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arXiv · gr-qc/0206063

Epicyclic orbital oscillations in Newton's and Einstein's dynamics

Marek A. Abramowicz·Wlodek Kluzniak
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Abstract

We apply Feynman's principle, ``The same equations have the same solutions'', to Kepler's problem and show that Newton's dynamics in a properly curved 3-D space is identical with that described by Einstein's theory in the 3-D optical geometry of Schwarzschild's spacetime. For this reason, rather unexpectedly, Newton's formulae for Kepler's problem, in the case of nearly circular motion in a static, spherically spherical gravitational potential accurately describe strong field general relativistic effects, in particular vanishing of the radial epicyclic frequency at the marginally stable orbit.

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Marek A. Abramowicz, Wlodek Kluzniak. 2002-06-20. Epicyclic orbital oscillations in Newton's and Einstein's dynamics. https://doi.org/10.1023/a%3A1021354928292

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