gravitygradient

Gravity gradient refers to the variation of gravitational acceleration across space. In Newtonian gravity, gravity is the gradient of a scalar potential Φ, and the gravity gradient describes how g = -∇Φ changes with position. The gravity gradient is formalized as a tensor, the gravity gradient tensor T, with components Tij = ∂gi/∂xj, or Tij = -∂^2Φ/∂xi∂xj. In regions with no mass, the trace Txx + Tyy + Tzz equals -∇²Φ, which is zero in vacuum, making the tensor traceless in free space. The diagonal components reflect curvature along principal axes, and the off-diagonal components describe coupling between directions. The gravity gradient is directly related to tidal forces: nearby bodies experience differential gravity due to spatial variations in the field.

Measurement and use of gravity gradients are performed by gravity gradiometers, which sense differential accelerations between test masses. Space missions such as the European Space Agency’s GOCE used a three-axis gravity gradiometer to map Earth's gravity field with high accuracy, enabling detailed geoid models and gravity anomaly maps. Gravity gradients can be derived from satellite tracking data and are incorporated into gravity field models produced by missions like GOCE and GRACE/GRACE-FO.

Applications of gravity gradient data span geodesy, geophysics, and earth science. They improve models of Earth's gravity field, aiding ocean circulation studies, hydrology, and mass-change monitoring. They reveal subsurface density variations, support precise orbit determination for satellites, and inform concepts such as gravity-gradient stabilization in spacecraft design, where the gravitational field induces torques that align extended structures with the local vertical.