6. McKeague Exercise 2.2.87: Sundials The Moorish sundial is designed so that th

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6. McKeague Exercise 2.2.87: Sundials The Moorish sundial is designed so that the shadow of the gnomon (the vertical triangular picce) is consistent at each hour from one day to the next. This allows the hours to be marked on the sundial using a single scale that is not affected by the changes in the Suns path during the year. If the sundial is positioned so that the gnomon is aligned along a longitudinal line from north to south, then at exactly noon the gnomon will cast a shadow due north. Figure 7 As the sun moves, the shadow will sweep out an angle toward the cast, la Figure 7, called the shadow, angle. This angle cun be alculated using th,formula beled in where is the latitude of the position of the sundial and h is a number or hours from noon. ( What is the sgnficance of the 15 factor in th argument o the tungent? How dos this relate to te apparent motion of the sun in the sky? (b) The latitude of San Luis Obispo, CA, is 35.282. Find the shadow angle for a sundial in San Luis Obispo at 2pm. Round to the nearest tenth of a degree. tan e Sin (35,262) tan (3 15) tan e Sin (35 282) ton Bo)

Explanation / Answer

A standard time zone covers roughly 15° of longitude, so any point within that zone which is not on the reference longitude (generally a multiple of 15°) will experience a difference from standard time equal to 4 minutes of time per degree.

so we will have a termof h.15 where h represents the amount of time in hrs from noon and this will account for the revolution of sun arount the sun which appears to be at angle of 150. If a sundial is located at, say, a longitude 5° west of the reference longitude, its time will read 20 minutes slow, since the sun appears to revolve around the Earth at 15° per hour. This is a constant correction throughout the year. .

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