2008/07/25 by Ka Hall, Hall, Ka
Physics and Astronomy · #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #History and Developments in Astronomy #Relativity and Gravitational Theory #gr-qc
paper · pdf · doi:10.48550/arxiv.0807.4109
7 pages, 0 figures
openalex publication_date 2008/07/25 · arxiv created 2008/07/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Exact results are derived, specifically the perihelion shift and the Kepler orbit, for a bound test particle in the Schwarzschild metric with cosmological constant Λ=0. A series expansion, of Δϕ= 2(2(1-2M/p(3-e))-1/2 K((4eM/p)/(1-2M/p(3-e)))-π), the exact perihelion shift, admits the standard approximation Δϕ=6Mπ/p as the leading order term. In a similar fashion, a series expansion of the exact Kepler orbit, represented by a Jacobi elliptic function, gives u(ϕ)=(1+ecosϕ)/p to first order. The results are valid for M/p<1/(2(3+e)) or rs<p/(3+e).