 Corotating point-mass tidal field

Use local axes radial, tangential in the orbital plane, and perpendicular to that plane around a circular Kepler orbit with ${\Omega }^2=GM/R^3$. The gravitational tidal tensor is ${\Omega }^2\mathrm{diag}(2,-1,-1)$. A uniformly corotating frame adds the gradient of centrifugal acceleration, ${\Omega }^2\mathrm{diag}(1,1,0)$, giving the displayed effective tensor for stationary offsets. Thus the radial differential acceleration is $3GMa/R^3$. These are accelerations, or forces per unit test mass; an actual differential force includes that mass. Moving offsets also experience Coriolis acceleration.