The vertical deflection (VD) or deflection of the vertical (DoV), also known as deflection of the plumb line and astro-geodetic deflection, is a measure of how far the gravity direction at a given point of interest is rotated by local mass anomalies such as nearby mountains. They are widely used in geodesy, for surveying networks and for geophysical purposes. The vertical deflection are the angular components between the true zenith–nadir curve (plumb line) tangent line and the normal vector to the surface of the reference ellipsoid (chosen to approximate the Earth's sea-level surface). VDs are caused by mountains and by underground geological irregularities and can amount to angles of 10″ in flat areas or 20–50″ in mountainous terrain). The deflection of the vertical has a north–south component ξ (xi) and an east–west component η (eta). The value of ξ is the difference between the astronomic latitude and the geodetic latitude (taking north latitudes to be positive and south latitudes to be negative); the latter is usually calculated by geodetic network coordinates. The value of η is the product of cosine of latitude and the difference between the astronomic longitude and the longitude (taking east longitudes to be positive and west longitudes to be negative). When a new mapping datum replaces the old, with new geodetic latitudes and longitudes on a new ellipsoid, the calculated vertical deflections will also change. Determination The deflections reflect the undulation of the geoid and gravity anomalies, for they depend on the gravity field and its inhomogeneities. Vertical deflections are usually determined astronomically. The true zenith is observed astronomically with respect to the stars, and the ellipsoidal zenith (theoretical vertical) by geodetic network computation, which always takes place on a reference ellipsoid. Additionally, the very local variations of the vertical deflection can be computed from gravimetric survey data and by means of digital terrain models (DTM), using a theory originally developed by Vening-Meinesz. VDs are used in astrogeodetic levelling: as a vertical deflection describes the difference between the geoidal and ellipsoidal normal direction, it represents the horizontal spatial gradient of the geoid undulations of the geoid (i.e., the separation between geoid and reference ellipsoid). In practice, the deflections are observed at special points with spacings of 20 or 50 kilometers. The densification is done by a combination of DTM models and areal gravimetry. Precise vertical deflection observations have accuracies of ±0.2″ (on high mountains ±0.5″), calculated