Reparametrizing the relativistic Kepler equation: a bridge to Levi-Civita-type models
Abstract
We establish a link between different relativistic variants of the Kepler problem. In particular, we show that solutions of the special relativistic model with fixed energy can be reparameterized as solutions of a generalized Kepler equation with an additional 1/r2 term in the gravitational potential. This yields a dynamics of the same type as the Levi-Civita correction, up to different coefficients.
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