History of geodetic measurement. Description of the geodetic model of the earth. Relationship between the ellipsoid, geoid, and earth’s surface. Measurement of long baselines. Gravity and the geoid. Relationship between terrestrial observations and grid coordinates.

1. Geodetic Reference Systems
Week 6
Lecture 1

2. Coordinate Systems
• Means of expressing point positions with
respect to the ellipsoid
• Origin, orientation of axes, and triplet
values are required
• Curvilinear or Cartesian (rectangular)

3. 3D Coordinate Systems
1. Geodetic Coordinates φ,λ,h – Curvilinear
2. Geocentric Coordinates X,Y,Z – Cartesian
3. Local Geodetic Coordinates e,n,u -
Cartesian

4. C
X
Y
Z

5. 3. Local Geodetic Coordinate System
• Origin and Axes:
– Origin at a local point φ, λ, h
– u-axis points up along the normal
– e and n axes point to east and north in the
local tangential plane
• Cartesian (Rectangular) Coordinates:
– e, n, u

6. Azimuth, Zenith Angle, Slant Range
• Local Geodetic coordinate system can be
defined at each instrument (e.g. total station)
setup
• Geodetic Azimuth, α
• Vertical (altitude) angle, v
• Zenith angle, z
• Slant range, r

8. Datums and
Spheroids

9. The Earth’s Shape and Size
©2008 Austin Troy
• Only recently have we known both
• Estimates of shape by the ancients
have ranged from a flat disk, to a
cube to a cylinder to an oyster.
• Pythagoras was the first to postulate
it was a sphere
• By the 5th century BCE, this was
firmly established.
• But how big was it?

10. The Earth’s Size
©2008 Austin Troy
Posidonius used the stars to
determine the earth's
circumference. He observed
that the star Canopus could
be seen just on the horizon at
Rhodes (Greece) but
appeared above the horizon
when viewed from Alexandria,
Egypt (1st century BCE).
-source: ESRI

11. Spheroids
©2008 Austin Troy
•Note how two different spheroids have slightly
different major and minor axis lengths
Source: ESRI

12. Surface Based Datums
©2008 Austin Troy
•NAD27 resulted in lat/long coordinates for about
26,000 survey points in the US and Canada.
•Limitation: requires line of
sight, so many survey points
were required
•Problem: errors compound
with distance from the initial
reference. This is why central
location needed for first point

13. Datum Shift
©2008 Austin Troy
• NAD83 is superior to NAD27 because:
• NAD83 is more accurate and NAD27 can result in a
significant horizontal shift
• When we go from a surface-oriented datum to a spheroid-
based datum, the estimated position of survey benchmarks
improves; this is called datum shift
• That shift varies with location: 10 to 100 m in the cont. US,
400 m in Hawaii, 35 m in Vermont
• Click here for an example from Peter Dana

14. Datum Shift Example
©2008 Austin Troy