Cuurent statuses of theories of gravity

[chaszz]

I know that Newton's theory of gravity fails to predict certain features of Mercury's orbit in comparison with GR, and also fails to predict the bending of spacetime around a star shown by the path of light. And perhaps one or two other failures which I forget. But I've read that Newton's laws are adequate for calculating pathways of spacecraft in the solar system, and are used by NASA and presumably other space agencies for their flights, because GR is so much more complicated to use. So, what is the current status of Newton's theory of gravity in physics? Is it considered a special case of Einstein's theory, or an entirely different theory? Is it considered valid in the realms it covers, or outdated and overturned? Does Einstein's theory *contain* Newton's? Is Euclidian flat space which I believe Newton uses, a special case of curved GR space, valid only for smaller realms like the solar system, or could Euclidian space be said to be able describe also a large large area of the universe, say several long walls of galaxies together? If a flight path to another star say, 400 million light years away were calculated with Newton's laws, would it be in error as compared with a calculation made with GR? As the laws of physics break down in a singularity, could Newton's laws be said to break down above a certain size of spatial area?

 

[K^2]

Yes, you can derive Newtonian gravity as a first order approximation to General Relativity. That's pretty much what it is understood to be and why it is useful for most orbital dynamics problems.

 

[Mike Anderson]

Newton's law of gravitation is basically a simplified form of einstein's theory of general relativity. It does not account for frame dragging and all that fancy relativistic stuff but it is sufficient to explain gravitational interactions to a high degree of accuracy.

 

[atyy]

Newtonian gravity is not a special case of GR. In the case of weak gravity, it is a good approximation to GR. However, even in weak gravity we can detect deviations from Newton's theory, such as the clock corrections that GR predicts are needed for the global positioning system (GPS) to run correctly.

 

[chaszz]

Thanks. What about the later part of my query? What is the relationship of Euclidian space to GR space? Am I describing that correctly, including the parts about small and large scales and Newton's laws breaking down at large scales?

I am very curious about the relationship between any kind of geometry of space, Euclidian or one of the more complex geometries, and real space, or real space-time. Is the geometry of GR considered to be

1. A depiction of a real spacetime, or
2. A model that merely mathematically represents a physical reality we do not really understand (in the way that we do not really understand wave-particle duality, but are forced to live with it)??