Despite the certainty of the physical surface of the Earth, it remains notoriously difficult to define in mathematical terms. The dilemma is illustrated by the ancient struggle to represent its curved surface on flat maps. There have been a whole variety of map projections developed over the centuries that rely on mathematical relationships between positions on the Earth's surface and points on the map. Each projection serves a particular application well, but none of them can represent the Earth without distortion.
As the technology of measurement has improved, the pressure for greater exactness in the definition of the Earth's shape has increased.
Plane surveying has traditionally relied on an imaginary flat reference surface, or reference frame (datum), with Cartesian axes. This rectangular system is used to describe measured positions by ordered pairs, usually expressed in northings and eastings, or y- and x- coordinates. Even though we have always known that this assumption of a flat earth is fundamentally unrealistic, it provided, and continues to provide, an adequate arrangement for small areas. The attachment of elevations to such horizontal coordinates somewhat acknowledges the topographic irregularity of the earth, but the whole system is always undone by its inherent inaccuracy as the area grow large. Even with electronic tools that widen the scope and increase the precision of the data, perfection is nowhere in sight.
The next lesson concerns some of the elements of the systems we inevitably use to accommodate the vagaries of assigning coordinates to the results of an earth-centered-earth-fixed positioning system based on signals from satellites.
At the successful completion of this lesson, students should be able to:
- demonstrate understanding of the basics of geodetic coordinates;
- describe a few pertinent ideas about geodetic datums;
- describe plane surveying;
- recognize the structure of some geodetic coordinate systems;
- define the elements of a geodetic datum;
- discuss the geoid; and
- explain the North American Datum 1983.
If you have any questions now or at any point during this week, please feel free to post them to the Lesson 5 Discussion Forum. (To access the forum, return to Canvas and navigate to the Lesson 5 Discussion Forum in the Lesson 5 module.) While you are there, feel free to post your own responses if you, too, are able to help out a classmate.