Exact Results for the Kepler Problem in General Relativity
| dc.creator | Hall, Ka | |
| dc.date | 2008-07-25 | |
| dc.date | 2008-07-27 | |
| dc.date.accessioned | 2026-07-07T09:52:57Z | |
| dc.date.available | 2026-07-07T09:52:57Z | |
| dc.description | 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 $u(ϕ)=(1+e\cosϕ)/p$ to first order. The results are valid for $M/p<1/(2(3+e))$ or $r_s<p/(3+e)$. | |
| dc.description | 7 pages, 0 figures | |
| dc.identifier | https://arxiv.org/abs/0807.4109 | |
| dc.identifier | http://arxiv.org/abs/0807.4109 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/165778 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | Exact Results for the Kepler Problem in General Relativity | |
| dc.type | text |