Astronomical-Gravimetric Leveling

a method of determining the altitudes ζ of auxiliary surfaces of a quasi-geoid or a geoid above a reference ellipsoid. It was developed by M. S. Molodenskii in 1937. The altitude ζ together with the normal or orthometric altitude determines the altitude of the corresponding point of the earth’s surface over the reference ellipsoid. Astronomical-gravimetric leveling is used for projecting an astronomical and geodetic network on an ellipsoid, transferring the altitudes ζ from the astronomical point P to the astronomical point Q. For the reference point, the altitude ζ is determined in advance.

In order to accomplish astronomical-gravimetric leveling of the quasi-geoid’s altitude, the astronomical latitude and longitude, the geodetic latitude and longitude of points P and Q, and the gravimetric survey of their surroundings must be known. In using orthometric altitudes and astronomical-gravimetric leveling of geoid altitudes, additional data on the density distribution within the earth is necessary. If only astronomical-geodetic data are used in determining ζ, then the process would simply be astronomical leveling, as proposed by the French scientist Y. Villarseau in 1871. Astronomical leveling requires such a density of astronomical points as to make possible a linear interpolation of the deflections from the vertical.