Quadrupolar point-mass tidal potential
= Quadrupolar point-mass tidal potential
{title2=$\psi_{\mathrm{tid}}=\tfrac12r_iT_{ij}r_j$}
Subtracting the constant and uniform-acceleration terms from the point-mass <relative potential> gives $\psi_{\mathrm{tid}}=Gm_p[3(\mathbf r\cdot\widehat{\mathbf r}_p)^2-r^2]/(2r_p^3)$, with force convention $\nabla\psi$. Its <tidal tensor> is $Gm_p(3\widehat{\mathbf r}_p\widehat{\mathbf r}_p^T-I)/r_p^3$. This is the leading term for target size small compared with separation.