2.1 Datums and Coordinates
Learning Objectives
After successfully completing this chapter you should be able to:
- identify and describe the essential elements of ellipse geometry
- differentiate between the ellipsoid and geoid and identify when measurements relate to each of these
- define and compare common horizontal and vertical datums in use today
- outline the history of the development of these datums
- explain the fundamental characteristics of the Australian Height Datum (AHD)
- demonstrate an understanding of the construction and use of geoid models
- apply values from geoid models to attain orthometric heights from GNSS surveying observations.
In the beginning…
A guy looked down a well.
What came next
Eratosthenes was a Greek mathematician, geographer, poet, astronomer and librarian. He was the first known person to calculate the circumference of the Earth, in around 240BC. And he did it all without leaving his home in the city of Alexandria.
Eratosthenes knew that at noon on the summer solstice, in what is now known as Aswan in Egypt, if a person was standing over a well their shadow would block the reflection of the Sun on the water in the well. At the same time in Alexandria, he measured the shadow of a rod on the ground. Using the well-known distance between Aswan and Alexandria (which was surveyed every year) he combined this information with some simple geometry to determine the circumference of the Earth. He didn’t get it exactly right, but given the technology of the day, he did a pretty good job!
Armed with this knowledge, Eratosthenes published a three-volume work called Geographika, and created the science we now know as Geography. Geographika contained the first model of the Earth that was covered with the grid we now recognise as latitude and longitude.
You can watch the NASA video explaining the history and applications of geodesy below.
Video 2.1: Looking down a well – a brief history of geodesy [2 mins, 25 secs]
Note: Closed captions are available by clicking the CC button in the clip below. This video is in the Public Domain.
Due to his enormous contributions to the field, Eratosthenes is often referred to as the Father of Geography.
All because some guy looked down a well.
The field of geodesy
Our understanding of the size and shape of the Earth has become known as geodesy, from the Greek word ge (earth) and daiein (divide).
The Offshore Petroleum Amendment (Datum) Bill defines geodesy as:
“The branch of applied mathematics which determines the shape and area of large tracts of country, the exact position of geographical points, and the curvature, shape, and dimensions of the earth.”
The surface of the Earth is very irregular, so when we measure things on the surface, we need to show them relative to some standard surface. A critical component of geodesy is developing these standard surfaces; mathematical models that represent the size and shape of the earth.
Ellipsoids
In the 17th century, Sir Isaac Newton reasoned t