dorsal/arxiv
View SchemaPerihelion Precession in the Special Relativistic Two-Body Problem
| Authors | M. A. Trump, W. C. Schieve |
|---|---|
| Categories | |
| ArXiv ID | physics/9805032 |
| URL | https://arxiv.org/abs/physics/9805032 |
Abstract
The classical two-body system with Lorentz-invariant Coulomb interaction V=-k/rho is solved in 3+1 dimensions using the manifestly covariant Hamiltonian mechanics of Stueckelberg. Particular solutions for the reduced motion are obtained which correspond to bound attractive, unbound attractive, and repulsive scattering motion. A lack of perihelion precession is found in the bound attractive orbit, and the semi-classical hydrogen spectrum subsequently contains no fine structure corrections. It is argued that this prediction is indicative of the correct classical special relativistic two-body theory for the limit of no magnetic interaction.
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"date_created": "2026-03-02T18:01:21.512000Z",
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"abstract": "The classical two-body system with Lorentz-invariant Coulomb interaction\nV=-k/rho is solved in 3+1 dimensions using the manifestly covariant Hamiltonian\nmechanics of Stueckelberg. Particular solutions for the reduced motion are\nobtained which correspond to bound attractive, unbound attractive, and\nrepulsive scattering motion. A lack of perihelion precession is found in the\nbound attractive orbit, and the semi-classical hydrogen spectrum subsequently\ncontains no fine structure corrections. It is argued that this prediction is\nindicative of the correct classical special relativistic two-body theory for\nthe limit of no magnetic interaction.",
"arxiv_id": "physics/9805032",
"authors": [
"M. A. Trump",
"W. C. Schieve"
],
"categories": [
"physics.class-ph",
"physics.plasm-ph"
],
"title": "Perihelion Precession in the Special Relativistic Two-Body Problem",
"url": "https://arxiv.org/abs/physics/9805032"
},
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