# EXERCISES

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he Equation of Time (ET) allows one to calculate the Standard Time at which the Sun will be found in a particular part of the sky. For example, if it is asked at what time does the Sun rise in Hilo, Hawaii, on March 21, we must know the ET on March 21 and the longitude of Hilo. The ET can be read from the graph and is approximately -8 min. . The longitude of Hilo is 155o W, corresponding to the example under Equation of Time. First, let us determine the time of sunrise at the Standard Meridian of 150o W, and then make the correction for Hilo's longitude. The apparent time at sunrise must be 4 minutes before 6 a.m. (The explanation of the 4 minutes is found under Sunrise and Sunset). From the definition of ET = Apparent time - Mean (or Standard) time, we see that the Standard time in this case is the App. time - ET, or, 5h 56min - (-8 min) = 6h 4min. This is now corrected for Hilo's longitude by adding 20 minutes, giving sunrise as 6h 24min or 6:24 a.m., HST (Hawaii Standard Time).

Another example: at what time will the Sun be on the local meridian to an observer in Boston on October 31? Remember that the local meridian is the great circle from north to south passing through the zenith. The ET on October 31 is approximately +16 minutes, and Boston is situated at longitude 71o W. The Apparent time when the Sun is on the meridian is 12 noon. Thus, Standard time = 12h 00min - (+16 min) = 11h 44min. This is the correct time at the Standard Meridian of 75oW, but Boston is 4o east of this, so the Sun crosses the Boston meridian 16 minutes before the 75th meridian. Hence, the answer is that the Sun crosses the meridian of Boston on October 31 at 11h 28min or 11:28 a.m., EST (Eastern Standard Time).

An interesting problem for the Hawaii student is to determine on what day and at what time the Sun passes directly overhead, i.e., through the local zenith. (Note that Hawaii is the only place in the United States where this can happen!) This requires the use of a table of the declination of the Sun for every day of the year and for the particular year in question, and such a table can be found in the American Ephemeris and Nautical Almanac (see REFERENCES). The declination of the Sun corresponds to latitude on the Earth, so that, when the declination of the Sun equals the latitude of the observer, the Sun will pass through the observer's zenith. Since the latitude of Hilo is 19o 43', we need to look for the day on which the Sun has a declination of 19o 43'. We then need to find the ET on that day and proceed to determine, as above, the HST at which that zenith crossing occurs. We like to call this a "shadowless" noon, for indeed, a flagpole has no shadow at that instant!

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