标题： 牛顿万有引力常数是否随时间作正弦变化？ 轨道运动给出了否定的答案。 显示英文标题

标题： Does the Newton's gravitational constant vary sinusoidally with time? Orbital motions say no

摘要： 近年来，文献中报道了在地球实验室中测量的引力常数 $G$ 值随时间呈现正弦变化的模式。我们检验了上述谐波变化可能直接且独立地与 $G$ 本身相关的假设。通过数值积分太阳系主要天体的特殊修改的动力学方程，我们发现行星轨道的改变会由于目前高精度的天文学测量而变得无法接受地大。 对于土星来说，其地心赤经$\alpha$、赤纬$\delta$和距离$\rho$将分别受到影响，最大达到$10^4-10^5$毫角秒和$10^5$公里；如今这些可观测量的残差小至约$4$毫角秒和$10^{-1}$公里。 \textcolor{black}\{我们解析计算了由假设的 $G$ 谐波变化引起的长期轨道效应，发现测试粒子的半长轴 $a$、偏心率 $e$ 和近拱点辐角 $\omega$ 的变化率非零。\} 对于LAGEOS卫星，预测的轨道半径增加量高达 $3.9$ 米每年 $^{-1}$，与观测到的衰减 $-0.203\pm 0.035$ m yr$^{-1}$ 形成对比。 土星的近日点进动异常值可达每世纪14弧秒，而最新的观测将其限制在 $10^{-4}$ 弧秒每世纪的水平。 水星提供的拒绝水平同量级。 显示英文摘要

摘要： A sinusoidally time-varying pattern of the values of the Newton's constant of gravitation $G$ measured in Earth-based laboratories over the latest decades has been recently reported in the literature. We put to the test the hypothesis that the aforementioned harmonic variation may pertain $G$ itself in a direct and independent way. We numerically integrated the ad-hoc modified equations of motion of the major bodies of the Solar System by finding that the orbits of the planets would be altered by an unacceptably larger amount in view of the present-day high accuracy astrometric measurements. In the case of Saturn, its geocentric right ascension $\alpha$, declination $\delta$ and range $\rho$ would be affected up to $10^4-10^5$ milliarcseconds and $10^5$ km, respectively; the present-day residuals of such observables are as little as about $4$ milliarcseconds and $10^{-1}$ km, respectively. \textcolor{black}{We analytically calculated the long-term orbital effects induced by the putative harmonic variation of $G$ at hand finding non-zero rates of change for the semimajor axis $a$, the eccentricity $e$ and the argument of pericenter $\omega$ of a test particle. For the LAGEOS satellite, an orbital increase as large as $3.9$ m yr$^{-1}$ is predicted, in contrast with the observed decay of $-0.203\pm 0.035$ m yr$^{-1}$. An anomalous perihelion precession as large as 14 arcseconds per century is implied for Saturn, while latest observations constrain it down to the $10^{-4}$ arcseconds per century level. The rejection level provided by Mercury is of the same order of magnitude.