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86

This whole question is a mistaken premise. There are spherical (or at least nearly spherical) galaxies! They fall into two basic categories - those elliptical galaxies that are pseudo-spherical in shape and the much smaller, so-called "dwarf spheroidal galaxies" that are found associated with our own Galaxy and other large galaxies in the "Local Group". Of ...


27

The direction of the gravitational force would not change under time reversal. Your object would feel a force downward, just as it does usually. It might be easier to imagine you had a movie of an object under the influence of gravity. Drop the ball from rest some distance above the floor. You'll see it move downward and speed up. You'd interpret this as a ...


16

Actually, there are parts of a galaxy that extend beyond the galactic plane: Galactic halo: This is actually the primary part of a galaxy that is not in the main galactic disk. It's made up of multiple sections, and is composed or an array of objects. Dark matter halo: This is a section of the galaxy's dark matter that exists in a semi-spherical shape. ...


14

All matter in the galaxy has to rotate (not necessarily in the same direction) so that a centrifugal force acts. Without the centrifugal force, all matter contained in the galaxy will collapse into the center of the galaxy due to gravitation. The rotation happens about an axis, a line about which all matter revolves in the galaxy. Now, the manner in which ...


14

There is no mistake. The laws of physics themselves are reversible in time, but the solutions not necessarily so. Thus, the "behavior" of the universe itself does not show symmetry under time reversal, primarily due to the second law of thermodynamics. The second law is about the behavior of the solutions, is not a fundamental law in itself. In your specific ...


13

Of course Coulomb's law has to be adapted! And it is therefore fortunate that there exist manifestly covariant formulations of electromagnetism that do not care how spacetime is curved. However, we should first briefly observe that Coulomb's law is not one of the fundamental laws of electromagnetism, though it has played a great role in its inception: ...


10

One of the problems you will encounter is causality. Imagine you have a ball resting on the ground. Without already knowing how it behaved in the past you cannot uniquely define the next frame of your game. You cannot tell if the ball should: move upwards vertically. move upwards in any direction. roll on the ground towards any direction. do nothing. ...


10

Yes, Newton's formula is just fine. No, the formula in your book doesn't describe reality. At first this sounded like an exercise, where the next sentence is probably something like "calculate the effect this has..." These sorts of hypothetical questions are meant to show you how you could distinguish between competing physical theories. Some more digging ...


9

It is due to the combined effect of rotation and "dissipation". A rotating cloud of gas consists of particles which interact strongly with each other (colliding physically) on relatively short timescales can radiate away some of their energy and momentum by emitting photons. For both of these reasons, a dense cloud of rotating gas will collapse to form a ...


8

"According to Newton's law the negative mass should be repelled" -- Nope, in both Newtonian physics and in general relativity, negative mass would be attracted gravitationally to positive mass, although negative mass would exert a repulsive gravitational effect on positive mass (but if the negative mass is small compared to the mass of the black hole this ...


7

Yes. Strictly speaking you can't apply Coulomb's law, or in general any law about the falloff of something with distance, in curved space. Instead you have to shift to a field-based formalism. You can calculate the way the electromagnetic field propagates through a curved background—basically you take Maxwell's equations in tensor form and replace ...


6

You mentioned elliptical galaxies, which the other answers haven't touched upon. Contrary to your statement about the galaxies being 2D, elliptical galaxies are "3 dimensional" in the sense that the stars are not confined to one plane; You could think of them as being "egg shaped". So why are elliptical galaxies not confined to a plane? Mostly because they ...


6

Terrific question. You had it right in your first sentence: “the same amount of energy must have been released during the Earth's history,” but then it gets a little mixed up when you look at various energies, some of which aren’t related to the question at hand (for example, the current internal energy contributes positive mass-energy to the Earth, rather ...


5

First we need to clear up a number of fundamental problems. Always use units. You give all these numbers, but no sense of whether they are meters or nanoseconds or newtons or furlongs. You should read up on significant figures. There is no point in writing out all those digits, since past the first one or two they are all uncertain. In science, writing out ...


4

The Einstein equation says: $$ {\bf G} = {\bf T} $$ where $\bf G$ is the Einstein tensor that describes the curvature, i.e. the gravity, while $\bf T$ is the stress-energy tensor. So the origin of gravity is the stress-energy tensor. This is typically dominated by mass, but includes less obvious contributions like pressure and momentum. Actually solving ...


