2007/02/02 by Gregory S. Adkins, Jordan McDonnell · 1 citation
Physics and Astronomy · #gr-qc
paper · pdf · doi:10.1103/physrevd.75.082001
published as Phys.Rev.D75:082001,2007 · 10 pages, 1 figure
arxiv created 2007/02/02 · arxiv updated 2009/12/01
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) = αrn and V(r) = αln(r/λ) in terms of the hypergeometric function 2F1 (1/2-n/2,1-n/2; 2; e2), 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.