"In general relativity gravity is curvature of spacetime caused by mass-energy. Changes in curvature propagate at c, the speed of causality."
I really hope you meant speed of light there.
Regardless, this thing is still a mystery to me. Why, if gravity propagates at c (or, better perhaps: Changes in the space-time curvature, which is caused by mass-energy, propagate at c), why doesn't the earth spiral into the sun or away from it? If the earth is attracted to the point where the sun was eight minutes ago and not to where it is right now, it's orbit should not be stable. It's a very big difference compared to the "gravity is instant" way of Newton.