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Newton v. Einstein gravitation


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The 'model' is certainly different, but the predictions made by GR and Newtonian gravity are the same in the low mass/energy limit.

At higher mass/energies, such as close to a deep gravitational well, we start seeing deviations due to 'curvature' ( Mercury's perihelion and its procession for example )

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You cannot directly calculate force in GR because gravity is not treated as a force.


And it isn't as simple as greater or less; the results are just different. In most cases, the differences are too small to be noticed. For example, in Newtonian gravity an object can be in a stable elliptical orbit around a star. The path will not change; the planet will keep going round the same ellipse. (Apart from external influences like other planets.) But if you work out the path using GR then the ellipse will change its position slightly (precess).


Newtonian gravity is good enough in most cases but (as noted above) we see a small anomaly for Mercury which can only be explained by GR.


There are various other things that the two theories give different results for, such as the amount of gravitational lens, "frame dragging, etc.

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I like to imagine two masses A and B, far enough from all other bodies that the gravitational attraction of the latter is negligible.


Newton gives us a formula for calculating the attractive force between A and B. Is the formula exact, even for very large / small masses, and for a very large / small distance between A and B ?


OR, does GR kick in and predict discrepancies even in this simplest of scenarios ?



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