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arXiv 0807.4109gr-qc
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广义相对论中开普勒问题的精确结果

Exact Results for the Kepler Problem in General Relativity

Ka Hall

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7 pages, 0 figures
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摘要：

精确的结果，特别是近日点位移和开普勒轨道，在史瓦西度规与宇宙学常数$Λ=0$的约束测试粒子。$Δϕ= 2(2(1-2M/p(3-e))^{-1/2} K((4eM/p)/(1-2M/p(3-e)))-π)$的一个级数展开式，即精确近日点位移，允许标准近似$Δϕ=6Mπ/p$作为首阶项。以类似的方式，用雅可比椭圆函数表示的精确开普勒轨道的级数展开给出了一阶的$u(ϕ)=(1+e\cosϕ)/p$。结果对$M/p<1/(2(3+e))$或$r_s<p/(3+e)$有效。

英文摘要：

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 $r_s<p/(3+e)$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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