[JP]

You can't do a simple conservation of energy-analysis of things in GR.  You need a full field theory treatment, using a stress-energy tensor (http://en.wikipedia.org/wiki/Stress-energy_tensor#In_general_relativity).  GR is certainly the more elegant theory, but I can't imagine a good reason for wanting to use it to answer this question.  You need to employ it when you need extreme precision, or when you're working with supermassive objects or huge scales that make Newtonian mechanics inaccurate.

Lightarrow: I think your KE is contained in that stress-energy tensor, which in turn depends on the interaction of the mass with the curved space-time.  (Since you fold time into the equations, you know its velocity from its path in space-time).

sophiecentaur: I took a graduate seminar on GR a few years back, and we did derive the elliptical orbits from GR.  The way we did it was to show that in the small-mass, large-distance limit, GR reduces to Newton's equations, and you can solve it from there.  []  GR ends up not having simple, closed-form solutions in most cases. 

[lyner]

sophiecentaur: I took a graduate seminar on GR a few years back, and we did derive the elliptical orbits from GR.  The way we did it was to show that in the small-mass, large-distance limit, GR reduces to Newton's equations, and you can solve it from there.   [] GR ends up not having simple, closed-form solutions in most cases.

That's interesting - so, basically, you get the answer via Newton rather than going directly there? It's reassuring, somehow.

SO, Newton is certainly the answer for someone who's question starts off "My Physics Teacher . . ."

[lightarrow]

The way we did it was to show that in the small-mass, large-distance limit, GR reduces to Newton's equations, and you can solve it from there.

Even for light's deflection near the mass?

[JP]

The way we did it was to show that in the small-mass, large-distance limit, GR reduces to Newton's equations, and you can solve it from there.

Even for light's deflection near the mass?

We worked in particular with massive objects orbiting other massive objects.  I don't know off the top of my head if you get zero deflection for light using the same limits, but I'd have to guess that you don't.

[Alan McDougall]

Hi guys,

You have all responded better than I could,

But this is my 1 cent peace.

If they were joined by great springs they would act no differently from objects held together by springs on earth but on an immense scale.

A lot of really frightening bouncing, jumping contortion, pogo stick madness. []

The universe has a better idea gravity, but it is a nice thought experiment.

Alan

[lyner]

A lot of really frightening bouncing, jumping contortion, pogo stick madness. wink

With a bit of maths we could do better than that.