Principles
Finding longitude is one of the oldest problems in navigation. For millennia, sailors would estimate their longitude by the system of dead reckoning. Speed and drift by currents were estimated over a period of time to approximate the east or west distance traveled. It was not until the late 18th century that the problem of finding longitude was finally solved by the invention of the portable chronometer by the Englishman, John Harrison. In fact, Captain James Cook carried one of the first "sea clocks" on his ship, Resolution, when it chanced upon the Hawaiian Islands in 1778, thus making Hawaii one of the first locations to have its longitude accurately determined.
The mathematics involved is really quite simple. As you learned in the Time Zone lesson, the Earth rotates through 15° of longitude per hour. You simply compare the time difference in hours between places and multiply by 15. You know your local time using the sun: when it reaches its highest point, it is noon at your location. So, lets say you have a clock set to Hawaii time and the sun is at its highest point when your clock says 9 am. The difference in time between your location (noon) and Hawaii (9 am) is 3 hours, so the longitude difference is 3 x 15 = 45°.
Finding the Longitude
Now the only thing you need to know is: am I east or west of Hawaii? If your clock reads later than noon, your position is to the west. If the clock reads earlier than noon, your position is to the east. So: using your clock and a sun observation, you have determined that your longitude is 45° east of Hawaii. Since Hawaii's reference longitude is 150° West, you must be at 150-45= 105° West. So for scenario 1 below, in words, you would say: "I calculate my longitude to be 105° W, which is 45° to the East of the reference longitude of 150° West." (Drawing a diagram would help visualize this relationship.)
Practice finding your longitude for the following scenarios (use the Coordinate Reference Tool below to help visualize):
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
|
Scenario
|
Reference Longitude
|
Time at Reference Longitude when it is noon at your
position
|
Time difference (from noon in hours)
|
Longitude Difference (differ. x 15)
|
Earlier or Later (than local noon)?
|
Am I to the East or West of Reference Longitude?
|
Your longitude
(col 5 E/W of col 2) |
|
1
|
150° West
|
9 AM
|
3
|
45°
|
Earlier
|
East
|
105° West
|
|
2
|
0°
|
10 PM
|
10
|
150°
|
Later
|
West
|
150° West
|
|
3
|
90° West
|
4 PM
|
4
|
60°
|
|
|
|
|
4
|
90° East
|
5 PM
|
5
|
|
|
|
|
|
5
|
30° East
|
8 AM
|
|
|
|
|
|
|
6
|
140° East
|
8 PM
|
|
|
|
|
|
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7
|
30° West
|
8 AM
|
|
|
|
|
|
|
8
|
120° East
|
6 AM
|
|
|
|
|
|
|
9
|
150° West
|
7 AM
|
|
|
|
|
|
Use the Table above with help from the Coordinate Finder Tool below
to answer the following questions:
49. What is your longitude for Scenario 3 (3rd line in Table above)? _____
50. What is your longitude for Scenario 4? _____
51. What is your longitude for Scenario 5? _____
52. What is your longitude for Scenario 6? _____
53. What is your longitude for Scenario 7? _____
54. What is your longitude for Scenario 8? _____
55. What is your longitude for Scenario 9? _____