Wide binary stars are used to test the modified gravity called Scalar-Tensor-Vector Gravity or MOG. This theory is based on the additional gravitational degrees of freedom, the scalar field G = G_N (1+α), where G_N is Newton's constant, and the massive (spin-1 graviton) vector field ϕ_μ . The wide binaries have separations of 2–30 kAU. The MOG acceleration law, derived from the MOG field equations and equations of motion of a massive test particle for weak gravitational fields, depends on the enhanced gravitational constant G = G_N (1+α) and the effective running mass μ. The magnitude of α depends on the physical length scale or averaging scale ℓ of the system. The modified MOG acceleration law for weak gravitational fields predicts that for the solar system and for the wide binary star systems gravitational dynamics follows Newton's law.

中文翻译：

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宽双星和修正重力（MOG）


宽双星用于测试称为标量张量矢量重力或 MOG 的修正重力。该理论基于附加引力自由度、标量场 G = G _N (1+α)，其中 G _N 是牛顿常数，而质量（自旋1 引力子）矢量场 phi _μ 。宽双星的间隔为 2-30 kAU。 MOG 加速定律由 MOG 场方程和弱引力场大质量测试粒子的运动方程导出，取决于增强引力常数 G = G _N (1+α) 和有效运行质量μ。 α 的大小取决于系统的物理长度尺度或平均尺度 ℓ。针对弱引力场的修正 MOG 加速定律预测，对于太阳系和宽双星系统，引力动力学遵循牛顿定律。