Abstract

To estimate the influence of “dark energy” on Keplerian orbits, we solve the general-relativistic equations of motion of a test particle in the field of a pointlike mass embedded in the cosmological background formed by the cosmological constant with realistic cosmological Robertson–Walker asymptotics at infinity. It is found that under certain relations between three crucial parameters of the problem—the initial radius of the orbit, the Schwarzschild and de Sitter radii—a specific secular perturbation caused by \(\Lambda\)-term becomes significant, i.e., can reach the rate of the standard Hubble flow. This fact is interesting both by itself and may have important consequences for the long-term dynamics of planets and stellar binary systems.

中文翻译：

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扩展宇宙中开普勒轨道的Lambda扰动

摘要

为了估算“暗能量”对开普勒轨道的影响，我们求解了一个点状质量场中被测试粒子运动的广义相对论方程，该点嵌入在由宇宙常数和现实宇宙学罗伯逊-沃克渐近性形成的宇宙背景中的点状质量场中在无穷大。发现在问题的三个关键参数（轨道的初始半径，Schwarzschild和de Sitter半径）之间存在一定的关系时，由\（\ Lambda \）项引起的特定长期扰动变得很明显，即可以达到标准哈勃流量的速率。这个事实本身很有趣，并且可能对行星和恒星二元系统的长期动力学产生重要影响。