标题： 广义修正引力理论的太阳系检验 显示英文标题

标题： The solar system test for the general modified gravity theories

摘要： 在过去几十年里，提出了各种版本的修正引力理论来模拟暗物质的作用。与传统的牛顿动力学或相对论动力学相比，这些理论在运动方程中包含一些额外的表观力项，以取代暗物质的作用。一般来说，这些额外的表观力项通常随半径变化，因此其效应仅在大尺度上显著，可用于解释星系或星系团中的质量缺失问题。然而，在像太阳系这样的小结构中，这种表观效应仍可能被观测到。本文中，我们推导了分析通用公式，用以表示由于广义修正引力理论导致的太阳系行星进动角度的贡献，其中额外的表观力项可以用半径的幂律（$r$）或指数函数（$r$）形式表达。我们测试了三种流行的修正引力理论：修正牛顿动力学（MOND）、新兴引力（EG）和修正引力（MOG）。特别是，基于太阳系数据，我们约束了MOND中两种常用通用插值函数所涉及的参数。我们的结果可以普遍应用于MOND的修正惯性和修正引力两种版本。 显示英文摘要

摘要： In the past few decades, various versions of modified gravity theories were proposed to mimic the effect of dark matter. Compared with the conventional Newtonian or relativistic dynamics, these theories contain some extra apparent force terms in the dynamical equations to replace the role of dark matter. Generally speaking, the extra apparent force terms usually scale with radius so that the effect would be significant only on large scale to explain the missing mass in galaxies or galaxy clusters. Nevertheless, the apparent effect may still be observable in small structures like the solar system. In this article, we derive analytic general formulae to represent the contribution of the precession angle of the planets in the solar system due to the general modified gravity theories, in which the extra apparent force terms can be written in a power law of radius $r$ or an exponential function in $r$. We have tested three popular modified gravity theories, the Modified Newtonian Dynamics (MOND), the Emergent Gravity (EG), and the Modified Gravity (MOG). In particular, based on the solar system data, we have constrained the parameters involved for two popular general interpolating functions used in MOND. Our results can be generally applied to both of the modified inertia and modified gravity versions of MOND.