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Vincentius

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- Thread starter Vincentius
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In summary: Mach's principle. However, this theory also predicts that G should vary slightly, but such variation is incompatible with General Relativity and experimental results appear to rule out any significant variation.Newtonian gravity is a reasonable approximation at the galactic level. However, the theory needs to be modified to allow for flat rotation curves. Otherwise, there is a small discrepancy between the gravitational potentials at different distances.

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Vincentius

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Jonathan Scott

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Vincentius said:

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Newtonian gravity is a reasonable approximation at the galactic level. In dimensionless terms (potential energy per rest energy), the Newtonian potential due to a collection of masses is simply the sum of -Gm/rc

If you try to extend Newtonian gravity to the whole universe, it doesn't work, because the sum of the potential due to every galaxy in the universe is of order 1 and the Newtonian approximation is not valid. This is of course quite a coincidence and suggests that there may be an exact connection between G and the distribution of mass in the universe, which has led to various alternative gravity theories based on the idea that "everything is relative", usually linked to "Mach's Principle". Such theories typically imply that G must vary slightly, but such variation is incompatible with General Relativity and experimental results appear to rule out any significant variation.

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Naty1

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After all, we live relatively close to the galactic center,

you better double check that...I thought we were on one of the outer spirals...

found a description:

The Milky Way is a barred spiral galaxy 100,000–120,000 light-years in diameter containing 200–400 billion stars. It may contain at least as many planets.[17][18] The Solar System is located within the disk, around two thirds of the way out from the Galactic Center, on the inner edge of a spiral-shaped concentration of gas and dust called the Orion–Cygnus Arm.

http://en.wikipedia.org/wiki/Milky_Way_Galaxy

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Vincentius

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Chalnoth

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Actually, as I understand it, you get the FRW equations just the same in Newtonian gravity (though the radiation contribution is wrong, of course). I am not certain whether this extends to perturbed FRW, but I strongly suspect it does to a pretty good approximation.Jonathan Scott said:If you try to extend Newtonian gravity to the whole universe, it doesn't work,

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Jonathan Scott

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Vincentius said:By "relatively" I mean as compared with an "average" position in space, i.e. likely an intergalactic position. I am looking for the effect of matter distribution on local gravitational potentials.

Even if you include enough hidden mass or "dark matter" to explain the rotation curves, the difference in Newtonian gravitational potential somewhere in a galaxy relative to anywhere in intergalactic space is still a very tiny fraction. Again, you can easily calculate that.

Gravitational redshift only becomes significant when you're very close to a very large mass, and in such locations you are more likely to find accretion disks than objects in stable orbits.

There is another way of approximating Newtonian gravity which works in a way which is more compatible with relativistic concepts. This assumes that the relative time dilation is proportional to the exponential of the Newtonian potential in its dimensionless form. That is, rather than taking the time dilation to be (1-Sum(Gm/rc

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Vincentius

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There is another way of approximating Newtonian gravity which works in a way which is more compatible with relativistic concepts. This assumes that the relative time dilation is proportional to the exponential of the Newtonian potential in its dimensionless form. That is, rather than taking the time dilation to be (1-Sum(Gm/rc2)) compared at different points, it works better to take it to be exp(-Sum(Gm/rc2)). This gives the same result for most cases, but is unaffected by taking into account more distant objects as well.

Do you have a reference on this approach Jonathan?

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Jonathan Scott

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Vincentius said:Do you have a reference on this approach Jonathan?

It's a common approach when discussing the Newtonian limit of General Relativity. It's probably in many textbooks - the only one in which I could immediately recall where to find it is Rindler "Essential Relativity" (revised second edition) equations 7.21 and 7.22.

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Vincentius

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Thanks!

The cosmic gravitational potential is a measure of the gravitational energy of a system of objects in the universe. It is determined by the distribution of mass and energy in the universe, and it affects the motion and interactions of these objects.

The value of the cosmic gravitational potential is calculated using the equations of Newton's law of gravitation and Einstein's theory of general relativity. It takes into account the masses and distances of all objects in the universe and their gravitational interactions.

The cosmic gravitational potential plays a crucial role in shaping the structure and evolution of the universe. It determines the formation of galaxies, clusters of galaxies, and other large-scale structures. It also affects the expansion of the universe and the distribution of matter and energy in it.

Yes, the value of the cosmic gravitational potential changes over time as the universe evolves. It is affected by the expansion of the universe, changes in the distribution of matter and energy, and the interactions between different objects in the universe.

The cosmic gravitational potential is closely related to dark matter and dark energy, which are two mysterious components that make up about 95% of the total mass-energy of the universe. These components have a significant impact on the cosmic gravitational potential and are crucial for understanding the structure and evolution of the universe.

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