### Examining Google Earth's Model of the Earth's shape and size.

OBJECTIVE: The primary objective is to apply your critical thinking skills to examine Google Earth's model of the shape and size of the Earth to see (1) whether it fits with models from your readings and lectures and (2) how it measures distances. Secondarily you will gain familiarity with Google Earth controls for measuring coordinates and distances.

Google Earth is an interesting resource for getting a quick image-based geographic overview. It is a modern, web-dependent, high-tech version of the "trusty old" globe, mashed-up with satelite imagery, aerial photographs and vector map data. You will use Google Earth to determine coordinates for several places, the distances between them (measured in meters), and compare those measures to see what they might reveal about the model of the Earth's shape used in this software. In particular, you will be looking to see whether GE uses a spheroid, an oblate spheroid, or a prolate one for its model, and whether it uses that model or its terrain model in calculating distances between points.

(If you do not have access to GE on a computer of your own, we can arrange access via one of the university's computer labs.)

Using Google Earth, it becomes easy to determine and record geographic coordinates, and to measure distances and the lengths of the routes between points. (I hope that you'll enjoy using this tool and will find it helpful this term. Take a little time to become familiar with it.)

Set up and Use Hints.
Tools : options : 3D View tab... Show Lat/Lon as decimal degrees. Show elevation in meters, and distances in meters,.
View : check "Status Bar".

Location of the pointer (hand) is displayed in the Status Bar as decimal degrees of latitude and longitude and meters of elevation. (You could transcribe these from there.)

Push-pin (place-marker), Polygon, and Path Tools. Click the tool. Enter a mnemonic name. Set style and color. Digitize. (finally) click "OK" to close the panel. (You can reset the "properties" of a place-marker, polygon or path; right-click its name in the side-bar.)

Ruler (measurement) Tool. Set the units (meters?). (How many different units of distance do they offer? What is the oddest one?) Select (straight) line or path length (connect the dots). Click the end points (or along the path). Read the result from the panel.

You can save the image (including your digitized paths) as a 'jpg' file. File : Save : Save Image...

You can save the coordinates of your push-pins and paths to a .kml file: In the side-bar, under the "Places" tab, Right-click the "My Places" (or "Temporary Places") line and select "Save as..." from the drop-down menu. Enter a filename (like, your initials + "-366.kml").

### Collect some Observations:

Measure the following distances (in meters) using the "ruler" tool. Record the distances as you go.

From Place (lat., lon.) To Place (lat., lon.) Distance on (Google) Earth (meters)
North Pole Equator
0d 00' 00" N, 0d 00' 00" E 0d 00' 00" N, 90d 00' 00" E
0d 00' 00" N, 0d 00' 00" W 0d 00' 00" N, 1d 00' 00" W
90d 00' 00" N, 135d 00' 00" W 89d 00' 00" N, 135d 00' 00" W
0d 00' 00" N, 100d 00' 00" W 1d 00' 00" N, 100d 00' 00" W
60d 00' 00" N, 5d 00' 00" E 60d 00' 00" N, 6d 00' 00" E
45d 00' 00" N, 180d 00' 00" E 45d 00' 00" N, 179d 00' 00" E

Now, collect some observations of distances across mountanous and flat terrain.

Measure the distance between N 28.05, E 86.85 and N 27.9, E 87.0 (across Mt Everest) with GE "terrain on" and "terrain off".
Mountainous Terrain Flat Terrain
Terrain on:
Terrain off:

Measure the similar distance between N 28.05, E 39.95 and N 27.9, E 40.1 with the terrain on and off.
Mountainous Terrain Flat Terrain
Terrain on:
Terrain off:

### THE REPORT:

Include a table or list of the distances you found. Write a brief description (about three paragraphs) on what your observations of distances in Google Earth suggest about the model of the shape of the earth that it uses. One paragraph should address: Is the GE model spherical, oblate, or prolate? Why do you think so? Another paragraph should address: Does Google Earth use terrain in measuring distance?

Submit this in hardcopy.

### Some things to think about:

Which observations that you made should be most useful in determining what model of the Earth GE is using?

Among the ways that GE might calculate distances between points seem to be at least these...

• Calculate the arc between the points with the Law of Cosines from spherical trigonometry and multiply by a scale factor to get a linear distance in km.
d = arcos( (cos(b)*cos(c) + sin(b)*sin(c)*cos(A)) * 111 km/degree
• Project the coordinates to a flat Cartesian (2D) space and calculate the distance with the Pythagorean Theorem:
d = ((X1-X2)^2 + (Y1-Y2)^2 )^0.5
• Work-out a geodesic on the 3D terrain surface model and sum the length of its segments in that 3D Euclidean space.
d = sum-over-segments [((X1-X2)^2 + (Y1-Y2)^2 + (Z1-Z2)^2)^0.5]
• Store a table of all interpoint distances.
• Something else?
As you do this exercise, keep an eye out for evidence for which method they use. Which do you think it is?