General Relativity Question (With a dash of Newton)

[DyerWolf]

I read somewhere (wiki?) that one of the reasons Einstein came up with the "mass curves spacetime" hypothosis had to do with geometry - ie that two parallel moving rays of light wouldn't converge (such as happens with gravitational lensing) if spacetime wasn't curved.

If I understand it, under this theory, gravity is not a "force" but rather the effect of mass-warped spacetime such that something that otherwise would be travelling in a straight line instead circles the denser object (like those coin wells in malls where the coin spins down into the center).

Does the relativity theory of gravity explain occurrences like the Lagrange points or three-body satellite capture (two moons approach a planet simultaneously, one gains energy and escapes, the other loses energy and orbits) etc., or do most people rely on Newtonian dynamics to describe those phenomena? If the answer is Newtonian dynamics, how do relativistic theories help us understand gravitational effects in a complex system?

(Should have put this in Q&A - Perhaps a Moderator could shift it?)

[Tensor]

I read somewhere (wiki?) that one of the reasons Einstein came up with the "mass curves spacetime" hypothosis had to do with geometry -

snip...

be travelling in a straight line instead circles the denser object (like those coin wells in malls where the coin spins down into the center).

Good, in a simplified way, so far.

Does the relativity theory of gravity explain occurrences like the Lagrange points or three-body satellite capture (two moons approach a planet simultaneously, one gains energy and escapes, the other loses energy and orbits) etc., or do most people rely on Newtonian dynamics to describe those phenomena? If the answer is Newtonian dynamics, how do relativistic theories help us understand gravitational effects in a complex system?

Yes, GR explains everything that Newtonian gravity does (if it didn't, it wouldn't be much of a gravitational theory). What you use really depends on what you want and the level of precision needed. While, in most instances, you can use Newtonian gravity (all our spacecraft use it for navigation to other planets), there are things that GR explains or matches observations better than Newtonian gravity (Mercury's precession, for example). If you don't need the precision of GR, it's much, much easier to use the Newotnian equations than the GR equations.

[Cougar]

Does the relativity theory of gravity explain occurrences like the Lagrange points or three-body satellite capture (two moons approach a planet simultaneously, one gains energy and escapes, the other loses energy and orbits) etc., or do most people rely on Newtonian dynamics to describe those phenomena? If the answer is Newtonian dynamics, how do relativistic theories help us understand gravitational effects in a complex system?

These types of occurrences were explained well before Einstein... using the differential equations associated with Newtonian dynamics. I just happen to be reading Celestial Encounters by Florin Diacu and Philip Holmes....

Starting with the story of Poincaré's work, Florin Diacu and Philip Holmes trace the history of attempts to solve the problems of celestial mechanics first posed in Isaac Newton's Principia in 1686. In describing how mathematical rigor was brought to bear on one of our oldest fascinations--the motions of the heavens--they introduce the people whose ideas led to the flourishing field now called nonlinear dynamics.

I haven't finished the book and don't know if relativistic considerations ever come into play, but most of the history of this problem is strictly newtonian. Adding GR would certainly complicate matters, but would be necessary for improved accuracy in extreme gravitational environments.

When not in such extreme environments, the GR adjustment is very slight. For example, the effect on Mercury's orbit amounts to ~43 arsseconds per century. That's pretty slight.

[DyerWolf]

Thanks for the responses thus far! ...can someone recommend a book (or two) on GR as it relates to gravity and Einstein's theories of curved space?


[...I don't have the strongest background in mathematics, but I am pretty good at grasping concepts and 'picturing' the interaction...]

[Nereid]

Moved, from Astronomy, to Q&A, per the OP's request.

[Tensor]

Thanks for the responses thus far! ...can someone recommend a book (or two) on GR as it relates to gravity and Einstein's theories of curved space?


[...I don't have the strongest background in mathematics, but I am pretty good at grasping concepts and 'picturing' the interaction...]

In that case, check out Kip Thorne's "Black Hole and Time Warps; Einstein's Outrageous Leagacy". You also get a lot of the history of Relativity. From Pre-Einstein to the last work up through the late 80s.