Physics – General Physics
Scientific paper
Jul 1988
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988phrva..38...19y&link_type=abstract
Physical Review A (General Physics), Volume 38, Issue 1, July 1, 1988, pp.19-25
Physics
General Physics
9
Scientific paper
For the nonrelativistic Kepler problem it is well known that there exists a transcendental equation (the so-called Kepler's equation) which gives a position in the orbit at a given time. The precessing orbit of the relativistic Kepler problem is reduced to the nonprecessing one by using the transformation related to a rotating Laplace-Runge-Lenz vector. This vector is an extension of the familiar conserved vector and is always oriented to the moving perihelion point of the precessing orbit. From the considerations on Kepler's equation and the rotating Laplace-Runge-Lenz vector, a relativistic Kepler's equation is newly defined to find a position in the precessing orbit at a given time. This equation has two expressions corresponding to the relativistic coordinate time and proper time. By using the equation, Lambert's theorem that gives the required time on the orbit is extended to the relativistic problem.
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