Newtonian Tidal Stretch Tensor
Turn a gravitational field gradient into stretching and compression and test its linear approximation.
Free theory articleTurn a gravitational field gradient into stretching and compression and test its linear approximation.
Concept & interpretation
The Newtonian tidal tensor describes how gravity varies near a reference point. When an object spans a finite distance in a gravitational field, the varying acceleration across its body produces tidal forces that stretch it radially and compress it transversely.
Exploring the Tidal Forces
Use the interactive model to observe tidal forces across varying radii, offsets, and directions.
- Set the Offset fraction to a small value (e.g., 0.01) to verify that the linear approximation very closely matches the exact difference vector.
- Increase the Offset fraction (e.g., to 0.1) and notice how the exact relative acceleration diverges from the linear approximation, causing a growing linearization error.
- Switch the Direction from Radial to Transverse. Observe that the relative acceleration vector flips its orientation to reflect transverse compression (negative eigenvalue) instead of radial stretching.
- Compare the Radial tidal eigenvalue with the Transverse tidal eigenvalue to see that the stretching force per unit length is twice as strong as the compressional force.