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According to Kepler's law of planetary motion, the earth revolves around the sun in an elliptical path with sun at one of its focus. However, according to general theory of relativity, the earth revolves around the sun in the curved space and it revolves in a circular path.

Which is correct? Does the planet moves in a circular path or an elliptical path?

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    What you say about general relativity is not precise. Hence the confusion. – MBN Mar 24 '13 at 11:43
  • The answers will essentially be duplicates of this post: http://physics.stackexchange.com/q/26408/2451 – Qmechanic Mar 24 '13 at 12:25
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    GR doesn't say things move on circular paths any more than Kepler. Can you provide a reference for this claim? Debunking that statement is really the heart of the issue. –  Apr 11 '13 at 05:57
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    This has been flagged by an anonymous user as being not a real question. I'm closing it as a duplicate to provide OP with some further pointers. – Qmechanic Jun 10 '13 at 13:01

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The notion that GR predicts that a planet moves in circular path is not really true. GR is just an extension (though it's complex math) for what we didn't understand over centuries. Not only newtonian mechanics, but any consistent theory that makes use of the inverse-square law uses the conics like parabolas, hyperbolas, ellipses and circles. Depending on the velocity at which the object arrives (comparable to gravity), its orbit can be any of the conics.

Now, this makes sense that any object isn't in elliptical or circular orbit always. It may or may not change, based on the objects it interacts along its path. Here's a simulator on the orbits of celestial objects. There are lot of presets. For instance, you can see the slingshot preset where a planet makes an asteroid to go out of orbit. So, it's not true that all orbits are elliptical always.

Waffle's Crazy Peanut
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There are many different types of orbits according to General Relativity - more that that according to Newtonian mechanics. For example:
http://arxiv.org/abs/1207.7041 Characterization of all possible orbits in the Schwarzschild metric revisited
(skip right to the figures in the end of the article). Elliptical path is one particular case of these.

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