轨道运动对G空间各向异性的观测约束
Observational constraints on spatial anisotropy of G from orbital motions
摘要：
牛顿引力耦合参数G的唯象各向异性变化ΔG/G，如果是真的，将以特定的方式影响引力束缚两体系统的轨道动力学.我们分析了长期的影响，这种假定的修改通常的牛顿平方反比定律将引起的轨道上的测试粒子绕中心质量。在不对测试粒子的轨道构型作任何先验简化假设的情况下，结果表明，它的密切半长轴a、偏心率e、近心\varpi和平均异常M经历长期的时间变化，而倾角I和节点Ω不受影响。此外，测试粒子的位置和速度矢量r和v的径向和横向分量经历每个轨道的非零变化，与平面外的变化相反。然后，我们通过将G（r）的梯度定向到银河系中心，并在所涉及的特征时间尺度上保持固定，来计算我们对太阳系一些主要天体的理论预测。通过将我们的计算结果与最新的观测结果进行比较，我们推断在大约1个天文单位内ΔG/G <= 10^-17。最后，我们还考虑了位于Sgr A^* 银河系中心的超大质量黑洞，主序星S2围绕它运行了大约16年，在1 kau的时间内，ΔG/G <= 10^-2。
英文摘要：
A phenomenological anisotropic variation ΔG/G of the Newtonian gravitational coupling parameter G, if real, would affect the orbital dynamics of a two-body gravitationally bound system in a specific way. We analytically work out the long-term effects that such a putative modification of the usual Newtonian inverse-square law would induce on the trajectory of a test particle orbiting a central mass. Without making any a-priori simplifying assumptions concerning the orbital configuration of the test particle, it turns out that its osculating semi-major axis a, eccentricity e, pericenter \varpi and mean anomaly M undergo long-term temporal variations, while the inclination I and the node Ωare left unaffected. Moreover, the radial and the transverse components of the position and the velocity vectors r and v of the test particle experience non-vanishing changes per orbit, contrary to the out-of-plane ones. Then, we compute our theoretical predictions for some of the major bodies of the solar system by orienting the gradient of G(r) towards the Galactic Center and keeping it fixed over the characteristic timescales involved. By comparing our calculation to the latest observational determinations for the same bodies, we infer ΔG/G <= 10^-17 over about 1 au. Finally, we consider also the Supermassive Black Hole hosted by the Galactic Center in Sgr A^* and the main sequence star S2 orbiting it in about 16 yr, obtaining just ΔG/G <= 10^-2 over 1 kau.
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