The Gravitational Tidal Tensor ($T$), derived from the negative second spatial derivatives of the gravitational potential ( $\phi$ ), describes the differential acceleration experienced by two adjacent particles in a gravitational field. This tensor is fundamental to understanding tidal effects, as it relates the change in acceleration (da) linearly to the particle separation vector ($d x$) via $d a^i=T_j^i d x^j$. Notably, the tensor is symmetric and, for a spherical mass distribution, its components $T_j^i= G M\left[\frac{3 x^i x^j}{r^j}-\frac{\delta_{j i}}{r^3}\right]$ reveal the dual nature of tidal forces: the off-diagonal terms are responsible for the shearing and stretching effects lateral to the mass center, while the diagonal terms govern the radial compression and stretching along the line of centers.
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