Volume 17: Pages 435-441, 2004

Orbital Period of a Binary System in the Field‐Boost Approach

J. Lucinda, D. W. Foryta, M. G. Rodbard

Departamento de Física, Universidade Federal do Paraná, Caixa Postal 19044, 81531‐990, Curitiba, PR, Brazil

We develop a dynamics for binary systems within a framework where velocities and the difference in gravitational potentials resemble “angles,” the argument of hyperbolic functions, in space‐time. After deriving the relativistic equations of motion for two mutually interacting bodies, we obtain a relativistic action‐reaction expression. The derivation of the one‐body equivalent equation of motion leads to a reduced relativistic Lagrangian, from which we obtain the dynamic quantities. We also discuss the equivalence between the measurements of a small angular “anomaly” and the relativistic correction on the planetary orbital period. Finally, we derive a relativistic third Kepler's law for binary systems.

Keywords: dynamics, binary systems, relativity, gravity, orbital period

Received: August 13, 2002; Published Online: December 15, 2008