4

You are correct that as you get very close to the center of the earth, the value of $g$ can become arbitrarily low. If you could somehow create a space there, you could potentially float in it because you would not be pulled in any particular direction with respect to the earth. But while gravity is not strong there, it is strong in other places (like your ...


4

Imagine a flowerpot sitting on a ledge. A breeze blows the pot off of the ledge, and it falls to the ground. When it hits the ground it shatters into a bunch of pieces, it kicks up dust, it makes a sound, it vibrates the ground, and the shards come to rest. The time-reversal of this is that some pieces of flowerpot are sitting on the ground. Suddenly a ...


4

To make such a game and have it make sense, you would have to use a much simpler physical system than anything you would reasonably encounter on Earth's atmosphere. For heat-dissipating systems, the laws of thermodynamics give time a direction: the direction of increasing entropy. Thus an object that falls to earth dissipates its energy, mostly as heat. You ...


4

It looks like a bit of artistic licence was taken (gosh :-) ). You are correct that, the bags would not float that high up -- at least if I'm correctly viewing them as having only a tiny air pocket at the top. The physics is simple: take the total mass of the bag+fish+bagwater, and calculate the equivalent volume of seawater for the same mass. That's ...


4

Object A increases in mass, and so increases in volume I'm going to make the assumption that we are adding mass to A by providing more material of the same density $\rho_{A}$, rather than exchanging the current material with denser material or adding varying densities. I don't have to make that assumption, but it seems like it's what you're going for ...


3

becaus ethe centripetal force due to the rotation in small compared with that of gravity. A calculation for Earth at the equator $(\omega = 2\pi/86164$ seconds, $r = 6378100$ meters) shows that an object experiences a centrifugal force equal to approximately 1/289 of standard gravity


3

If you are in a circular orbit what you need is a Hohmann transfer, from Wikipedia: In orbital mechanics, the Hohmann transfer orbit /ˈhoʊ.mʌn/ is an elliptical orbit used to transfer between two circular orbits of different radii in the same plane. It works like this assuming the planet is in a circular orbit. Then the amount of delta v needed to ...


3

This effect is called Capillary Action. Yes we do in fact observe it in nature in a large scale: How do you think plants are able to "suck up"1 water through its roots and send it to the leaves? One of the major forces responsible for it is capillary action. Here, have a quote from the article mentioned above: Wicking is the absorption of a liquid by a ...


3

The answer is it depends on which observer we are talking about - an observer "with" the collapsing mass sees it and them crushed to a singularity; an external observer "sees" (though see below) the mass frozen just at the event horizon. In GR and a standard black hole, there is only one future for a mass that finds itself at or inside the event horizon, ...


3

Classically they are clearly topological. The metric does not appear, and you don't need a metric for integration on manifolds to make sense. Now in dimension 3 you can cast the Einstein-Hilbert action into a Chern-Simons theory as you say. The connection takes it values in the Lie algebra of the Poincare group. In higher dimensions you need to use higher ...


3

The spherical pendulum conserves angular momentum about a vertical axis running through the fixed point of the pendulum. Consider when the pendulum reaches its lowest elevation, so that its velocity is completely horizontal. Its angular momentum at this point is $L = mvr$, where $m$ is the mass of the pendulum bob, $v$ is its velocity, and $r$ is the ...


2

If the density is constant, it is guarantedd that M and G will fall into the same vertical line. However, if the density is not constant, it is not difficult to find a counterexample that will have G and M on diffrerent vertical lines.


2

The case on the left is correct. Gravitational gradient goes in the direction of the source of gravitational force. Think about the extreme case: if the object was leaning almost all the way over at 89.9$^o$, the center of gravity would necessarily be almost directly below the center of mass.


2

From my knowledge, gravity is infinite and extends throughout all of space. It diminishes as distance increases but is still present everywhere. So given enough time, no matter where something is in the universe, it would accelerate due to the gravitational force of something in the universe. You must mean "the effect of gravity reaches to infinity" . ...


2

There is no maximum gravity. Assuming constant density, mass grows as $r^3$, while gravity attenuates as $r^{-2}$. Therefore as long as density is constant, the force of gravity between two touching spheres will grow like their radii (or the cube root of their masses), meaning there is no sweet spot. Of course, real matter does compress under enough ...



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