  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. ==measurement procedure== 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 geopotential == the earth's gravity field can be described by a potential as follows: : \mathbf{g} = \nabla w = \mathrm{grad}\ w = \frac{\partial w}{\partial x}\mathbf{i} +\frac{\partial w}{\partial y}\mathbf{j}+\frac{\partial w}{\partial z}\mathbf{k} which expresses the gravitational acceleration vector as the gradient of w, the potential of gravity. the vector triad \{\mathbf{i},\mathbf{j},\mathbf{k}\} is the orthonormal set of base vectors in space, pointing along the x,y,z coordinate axes. note that both gravity and its potential contain a contribution from the centrifugal pseudo-force due to the earth's rotation. we can write : w = v + \phi\, where v is the potential of the gravitational field, w that of the gravity field, and \phi that of the centrifugal force field. the centrifugal force is given by : \mathbf{g}_c = \omega^2 \mathbf{p}, where : \mathbf{p} = x\mathbf{i}+y\mathbf{j}+0\cdot\mathbf{k} is the vector pointing to the point considered straight from the earth's rotational axis. it can be shown that this pseudo-force field, in a reference frame co-rotating with the earth, has a potential associated with it that looks like this: : \phi = \frac{1}{2} \omega^2 (x^2+y^2). this can be verified by taking the gradient (\nabla) operator of this expression. here, x, y and z are geocentric coordinates. ==units of gravity and geopotential== gravity is commonly measured in units of mÂ·sâ2 (metres per second squared). this also can be expressed (multiplying by the gravitational constant g in order to change units) as newtons per kilogram of attracted mass. potential is expressed as gravity times distance, m2Â·sâ2. travelling one metre in the direction of a gravity vector of strength 1 mÂ·sâ2 will increase your potential by 1 m2Â·sâ2. again employing g as a multipier, the units can be change
Geodesy Geophysics Gravitation