In Newtonian mechanics, the action for a true trajectory between two spacetime events A and B is a minimum if the final event B occurs before the kinetic focus of the initial event A; otherwise, the action is a saddle point. We give a simplified proof of an analogous theorem in differential geometry for worldlines in a curved spacetime. We locate the kinetic focus for orbits in a Schwarzschild field in the lowest-order post-Newtonian approximation and show that the kinetic focus is shifted beyond its Newtonian value of one angular cycle by a fractional amount of order O(v2/c2).

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