This note gives the lagrangian in Cartesian coordinates as Eq. (25), which must be solved with the four simultaneous Euler Lagrange equations (7) to (10). In the non relativistic limit the lagrangian reduces ot Eq. (5). In the earth sun system the ECE2 relativistic lagrangian reduces to Eq. (27), which is to be solved simultaneously with Eqs. (7) and (8). In the non relativistic limit the earth sun lagrangain reduces to Eq. (13), to be solved with Eqs. (7) and (8). Initial conditions can be taken from the Hulse Taylor binary pulsar at the periastron. Solving as in this note gives the periastron, apastron, and perihelion and aphelion of individual orbits around the center of mass. Finally this general formalism is also applicable to an S2 star orbiting a very large mass. This will be the subject of the next note.

a375thpapernotes8.pdf

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