Gravity field

Physical geodesy is the study of the physical properties of the gravity field of the Earth, the geopotential, with a view to their application in geodesy.

Traditional geodetic instruments such as theodolites rely on the gravity field for orienting their vertical axis along the local plumb line or local vertical direction with the aid of a spirit level. After that, vertical angles (zenith angles or, alternatively, elevation angles) are obtained with respect to this local vertical, and horizontal angles in the plane of the local horizon, perpendicular to the vertical.

Levelling instruments again are used to obtain geopotential differences between points on the Earth's surface. These can then be expressed as "height" differences by conversion to metric units.

The Earth's gravity field can be described by a potential as follows:

which expresses the gravitational acceleration vector as the gradient of ${\displaystyle W}$, the potential of gravity. The vector triad ${\displaystyle \{\mathbf {i} ,\mathbf {j} ,\mathbf {k} \}}$ is the orthonormal set of base vectors in space, pointing along the ${\displaystyle X,Y,Z}$ coordinate axes.

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