1. Geography 370 Locating Positions on the Earth
The size and shape of the Earth
(Ellipsoid, Geoid, Latitude/longitude)
Datum
Map projection

2. So the Earth is Round, Right?
So everyone knows the Earth is round, even Columbus. Case closed right?
Not exactly, the earth isn’t perfectly round either. What shape is it?

3. Eratosthenes (276-196 B.C.) Measured the circumference of the earth.
His measurement: 40,250 km
Modern Measurement: 38,762 km
Era-tos-thenes
He had heard of a well in Syene (near modern Aswan Egypt - Tropic of Cancer) where the sun’s reflection could be seen in the water at noon on June The sun was directly overhead. At the exact moment the sun could be seen in the well he measured the height of an obelisk in Alexandria. Then using some basic geometry he was then able to calculate the circumference of the earth by creating a triangle between Alexandria, Syene and the Sun.
He got pretty close…

4. Eratosthenes

5. Size and shape of the Earth
17th and 18th centuries
The Earth’s shape
A Spheroid
An Ellipsoid

7. f = (r1-r2)/r1
r2=1
r2=1
r1=2
r1=1
Flatten factor?

9. The Earth as an Ellipsoid
Here are some other commonly used ellipsoids. You don’t need to memorize any of this.
Just keep in mind the term reference ellipsoid. That’s what an ellipsoid is used for… reference. It’s a starting point to calculating a position on the earth.

10. Why not use the same ellipsoid?
Earth’s true shape diverges from the shape of an ellipsoid
Ellipsoidal parameters were fit for each continent or large survey area
Different sets of measurements in each region or continent

11. Globally applicable ellipsoids
WGS72
WGS84
GRS80
Continuing measurements from satellite and GPS may lead to further ellipsoid refinements.

12. The Earth as Geoid
But the earth is not completely uniform. So we can use a geoid to model the earth’s surface instead of an ellipsoid.
And surveyors DO use the geoid to make precise locational calculations. But for our purposes, and for most purposes in GIS, we don’t use the geoid. It’s too complex.
Instead, we use an ellipsoidal model.

14. The Earth as a Geoid
Geoid -- The surface on which gravity is the same as its strength at mean sea level
The surface that would exist if the sea
was admitted under the land portion of the earth by small
frictionless channels.

15. Earth Surfaces
The topographical surface of the earth is the actual surface of the land and sea at some moment in time.
Gravity models attempt to describe in detail the variations in the gravity field. Local variations in gravity, caused by variations in the earth's core and surface materials, cause this gravity surface to be irregular.
notes/datum/datum_f.html

16. Reference for elevation:
Ellipsoid
Geoid
Local sea level

17. Spatial Location and Reference: Latitude / Longitude
Most commonly-used coordinate system
Lines of latitude are called parallels
Lines of longitude are called meridians
Parallels parallel to each other; circle the globe ew
Max value of angular measurement N and S from the equator: 90 degrees
Meridians: perpendicular to parallels
Prime meridian: Greenwich, England
Meridians run 180 degrees E and W of the prime meridian (until reach International Date Line)

18. Latitude / Longitude
Prime Meridian & Equator are the reference points used to define latitude and longitude

20. Determine distance between any pair of points
Great circle

21. Geodetic Datum
Datum -- n. (dat - m) \ any numerical or geometric quantity which serves as a reference or base for other quantities e
Horizontal datum
Vertical datum
So we have datums. Now, I said we need a simpler way, and simple is a relative term. Datums are complex models in and of themselves. But the key to the Geodetic Datum is that it provides a link between locations on the sphere ellipsoid and geoid.
For instance in economics if you want to calculate price indicies you use a base year (1960) that’s an example of datum.

22. Geodetic Control Networks
Surveyors use these known points in the control networks for surveys and mapping.

25. Geodetic Control Network
Over 800,000 points in the U.S.
Sundial -- EZ1375
Keep your eyes out for others as you walk around campus.

26. Three main horizontal datums
North American Datum of 1927 (NAD27)
26,000 survey stations in United States and Canada.
North American Datum of 1983 (NAD83)
250,000 stations and 2,000,000 distance measures
World Geodetic System of 1984 (WGS84)
(updated based on satellite measurements)

27. Ellipsoids & Datums: Importance
Differences exist between different ellipsoids & datums
Coordinates different in each  can be significant distance
Elevation  can be major differences at large scales
Note: Be aware of the ellipsoid & datum for datasets you are working with