Introduction to the Mapping Sciences
Introduction to Mapping Science Name:_______________________
Exercise #4 – Size, Shape and Location on Earth
1. On the graph use Cartesian coordinates to locate the following points. Assume that each grid square represents one unit.
Point X Y
1 5.5 6.6
2 -3.5 -4.5
3 -7.5 2.0
4 5.0 -3.5
[pic]
2. What is the distance between points 1 and 2?_________ 3 and 4?__________4 and 2?__________
SHOW YOUR WORK:
3. For each location on the map [1-5] write its latitude and longitude in the following table.
|Point |Latitude |Longitude |
|1 | | |
|2 | | |
|3 | | |
|4 | | |
|5 | | |
[pic]
4. Convert each of the following locations to decimal degrees: .
1. 40̊ 30’ 15” N 75̊ 45’ 21” W
2. 45̊ 25’ 05” S 35̊ 55’ 01” E
3. 10̊ 35’ 15” N 55̊ 25’ 18” E
|Point |Latitude |Longitude |
|1 | | |
|2 | | |
|3 | | |
Show your work:
5 - Great Distance Measurements
When measuring long distances we need to account for the curvature of the earth. In this case the procedure is to calculate the number of degrees of great circle arc between the two places and then convert the arc measure, which is in degrees, to distance measure by multiplying by 69 [for converting to miles].
Given the latitude and longitude of two places, use the following formula to determine the number of degrees in the arc of the great circle connecting the two places:
θ° ’ Arccos ((Sine(Lat1)*Sine(Lat2)) + (Cosine(Lat1)*Cosine(Lat2) * Cosine(|Long1 - Long2|)))
You can find the required trigonometric functions on any scientific calculator. On many calculators you access the arccosine function by pressing the Inverse or second function key and then pressing the cosine key.
In Windows you can access a calculator, pictured here, by clicking on Start–> Programs –> Accessories –> Calculator. The illustration highlights the trigonometric function keys and the Inverse check box. Note that for the formula giver here you need to specify angular measurements in degrees, so you should click in the Degrees option box.
The map depicts Philadelphia and San Francisco. The following table displays the latitude and longitude of each place. Use the data in the table to calculate the numbers of degrees of great circle arc between the two places and then convert the degrees into miles.
Here are the steps you need to follow:
1. Convert the degrees, minutes, and seconds to decimal degrees.
2. Use the formula to determine the number of degrees of great circle arc separating the two places.
3. Multiply the number of degrees by the length of a degree in linear measure [69 in the case of miles].
Global Coordinates
|Place |Longitude |Latitude |
|Philadelphia | 75̊ 18' 13" W |40̊ 3' 4" N |
|San Francisco |121̊ 42' 53" W |36̊ 26' 7" N |
Decimal Degrees
|Place |Longitude |Latitude |
|Philadelphia | | |
|San Francisco | | |
Sine Lat1 = Sine Lat2 =
Cos Lat1 = Cos Lat2 =
Cos (| Long1 - Long2|) =
((Sine Lat1) * (Sine Lat2)) + (Cos Lat1 * Cos Lat2 * Cos (| Long1 - Long2 |) ) =
Arccos of result in previous line. degrees.
Degrees = Distance = Miles
Show your work:
6 - World Time Zones Worksheet (use page 27 Dates and Times to help you answer)
* Where is all time measured from?
________________________________________
* How many world time zones are there? Why?
________________________________________
* Approximately how wide is each time zone?
________________________________________
* Explain why time zone boundaries are not completely straight.
________________________________________
* Name the four major United States time zones.
________________________________________
If the time in London is 12:00 P.M. GMT, Wednesday what time is it in:
Chicago _____________________________ Paris _____________________________
Moscow _____________________________ Tokyo ___________________________
Buenos Aires ________________________
If the time in Philadelphia is 12:15 P.M., Wednesday what time is it in:
Chicago ____________________________ Paris ______________________________
Moscow ___________________________ Tokyo _____________________________
Sydney ____________________________ Buenos Aires ________________________
Show your work:
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