The development of an accurate system for keeping time stems from the motion of Earth as it rotates on its axis. Time and position on Earth's surface are interrelated by the concepts of longitude and latitude, so we will start our work with problems involving time by taking a closer look at these concepts.

1. When the time at Washington, D.C. (39°N, 77°W) is 4 PM EST, what is the longitude of the Sun?

Since the Sun must be overhead at the longitude where it is 12:00 noon, this problem is simply asking where it will be 12:00 noon when it is 4 PM EST at Washington, D.C. Eastern Standard Time is centered at 75°, so the Sun must have passed this point 4 hours earlier as it moved across the sky toward the west, since it is now 4 PM. For each hour of time, the Sun traveled 15°, so it will now be 15° x 4 = 60° west of the 75° longitude location. This places it at 75° + 60° = 135°, which happens to be the central meridian for the Pacific Standard Time zone. The Sun has moved to California. You can use Figures 16.8 or 16.9 in the textbook to help you visualize this time difference.

2. What is the latitude of an observer in the Northern Hemisphere who sees the noon sun at an altitude of 15° above his horizon on December 21?

First, we must know that the declination of the Sun on this day of each year is 23.5° and that the zenith angle is needed to locate the position of the observer. The zenith angle is equal to 90° - 15° in this case, so we will be working with a zenith angle of 75°

For the observer to see the Sun at a zenith angle of 75°, the line of sight to the Sun must also be 75° away from the observer's zenith position. Since the Sun is 23.5° south of the equator, the angle 75° must represent the latitude of the observer plus this angle south of the equator.

75° = latitude + 23.5°

This means: latitude = 75° - 23.5° = 51.5°N

3. When the time in Chicago (42°N, 88°W) is 8 AM CST, what is the time at Greenwich, England (49°N, 0°)?

The central meridian for CST is at 90°W (see Figure 16.7 in the textbook), so the angular distance to Greenwich is 90° - 0°, and since each degree represents 4 minutes, the corresponding time difference will be 90° (4 min/degree) = 360 min (1 h/60 min) = 6 h. We could also have found this using the fact that 15° = 1 hour, so 90° /15°/h = 6 h of time difference. Since Greenwich is to the east, the time must be later, and so it is 8 A.M. + 6 h, or 14 o'clock. Unless you are used to using military time, this can best be considered as 12:00 noon + 2 h, or 2 P.M. So the time at Greenwich is 2 P.M. GMT when it is 8 A.M. CST in Chicago.

4. An observer at 40°N sees the noon Sun at an altitude of 73.5° above his southern horizon. What season of the year is it?

Since the altitude of the Sun is 73.5°, the zenith angle must be 90° - 73.5° = 16.5° . This means that the angle between the 40° location and the line of sight to the Sun for a person who sees the Sun directly overhead (at the zenith) would also be 16.5° (see Figure 16.15 in the textbook for a similar exercise). Since this is the case, the angle between the equator and the zenith line for the person who sees the Sun directly overhead must be 40° - 16.5° = 23.5°, and the observer will still be north of the equator. Since the Sun is directly overhead at 23.5° and this can only occur on June 21, this makes the season the beginning of summer in the Northern Hemisphere.

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