Introduction - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 14

higher latitudes is longer than that at lower latitudes. Kangxi also decided to
determine the length of “Li” by setting the meridional arc length per degree as
200 Li.

Development of Geometric Geodesy

From the nineteenth century, many countries had started national astro-geodetic
surveying, aimed at determining the size of the Earth ellipsoid, and, more impor-
tantly, providing accurate geometric positions of numerous surface points for
national topographic mapping. To serve this purpose, a series of theoretical and
technical problems had to be solved, which promoted the development of geometric
geodesy. First, in order to test the abundant observational data from astro-geodetic
surveying and eliminate their contradictions, on the basis of which to determine the
most reliable result and assess observation accuracy, A.M. Legendre from France
first published the theory of the least squares method in 1806. In fact, early in 1794,
the German mathematician and geodesist C.F. Gauss had already used this theory to
derive the asteroid orbit. Later, Gauss dealt with astro-geodetic survey results by the
method of least squares and improved the method considerably, bringing about the
adjustment of the observation method that is widely used in geodesy today and will
be used in the future. Second, both the solution of a spheroidal triangle and the
deduction of geodetic coordinates have to be done on the ellipsoid surface. Gauss
proposed the solution to spheroidal triangles in his Theorema Egregium in 1828.
Many scholars have worked out various formulae regarding deduction of geodetic
coordinates. Gauss also published the conformal projection from the ellipsoid onto
the plane in 1822 (which is why we call it the “Gauss conformal projection”). This
is the best method to convert the geodetic coordinates into plane coordinates and is
still extensively applied today. In addition, in order to use the results from astro-
geodetic surveying to calculate the semimajor axis and the flattening of the Earth
ellipsoid, F.R. Helmert from Germany proposed a method for solving the fittest
ellipsoid parameters for the geoid of the survey area under the condition that the
sum of squares of the vertical deflection of all astronomical points is the least in an
astro-geodetic network. This method was later called the “area method.”

Development of Physical Geodesy

Since Clairaut published Th ´orie de la figure de la Terre in 1743, the most
important development in physical geodesy has been the Stokes theorem developed
in 1849 by Sir. G.G. Stokes from the UK. According to this theorem, the shape of
the geoid can be studied by terrestrial gravimetric results. However, the theorem
first required reduction of the ground gravimetric results to the geoid, which was
rather challenging. In spite of that, Stokes' theorem still promoted research on the
geoid shape. About 100 years later in 1945, Mikhail Sergeevich Molodensky
(

Михаи л Сергеевич Мо л оденский ) from the former Soviet Union advanced