In general, geodetic science works with the shape and size of the earth, and point positioning.  (Geodesy also deals with the earth’s gravity, which will not be discussed here.)  More specifically for our purposes working with the PLSS, geodesy uses coordinate systems such as latitudes and longitudes to describe locations on the surface of the earth.  And this, then, depends upon the shape of the earth.

Shape
While it is commonly thought that the earth is a sphere, it is actually an irregular object closer in shape to an ellipsoid (a three dimensional ellipse).  The earth is like a sphere somewhat flattened at the top and bottom. The earth is flattened at the poles by about twenty kilometers off of what would make a true sphere.  Consequently, we need to use ellipsoid shaped earth models for accurate distance and direction calculations over long distances.  Ellipsoid models applied to specific locations on the earth are known as datums.

World Geodetic System 1984 (WGS 84) defines an ellipsoid widely accepted as the best fit for the overall shape of the Earth.  Latitudes and longitudes can differ by several hundred meters for the same point on the earth's surface depending on whether you use WGS 84 or another geodetic datum.  There are over 240 other geodetic datums currently in use around the world.  Worthy of special note is the fact that referencing geodetic coordinates to the wrong datum can result in position errors of hundreds of meters.

In geodesy, you will also hear talk about the geoid.  Generally speaking, the geoid is the undisturbed water surface, or its extension into the land areas, of the equipotential surface of the earth.  Because of the mass excesses and deficiencies with the earth, the shape of the geoid is irregular and can be determined only approximately.  Like the physical surface, the geoid is unsuitable as a mathematical model for computations because it is defined by an infinite number of parameters.

Point Positioning
The geodesy of point positioning is used for accuracy in determining distance and direction from one point to another.  This is actually the essence of the PLSS datum discussed above.

Conventional methods include triangulation, trilateration, or traverse (distances and angles).  Recently with geodesy accuracy becoming obtainable in an economical manner, Global Positioning Systems (GPS) technology is also being used for geodetic point positioning.  If survey boundaries are set based on different datum points, or different geodetic systems, then boundaries between countries, states, or property will not coincide.  Thus there is an important need for geodetic point positioning.

A land survey, then, relies on geodetic datum for control.  Said another way, a land survey must be on a geodetic datum for locational reference on the earth’s surface.

A geodetic coordinate is the horizontal position (latitude/longitude) And vertical position (height above or below the ellipsoid) of a location on the earth.  Because every measurement contains error, when working with a point coordinate value it is essential to know the magnitude of the uncertainty (the error).

Control points are identified locations on the earth which can be used as geodetic reference points.  The reference points can then be used as a basis for surveys.  The National Geodetic Survey has established horizontal control stations which can be used for just this purpose.  The Manual of Surveying Instructions 1973 states that a PLSS surveyor should note the location of the SE corner of a township as it relates to a geodetic control point.  Since 1980, the PLSS surveyor has been required to measure between a geodetic control point and at least one PLSS corner for each survey.
 

Note also, that in addition to being a scientifically based datum, the PLSS datum is also a legal datum, inasmuch as it represents legal survey information used for determining ownership, rights, and uses of land. The GIS Specialist is the one who brings the legal datum into the realm of computer display and analysis, realizing that once represented in the GIS, the data is no longer the actual legal record.  The GIS data is information used for display, analysis, and planning, but not for legal decision and action.  For more on this, see Using Cadastral Data In A GIS, in Part Two.