# Outline

1. Principles
• Earth's Rotation
• Latitude and Longitude
• Calculating Time
• Calculating Time Through the International Date Line
2. Example Calculations
• The Process
• Through the International Date Line
3. Review Questions

## Principles

The earth is one of the nine planets that make up our solar system. Though it isn't one of the largest planets, it still has a circumference of 25,000 miles or 40,000 kilometers. It is also constantly in motion. In fact, the Earth orbits the sun at an incredible 66,500 rate of miles an hour. Yet, it still takes the earth 365 days, or one year, to complete a full rotation around the sun. Moreover, as the Earth orbits the sun, it spins on its axis in a counter-clock wise motion. It too rotates at a fast pace of 1042 miles per hour. On its axis, the earth rotates 360 degrees every 24 hours. Or you can look at it as it takes one day to complete a full circle. Divided up into an hourly rate, the earth rotates 15 degrees every hour (360/24). This number plays an important role in determining time zones.

An important factor in determining time zones is the lines of latitude and longitude. Imaginary lines known as latitude and longitude divide the Earth. Latitude lines are "drawn" east and west and they measure north and south. The lines start at the equator and measure distance from 0 degrees to 90 degrees north and also 0 degrees to 90 degrees south. They also become shorter the farther away they get from the equator. On the other hand, longitude lines are "drawn" north and south and they measure east and west. They start at the Prime Meridian (or 0 degrees) and measure from 0 degrees to 180 degrees east and 180 degrees west. Unlike lines of latitude, these lines are fairly equal in length. The origin of this spherical coordinate system is at 0 deg. latitude and 0 deg. longitude. This spot can be found in the Atlantic Ocean just south and west of Africa. Also, the two lines connect at 180 degrees or at the International Date Line. This too helps to determine the different time zones throughout the world.

Together all of the above information can be used to calculate the difference of time between two locations. First, you need to know what longitude the two places are located in. Next, you would need to find the differences in longitude (in degrees) between the two places. If both places are located on the same side of the Prime Meridian, then the numbers are just simply subtracted to find the difference. If they are on the opposite side of the Prime Meridian then the two numbers should be added together to find the difference. Second you need to divide the difference (measured in degrees) by 15 since there are 15 degrees in every hour. This will give you the difference in time between the two locations. So if you know what time it is in one location, and the longitude of another location, then just simple addition or subtraction problem will give you the time in a different time zone. Let's look at another way we may have to calculate the difference between time of two locations.

Another calculation you may have to make is over the International Date Line. This line is strategically placed in the Pacific Ocean so that no two neighboring cities are one day apart in time. It can be difficult to calculate though the International Date Line when trying to determine the amount of time difference between locations on either side. This calculation is very similar to the situation with the Prime Meridian. You must start by finding the difference in longitude (or degrees) of the two places. You do this by adding the two numbers. Then, divide by the 15 degrees that occurs in one hour and this will give you the time difference between two locations through the International Date Line. And again, just add or subtract that difference from the time that you already know to come up with the new time in the new time zone.

## Example Calculations

To review, to find the difference between the two longitudes and divide by 15, this gives you the difference in hours between the two locations. Second, add or subtract the number of hours from the time of day that was already known, you will need to add the numbers if you are going east, and subtract if you are going west. Here are some examples of how we may need to calculate the difference of time zones.

If you are in London at 12:00, and want to know what time it is in Japan, you would need to first figure out that London is 0 degrees (right on the prime meridian), and Japan is 135 degrees East. So the difference is 135 degrees (135-0), divided by 15 which equals 9. Which means there is a 9-hour difference between London and Japan. Since Japan is further east than London is, you would add 9 hours to 12:00. The answer is at 12:00 noon London time, it is 9:00pm in Japan.

Now how about going through the International Date Line. Pretend you are in Japan, which is 135 degrees east and you wanted to know what time it is in Hawaii, which is 150 West. Well, there is 45 (180-135) degrees difference between Japan and the IDL. Also there is 30 (180-150) degrees difference between the IDL and Hawaii. Therefore the difference in time is (45+30/15=5) 5 hours. Now the tricky part is that Japan and Hawaii are on different days. It is one day ahead on the left side of the IDL compared to the right side. If it is 3:00pm in Japan on Thursday that means it is 3:00+ 5 hours = 8:00pm in Hawaii. However notice that when crossing the IDL we subtract a day going east. So, in Hawaii it is 8:00pm on Wednesday.

## Review Questions

1. Lines of latitude: A. begin with the prime meridian; B. are designated by being East or West from an origin; C. are of equal length; D. become shorter away from the equator; E. none of the above.

2. All of the following are true statements about longitude, except: A. has its origin at the prime meridian; B. extend east and west to 180 degrees longitude; C. are relatively equal in length; D. could be determined by sailors using a device called the sextant; E. could not be determined by sailors until the introduction of the chronometer.

3. You are told that the earth rotates on its axis at a speed of about 1042 miles per hour. Given that the rotation occurs in 24 hours, what is the circumference of the earth? A. 40,000 miles; B. 25,000 miles; C. 2400 miles; D. 76,000 miles; E. none of the above.

4. How many degrees of a full circle can you travel eastward or westward from the zero (prime) meridian before heading back toward the Prime Meridian? A. 60deg. B. 90deg. C. 360deg. D. 180deg. E. none of the above.

5. 0deg. longitude and 0deg. latitude is located: A. over central Australia; B. in Brazil; C. in the Atlantic south and west of Africa; D. at the South Pole; E. none of the above.

6. To find longitude, a sailor needs to know: A. the elevation of the sun above the horizon; B. the latitude at the prime meridian; C. local time and the time at another line of longitude; D. the relative space; E. none of the above.

7. Latitude and longitude is a spherical coordinate system with its origin at 0deg.latitude and 0deg. longitude. This point is in the Atlantic Ocean just below the African country of the Ivory Coast. Locations are measured in degrees away from this origin in north, south, east, and west directions. 23.34deg. S and 46.38deg.W is probably located in: A. Russia; B. Canada; C. South Africa; D. South America; E. none of the above.

8. The circumference of the earth at the equator or along any line of longitude is approximately: A. 25,000 KM; B. 40,000KM; C. 36,000 KM; D. 46,000 KM.

9. It is 1:00 PM on Friday at 90deg. W. what time is it at 90deg. E? A. 7:00 PM Friday; B. 7:00 AM Friday; C. 7:00 AM Saturday; D. 1:00 AM Saturday; E. 1:00 PM Saturday.

10. It is 12 noon, Monday at 90deg. W. what time and day should it be at 75 degrees east longitude? A. 11PM, Monday; B. 11 AM; Tuesday; C. 1 AM; Monday; D. 11 PM; Tuesday; E. 6 AM; Monday.

Answer Key: 1. D 2. D 3. B 4. D 5. C 6. C 7. D 8. B 9. D 10. A

Resubmitted by Tessa Layton 12/07/99. Resubmitted by Jackie Froendt 5/16/97. Resubmitted by Allison Beary. Submitted by Lisa Berry on 10/1/96. Originally submitted by Michelle Balkus on 2/8/96