Corotating point-mass tidal field (source code)

= Corotating point-mass tidal field
{title2=$T_{\rm eff}=\Omega^2\operatorname{diag}(3,0,-1)$}

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 $\Omega^2\operatorname{diag}(2,-1,-1)$. A uniformly corotating frame adds the gradient of <centrifugal acceleration>, $\Omega^2\operatorname{diag}(1,1,0)$, 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>.