  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 $G=G_N(1+\alpha)$, where
$G_N$ is Newton's constant, and the massive (spin-1 graviton) vector field
$\phi_\mu$. 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 $G=G_N(1+\alpha)$ and the effective running
mass $\mu$. The magnitude of $\alpha$ depends on the physical length scale or
averaging scale $\ell$ 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.
