🎬Clarifying the Contributions of the Tidal Tensor Components

The familiar tidal deformation (stretching along the radial axis and compressing laterally) is achieved through the superposition of two independent forces. One force, arising from the Radial/Shearing Term ( $\propto x^i x^j$), drives the strong elongation and separation of particles along the line connecting the cluster to the massive body. The second force, arising from the Isotropic Compression Term ( $\propto \delta_{i j}$), causes a baseline, uniform inward squeeze due to the natural convergence of gravitational field lines. Isolating these two terms confirms that the complex tidal effect is the mathematical summation of these two simpler, physically distinct actions.

Derivation and Calculation of the Gravitational Tidal Tensor | Proof and Derivationviadean on Notion