Quote:
Originally Posted by peteshimmon
A question I always had, a body in a perfectly
circular orbit around a dense star. How does
the advance of perihelion effect manifest
itself? A slightly faster orbit time than
Newtonian or by degrading to an eliptical
orbit?
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Yes, it's a slightly faster circular orbital speed than Newton. While radial Schwarzschild geodesics are fairly simple, going to 2D and orbital geodesics gets more complex. If you're familiar with the basic Newtonian orbital equations in polar coordinates, those get modified with additional terms. IIRC, you get two circular orbital solutions (that converge to the single classic Newtonian circular orbit in the weak field limit), one stable and the other unstable. In the unstable case, the slightest perturbation sends it flying wild.
In Newton, circular orbital speed is always less than radial free fall speed at a given radius. In Schwarzschild, circular orbital speed exceeds free fall speed at some point, and becomes light speed at 1.5 Schwarszschild radii. (and this is unstable -- the last stable circular orbit is at 3 radii).
-Richard