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Orbital precession due to central-force perturbations

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arxiv gr-qc/0702015 v1 pith:AKFC34SY submitted 2007-02-02 gr-qc

Gregory S. Adkins , Jordan McDonnell This is my paper
classification gr-qc
keywords precessionresultsalphacentral-forceconstantformoftenperturbations
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We calculate the precession of Keplerian orbits under the influence of arbitrary central-force perturbations. Our result is in the form of a one-dimensional integral that is straightforward to evaluate numerically. We demonstrate the effectiveness of our formula for the case of the Yukawa potential. We obtain analytic results for potentials of the form V(r) = \alpha r^n and V(r) = \alpha \ln(r/\lambda) in terms of the hypergeometric function {_2F_1} (1/2-n/2,1-n/2; 2; e^2), where e is the eccentricity. Our results reproduce the known general relativistic (n=-3), constant force (n=1), and cosmological constant (n=2) precession formulas. Planetary precessions are often used to constrain the sizes of hypothetical new weak forces--our results allow for more precise, and often stronger, constraints on such proposed new forces.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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  2. Quantum Black Holes: Perihelion Advance, Quasi Normal Modes and Classical/ Topological Thermodynamics

    gr-qc 2025-07 conditional novelty 4.0 of 10

    A quantum-corrected Schwarzschild black hole is shown to be stable under scalar and electromagnetic perturbations, with thermodynamic topology identical to Reissner-Nordström.

  3. Observable thin accretion disk around a self-dual black hole in loop quantum gravity

    gr-qc 2025-09 conditional novelty 3.0 of 10

    A self-dual loop quantum black hole is shown to look smaller and brighter than Schwarzschild in thin disk models, with the polymer parameter P bounded by Mercury and S2 star data.

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