History
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.
Finding the Longitude Difference from a Known Location
The mathematics involved is fairly straighforward. As you learned in the Time Zone lesson, the Earth rotates through 15° of longitude per hour. To find the longitude difference from a known location, simply compare the time difference in hours between places and multiply by 15. You find your local time using the sun: when it reaches its highest point, it is noon, or 12 pm, at your location. You know the time at a reference location by carrying a clock set to its time. Lets say that you are sailing and carrying a clock set to Hawaii time. You track the sun and it reaches its highest point when your Hawaii clock says 9 am. The time difference between your location (12 pm) and Hawaii (9 am) is 3 hours, so the longitude difference is 3 x 15 = 45°.
Are you East or West of the Known Location?
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 of Hawaii . If your clock reads earlier than noon, your position is to the east. Since your Hawaii clock reads 9am, which is earlier than noon, you have determined that your longitude is 45° east of Hawaii, e.g. your sailboat's longitude is 45° east of Hawaii's longitude. Since Hawaii's reference longitude is 150° West, you must be at 150-45= 105° West. This process is summarized in Scenario 1 in the table below. Drawing a diagram or looking at a map will help visualize this relationship.
Practice finding your longitude for the following scenarios:
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
|
Scenario
|
Reference Longitude
|
Time at Reference Longitude when it is noon (12 pm) 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
(column 5 East or West of column 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
|
|
|
|
|
|
|
7
|
30° West
|
8 AM
|
|
|
|
|
|
|
8
|
120° East
|
6 AM
|
|
|
|
|
|
|
9
|
150° West
|
7 AM
|
|
|
|
|
|
Use the Table above
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? _____