The distinction between the mean anomaly $\mathcal{M}(t)$ and the mean anomaly at epoch $η$, and the mean longitude $l(t)$ and the mean longitude at epoch $ε$ is clarified in the context of a possible use of such orbital elements in post-Keplerian tests of gravity, both Newtonian and post-Newtonian. In particular, the perturbations induced on $\mathcal{M}(t),\,η,\,l(t),\,ε$ by the post-Newtonian Schwarzschild and Lense-Thirring fields, and the classical accelerations due to the atmospheric drag and the oblateness $J_2$ of the central body are calculated for an arbitrary orbital configuration of the test particle and a general orientation of the primary's spin axis $\boldsymbol{\hat{S}}$. They provide us with further observables which could be fruitfully used, e.g., in better characterizing astrophysical binary systems and in more accurate satellite-based tests around major bodies of the Solar System. Some erroneous and misleading claims by Ciufolini and Pavlis appeared in the literature are confuted. In particular, it is shown that there are no net perturbations of the Lense-Thirring acceleration on either the semimajor axis $a$ and the mean motion $n_\mathrm{b}$. Furthermore, the quadratic signatures on $\mathcal{M}(t)$ and $l(t)$ due to certain disturbing non-gravitational accelerations like the atmospheric drag can be effectively disentangled from the post-Newtonian linear trends of interest provided that a sufficiently extended temporal interval for the data analysis is assumed. A possible use of $η$ along with the longitudes of the ascending node $Ω$ in tests of general relativity with the existing LAGEOS and LAGEOS II satellites is suggested.
A flyby anomaly for Juno? Not from standard physics
最近在文献中出现了一个经验公式，用来解释伽利略、NEAR和罗塞塔航天器在其过去沿非束缚双曲线轨道通过近地点时，在地心距离率$\dotρ$中观测到的约为$Δ\dotρ\approx 1-10$ mm s $^{-1}$的异常。它预测了2013年10月9日发生的朱诺号最近飞越的$6$ mm s $^{-1}$数量级的异常。目前正在进行数据分析，以证实或反驳这一点。我们数值计算的一些经典的和广义相对论的动力学效应，这是未建模或错误建模到一定程度的软件中用于处理数据的地心朱诺的范围率的影响。它们是：a）地球引力势多极展开的第一偶纬向谐波系数$J_2$，它在$\left.{\rm a}^{'}\right)$牛顿（$J_2$）和$\left. {\rm a}^{''}\right)$第一后牛顿水平（$J_2 c^{-2}$）引起轨道扰动b）地球引力场的后牛顿引力电（GE）类史瓦西分量c）后牛顿引力磁（GM）透镜-瑟林效应。它们的错误建模和标称距离变化率特征的幅度为：$\left. {\rm a}^{'}\right)$ $Δ\dotρ_{σ_{J_2}} \approx 1$ $μ$ m s $^{-1}$ $\left. {\rm a}^{''}\right)$ $Δ\dotρ_{J_2 c^{-2}} \approx 0.015$ $μ$ m s $^{-1}$ b）$Δ\dotρ_{\…
Measurements of the Low-Acceleration Gravitational Anomaly from the Normalized Velocity Profile of Gaia Wide Binary Stars and Statistical Testing of Newtonian and Milgromian Theories
提出基于 Gaia 宽双星归一化速度剖面的 Monte Carlo 检验方法，测得低加速度区引力增强因子 1.37，并在 5.8σ 上排除牛顿引力而支持 Milgrom AQUAL。
Jupiter, Saturn and the Pioneer anomaly: a planetary-based independent test
在本文中，我们使用对木星和土星近日点的标准牛顿/爱因斯坦长期岁差的修正比率，最近由俄罗斯天文学家E. V. Pitjeva通过将近一个世纪的数据与天文历表拟合来估计，对先锋异常（PA）的假设进行独立的，基于行星的测试，因为它目前已知在5-10 AU区域，是引力的起源考虑到确定的拱线额外率和木星和土星轨道上PA加速度值的误差，答案是否定的。如果对整个先锋10/11的重新分析完成，就可以得出更确切的结论。此外，其他天文学家团队独立估计他们自己对近日点岁差的修正也很重要。
Solar System tests of some models of modified gravity proposed to explain galactic rotation curves without dark matter
考虑最近估计的太阳系几颗行星近日点\varpi的牛顿/爱因斯坦长期岁差的修正Δ \dot \varpi，以评价它们是否与长期修正引力模型所预测的岁差相一致，该模型是为了解释星系自转曲线的某些特征而提出的，而不诉诸于暗物质。特别地，我们考虑了牛顿引力势的一个牛顿型修正和一个f（R）启发的幂律修正。通过对不同行星对的拱点率的比值得到的结果表明，本文所研究的牛顿势的修改与E. V. Pitjeva估计的太阳系行星近日点的长期额外岁差是不相容的，作为解决参数处理近一个世纪的数据与最新的星历。
Can the Pioneer anomaly be induced by velocity-dependent forces? Tests in the outer regions of solar system with planetary dynamics
本文分析了最近提出的一些速度相关力对太阳系外行星（从木星到冥王星）轨道运动的影响，并将他们的预测（近日点\varpi或半长轴a的经度和偏心率e的长期变化）与E. V. Pitjeva使用EPM 2006星历表进行的最新观测测定相比较。事实证明，虽然预测的a百年位移是如此之大，以至于除了海王星之外，所有行星都可以很容易地检测到，但预测的\varpi异常岁差太小了，除了木星之外，所以它们仍然与标准牛顿-爱因斯坦近日点岁差的估计修正相一致。因此，我们倾向于放弃那些预测a和e长期变化的额外力，也是出于其他一些原因，而给那些预测仍然无法检测到近日点岁差的模型一个机会，至少在观测上是这样。当然，必须为它们找到充分的理论基础。
Post-Newtonian secular dynamics of hierarchical triples. I. Eccentricity-, inclination- and node-dependence of the multiple-scale formulation, and its canonical consistency
Revisiting Data Quality Control and Multiple-star Modeling in Wide Binary Gravity Tests: Confirmation of MOND-type Gravitational Anomaly at Low Acceleration
Detection of Gravitational Anomaly at Low Acceleration from a Highest-quality Sample of 36 Wide Binaries with Accurate 3D Velocities
Sejong University（世宗大学）；Korea Astronomy and Space Science Institute（韩国天文与空间科学研究所）；Universidad Nacional Autónoma de México, Instituto de Astronomía（墨西哥国立自治大学天文研究所）；Yonsei University（延世大学）；University of Pittsburgh（匹兹堡大学）
