this leaves out the magnetic force on a ...

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I'll post the same answer here that I posted on Worldbuilding: Under the circumstances you describe, my immediate reaction is that it would not be possible. The issue here is that the cluster would be fairly unstable. The black holes would all be mutually attracted to each other, and would soon coalesce into one large black hole - taking the Imperial ...

1

We can start at the relationship: $W=-\Delta U$, which is work done by a conservative force. The math A (conservative) force $F$ will do this work on an object when doing a displacement $\Delta x$, and $W=F \Delta x$. In the general case, the force might be different at different points as the object is moved (the force of gravity is not constant along ...

2

I) In Palatini $f(R)$ gravity, the Lagrangian density is $${\cal L}~=~ \sqrt{-g} f(R),$$ with $$R~:=~ g^{\mu\nu} R_{\mu\nu}(\Gamma),$$ and where $\Gamma^{\lambda}_{\mu\nu}=\Gamma^{\lambda}_{\nu\mu}$ is an arbitrary torsionfree$^1$ connection. II) As OP mentions, the word Palatini refers to that the metric $g_{\mu\nu}$ and the connection ...

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I realised why this happens. Objects moving at different speeds have different trajectories in spacetime, so they naturally follow different geodesics. This is explained very well here: http://curious.astro.cornell.edu/question.php?number=649

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The solution might be the fact that it is supposed that gravitation is propagating at light speed. Movements at light speed are particular as it is shown for photons in vacuum: The (hypothetical) proper time of photons is always zero, that means that there is no time passing from the hypothetical point of view of photons. By consequence, photons cannot ...

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Whether the upward direction will be taken as positive & the downward direction as negative or vice versa simply depends upon you. It does not bother any physics. Generally, the downward direction is taken as negative. The negative sign indicates the opposite direction only of what you have assigned the positive direction. In Principles of Physics by ...

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It depends on what direction you assign to be positive in your coordinate system. To avoid confusion, just remember which direction acceleration is acting and which direction you assigned to be positive.

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Well, things don't fall up, so gravity would be negative. The longer version: For classical mechanics, the direction of a coordinate system is often arbitrary. For free fall problems I generally choose down to be positive (especially when I'm not dealing with an initial velocity, but it's a matter of preference). What you do need to know, no matter what ...

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If up is positive, and gravity points down, then $a$ (acceleration due to gravity) would be downwards, so it will have a negative magnitude.

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When you open the tube, yes, air will be drawn into it. This is indirectly due to gravity, in the sense that what will drive the flow is a pressure gradient. The pressure in the tube is lower than the pressure outside (after you pump air out and let things settle down, this is true no matter where you open the hole), so air is drawn in. Gravity has a role in ...

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This particular orientation sensing protocol is not wonted to me, but the following, given the data you cite, will indeed give you your orientation in space: Magnetometer gives $\vec{N}_0$ north direction (in general, not parallel to the "ground" because it has magnetic dip included); Gravity accelerometer gives $\vec{D}$ "down" direction; Then ...

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I'll try to write this up into a quick answer. Maybe it will help. What exactly is a? $a$ is the universal scale factor. It is also written as a function of time: $a=a(t)$. As you can see, it features prominently in the Friedmann equations (and is featured in the FLRW metric), and is important when studying the expansion of the universe. As is the ...

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The apparent radial accelleration due to moving in a circle is ω2R. For earth, ω = 2π rad/24 h = 73 x 10-6 rad/s. Earth's radius is about 6.37 Mm. Therefore the upwards accelleration at the equator is 34 mm/s2. That's pretty small compared to the 9.8 m/s2 downwards accelleration due to gravity, so we generally ignore it. Then there is ...

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Gravity definitely does exist. Einstein did not provide a model without gravity, he simply found a new way to think about it. Gravity, as we experience it, is a consequence of bodies moving along so-called geodesics, which can in simple terms described as "shortest paths through spacetime". The effect of gravity now arises if there is motion along geodesics ...

