Investigation of secular increase in astronomical unit in terms of verification of gravitational theories

我们研究了Krasinsky和Brumberg从行星雷达和航天器轨道跟踪数据中报告的天文单位的长期增加，从引力理论的验证来看，15+/-4米/世纪。为此，我们导出了描述太阳系暗物质密度随时间变化的爱因斯坦场方程的近似度规，(B)给出了利用基于Synge世界函数的时间传递函数计算含时引力场中光/信号传输的方法，(C)我们得到了非齐次LTB模型所产生的微扰力，并评价了它对行星运动的影响，以及(D)基于轨道角动量守恒定律，我们提出了解决天文单位长期增加的新方案。

We investigated the secular increase in astronomical unit reported by Krasinsky and Brumberg from the planetary radar and spacecraft orbital tracking data, 15 +/- 4 m/century in terms of verification of gravitational theories. For this purpose, (a) we derived the approximate metric of Einstein's field equation which can describe the time variation of dark matter density in solar system, (b) we showed the method which can calculate the light/signal propagation in the time-dependent gravitational field by using the time transfer function based on Synge's world function, (c) we obtained the perturbation force due to inhomogeneous LTB model, and evaluated its effect on the planetary motion, and (d) based on the orbital angular momentum conservational law, we proposed new scenario to resolve the secular increase in astronomical unit.