Historical  method of determining the ellipsoid  Assume the astronomic latitudes of two endpoints, φs (standpoint) and φf (forepoint), are precisely determined by astrogeodesy, observing the zenith distances of sufficient numbers of stars (meridian altitude method). The radius of curvature at the midpoint of the meridian arc can then be calculated from: R = Δ'/(|φs-φf|). where Δ' is the arc length on mean sea level (MSL). High precision land surveys can be used to determine the distance between two places at nearly the same longitude by measuring a baseline and a triangulation network  . The meridian distance Δ from one end point to a fictitious point at the same latitude as the second end point is then calculated by trigonometry. The surface distance Δ is reduced to the corresponding distance at MSL, Δ'. A second meridian arc will allow the derivation of two parameters required to specify a reference ellipsoid. Longer arcs with intermediate latitude determinations can completely determine the ellipsoid that best fits the suveyed region. In practice, multiple arc measurements are used to determine the ellipsoid parameters by the method of least squares adjustment. The parameters determined are usually the semi-major axis, , and either the semi-minor axis, , or the flattening, . Geodesy  no longer uses simple meridian arcs , but complex control networks with hundreds of fixed points linked by the methods of satellite geodesy  .
Determination Arc measurement is the historical method of determining the ellipsoid . Assume the astronomic latitudes of two endpoints, φs (standpoint) and φf (forepoint), are precisely determined by astrogeodesy, observing the zenith distances of sufficient numbers of stars (meridian altitude method). The radius of curvature at the midpoint of the meridian arc can then be calculated from: R = Δ'/(|φs-φf|). where Δ' is the arc length on mean sea level (MSL). High precision land surveys can be used to determine the distance between two places at nearly the same longitude by measuring a baseline and a triangulation network linking fixed points . The meridian distance Δ from one end point to a ficticios point at the same latitude as the second end point is then calculated by trigonometry. The surface distance Δ is reduced to the corresponding distance at MSL, Δ'. A second meridian arc will allow the derivation of two parameters required to specify a reference ellipsoid. Longer arcs with intermediate latitude determinations can completely determine the ellipsoid that best fits the surveyed region. In practice, multiple arc measurements are used to determine the ellipsoid parameters by the method of least squares adjustment. The parameters determined are usually the semi-major axis, , and either the semi-minor axis, , or the flattening, . Regional-scale systematic effects observed in the radius of curvature measurements reflect the geoid undulation and the deflection of the vertical, as explored in astrogeodetic leveling. Modern geodesy no longer uses simple meridian arcs or ground triangulation networks, but the methods of satellite geodesy , especially satellite gravimetry .
R
Historical
Determination
A
Arc measurement is the historical
A
.
A
linking fixed points
R
fictitious
ficticios
R
suveyed
surveyed
R
Geodesy
Regional-scale systematic effects observed in the radius of curvature measurements reflect the geoid undulation and the deflection of the vertical, as explored in astrogeodetic leveling.
A
Modern geodesy
R
, but complex control networks with hundreds of fixed points linked by
or ground triangulation networks, but
A
, especially satellite gravimetry