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Yes, it does protect against G forces because it spreads the pressure on the support surfaces of the body evenly. For example, and interesting article here

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Yes the effect is real, potentially at least, but no it's not measurable. As an aside, the redshift of light by its gravitational interaction with (homogeneous and isotropic) dust is exactly what the FLRW metric predicts, but this clearly isn't what the question means. The gravitational field of a beam of light is calculated in the paper On the ...

1

It's only a way of modeling motion as we see. You can think in that way about General Relativity, but physicists strongly believe that there exists theory of quantum gravity, which means that there exists a corresponding fundamental particle called the graviton. The most developed examples of quantum gravity theories are String Theory and Loop Quantum ...

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Physics does not answer existential problems. It gathers data and observations and models them with mathematical equations and functions, and then can explain the data with the model and predict new observations. This has been going on for centuries, and what we see if we study the history of physics is that there are regions of validity for the ...

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A few assumptions before we get started: 1) The satellite that you refer to is traveling in an orbital path around the Earth, as opposed to some other type of motion (You did not specify whether the satellite was in orbital or sub-orbital flight. If assumed incorrectly, please let me know with a comment.) 2) Relative to the satellite, the spoon is ...

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The spoon will keep moving until orbital decay takes control and it reaches the earth over several orbital periods. To explain why, imagine a spoon hung to a satellite traveling at a constant velocity (ignoring any accelerations, for ease of understand) of $x$ and therefore all its components must be travelling at the exact same velocity to make sure their ...

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Ultimately, the only thing that can explain a physical theory is a better theory. Newton's force law used to be the entire theory of gravitation up until the early 1900's. Newton himself had no explanation for what "caused" the force. Einstein gave us General Relativity, which describes how gravity is the geometry of space and time. In GR, energy and ...

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Here are couple of references that describe professional uses of a post-Newtonian formalism to model the planets and the Earth's Moon: Standish, et al. "Orbital ephemerides of the Sun, Moon, and planets," Explanatory Supplement to the Astronomical Almanac (1992): 279-323. The relevant equation is 8-1 on page 3. Petit and Luzum (eds.), "IERS Technical Note ...

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Currently there is no generally accepted explanation of why objects attract each other. There are hypotheses such as Le Sage's, but none remained popular. The most basic (simplest) theory of gravitation is still Newton's law of universal gravitation.

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The following has ben found via Wikipedia page “Gravitational interaction of antimatter”. Another experimental test has been provided by the supernova SN1987a (anti)neutrinos, and this has been published in two brief reports in Phys. Rev. D in 1988 [1] and 1989 [2]. After the explosion of this supernova, 19 antineutrinos have been detected at IMB and ...

3

To be exact Einstein made a claim that it is gravity that curves space-time. You can follow his reasoning in his "Relativity: The Special and General Theory." Einstein started off with comparing acceleration caused by gravity to acceleration in a lift (assuming it moves with accelerated motion) going up. He claimed that these two accelerations are ...

2

According to the excellent and very well researched scientific biography "Subtle is the Lord" by A. Pais, as late as 1912 Einstein was still assuming a flat Euclidean space (at that point he had been working on the general theory for 5 years). Then (in 1912) Some time between August 10 and August 16, it became clear to Einstein that Riemannian geometry ...

4

As well as the antihydrogen experiments, ALPHA, AEGIS and GBAR that were mentioned in other answers, there are a couple of other experiments, though they haven't had any results. In the 60's, they tried the obvious thing of dropping positrons down a metal tube (paper), but it didn't work, for the subtle reason that the electrons in the metal sag under ...

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For visible stars, the answer is no. In Newtonian physics, a star that would pull something travelling at light speed back to itself, i.e. a star for which the escape velocity were $c$, was called a dark star and seems to have been first postulated by the Rev. John Mitchell in a paper to the Royal Society in London in 1783. The great Simon Pierre de Laplace ...

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The only experiment I know of was done by the ALPHA team at CERN. The results are published in this paper. The error bounds are huge - all the team were able to say is that the upper limit for the gravitational mass of antihydrogen is no greater than 75 times its inertial mass! However I believe an updated version of the experiment, ALPHA2, is in progress ...

