Reference Ellipsoid and the Geodetic Coordinate System - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 167

5.2 Reference Ellipsoid
5.2.1 Reference Surface for Geodetic Surveying
Computations
Section 4.2 introduced the concept of the Earth ellipsoid. It can also be used as the
reference surface for geodetic surveying computations, which is called the refer-
ence ellipsoid.
Because of the irregularity of the actual shape of the Earth, a regular curved
surface should be selected as the reference surface for the performance of geodetic
computations. Conventional terrestrial surveys can only determine directions, dis-
tances, and astronomical azimuths between points on the Earth's surface, whereas
to obtain coordinates of the horizontal control points, a series of computations need
to be carried out and a reference surface upon which computations are performed is
therefore needed.
The reference surface that fits for the geodetic surveying computations should
satisfy the following three conditions:
1. The reference surface should be a curved surface that approximates the physical
shape of the Earth, so that the corrections for reduction of the terrestrial
observations are small.
2. The curved surface should be a mathematical surface on which computations are
easily performed so as to assure the possibility of calculating coordinates
through observational quantities.
3. The positions of the curved surface relative to the geoid should be fixed so as to
establish the one-to-one correspondence between the points on the Earth's
surface and those on the reference surface.
We know that an oblate ellipsoid of rotation approximates the geoid with a bulge
at the equator and flattening at the North and South Poles. In fact, precise observa-
tions have shown that the North Pole bulges out by 16 m and the South Pole is
depressed by approximately 16 m when the geoid is compared with a properly
defined ellipsoid (cf. Fig. 5.4 ). The Earth is thus claimed to be “pear-shaped,” which
is somewhat exaggerated. This slight difference, however, compared to the differ-
ence of 21.4 km between the Earth's equatorial radius and the polar radius is
insignificant.
The intersection line between the geoid and the equatorial plane is not a perfect
circle, but more closely approximates an ellipsoid. The major axis of the ellipsoid
on the equator is at 15 west longitude. The difference between the semimajor axis
(equatorial radius) and the semiminor axis (polar radius) is 69.5 m. The equatorial
flattening is 1:91,827, which is approximately one three-hundredth of the polar
flattening (cf. Fig. 5.5 ).
As a result, the “pear-shaped” sphere or the triaxial ellipsoid is a mathematical
surface that is an approximation to the true shape of the Earth. However, it will be