1

There would be a slight restorative force from the gravitational pull of the atmosphere itself. First, imagine an ocean world with a very small core. If the core was more dense than the ocean it will be "sink" to the center. Similarly, if your "core" was a shell, it would also "sink" to the center. Thus, if you had both a sphere and a shell they would ...

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I think you are missing the positive feedback effects of winds flowing from high to low pressure areas as the shell moves. At best you would have a parachute effect to slow things down.

3

This is due to spinning forces, such as centrifuged force. Remember that galaxies form (at least the regular ones) from the spinning of matter around a galaxy nucleus. So, you're not wrong. Gravity is isotropic, but in this cases the spinning forces are the definition to the galaxy form.

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I would tell her the bubbles contain water, and that water is sticky. I would remind her that even after she lets water run off her hands by gravity, she still needs to dry them off with a towel (unless you use an electric hand dryer), because some of the water sticks. It's easier to see the foam than it is to see the water, because the foam is puffed up ...

3

The gravitational analogue of magnetism is called "gravitomagnetism" (and the general mathematical analogy between Maxwell's equations and gravitation in general relativity is called gravito-electromagnetism), which deals with the gravitational interactions of currents of mass/energy, just as magnetism deals with interactions of currents of charge. According ...

0

because both objects, the earth and the moon have their own unique gravity force due to their mass., there is a place between the two where gravity works independently that keeps the separated. the moon is not falling towards the earth. actually, from some research I've done. the moon is actually moving away from the earth by 1 1/2 inches a year.. not much ...

0

About.. locally measured your time never differ, aka, 'c' relative your wristwatch for example, although some might want to argue that a acceleration is different there, which I don't agree too. But we can keep it to uniform motions and then also conclude that this fact is what makes 'repeatable experiments' work, as well as constants. Assume this wrong, ...

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The criterion for gravitational radiation is (conjectured to be, pending direct evidence) a changing quadrupole moment in the mass distribution, so an accelerating mass distribution does not always radiate, but can do so if the acceleration changes the quadrupole moment. This is in contrast to electromagnetic radiation, which occurs when the charge ...

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In a theoretical case, this should work. In real world situations, there are a couple of reasons you could run into difficulty. *) Non rigid bodies and shift of mass distribution. If you've got a car or a statue, you'd be pretty close. But a person or a rhino wouldn't work as well. As the body moves, the proportion of weight on one end or another shifts, ...

1

The answer is: Solve Newton's second law. Really, $\vec F = m\vec a$ is meant to be a second-order differential equation, with the force dependent on position (and, sometimes, time). Writing it as $$\vec F(\vec x,t) = m \frac{\mathrm{d}^2\vec x}{\mathrm{d}t^2}$$ makes manifest that the distance travelled by something, is, in general, the solution \$\vec ...

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I'm not sure whether these theoretical ideas are is included in what you have in mind. They are only good (and the first , as far as I know, only in theory) for fundamental particles and not for measuring masses of everyday things, but here goes. The second - inference from cross coupling co-efficient between otherwise dispersionless, massless states - is ...

2

Since gas molecules are affected by gravity, wouldn't that make gas molecules at higher than average elevation slower (at the top of their ballistic parabola) and thus colder than air molecules accelerating to the ground? In non-relativistic theory no, because in thermodynamic equilibrium temperature has to be the same everywhere. The slowing down does ...

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Your position that mass measurement is done by measuring gravitational force is not quite correct. A balance measures the mass of an object by comparing the force of gravity on the mass in question to the force of gravity exerted on a reference mass. In some cases there is also a factor based on the geometry of the scale. The measurement is based on the ...

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Well, As far as I know mass is normally calculated using force exerted and calibrating to local gravity. I suppose if you really wanted you could build a device to measure mass based on its inertia, but it would likely be large and hard to use. The most convenient and the easiest to use is probably the scale that uses force exerted. Did that answer your ...

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