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Index
1. Stargazers 1a. Celest. Sphere 1b. Pole Star 2. The Ecliptic 2a. The Sundial 3. The Seasons 3a. Angle of sunlight 4. The Moon (1) 4a. The Moon (2) 4b. Moon Libration 5.Latitude and Longitude 5a. Navigation 5b. Cross-Staff |
(Attributed to an essay by a student in elementary school.)
As the Sun rises, passes the highest point in its path (at noon and to the south, in the northern hemisphere) and sets, the shadow rotates around the stick in a clockwise direction, and its position can be used to mark time. Indeed, it has been claimed that the "clockwise" direction in which the hands on a clock rotate was chosen for this reason. A sundial with a vertical pointer ("gnomon") will indicate noon correctly when its shadow points north or south. [North in northern middle latitudes, south in southern ones, while near the equator it can be either way, depending on season.] However, the direction of the shadow at some other time of the day may depend on the season--its value in summer, when the Sun's path is high, may differ from what it is in winter, with Sun low above the horizon.
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Such a sundial will however work equally well at all times if the pointer is slanted, to point towards the pole of the celestial sphere (click here for an explanation--but be warned, it is a bit complicated!). The angle between it and the base then equals the geographic latitude of the user.
A Paper SundialOrnamental sundials are often found in parks and gardens, with the pointer widened into a triangular fin, which must point northwards. A sundial of this type can be constructed from folded cardboard or stiff paper: click here to see the basic design used around latitude 38 North of the equator, here for a corresponding one in the southern hemisphere. Either can be printed and then photo-copied onto suitable sheets of stiff paper or cardboard [You may want to use the "option" menu to reduce size to 90% before printing--but make sure to return the setting to 100% afterwards!]. It is meant to be used at a latitude of 38 degrees and should work adequately in most of the continental US.
Instructions:
If you want to make a sundial of more durable materials, draw the pre-noon hour lines at the angles to the fin (given in degrees) given below. These lines are meant for a latitude of 38 degrees; if your latitude is markedly different, see note at the end.
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6 -- 90° | 9 -- 31.6° |
7 -- 66.5° | 10 -- 19.6° |
8 -- 46.8° | 11 -- 9.4° |
AccuracyThe sundial will obviously be one hour off during daylight saving time in the summer, when clocks are reset.In addition, "clock time" (or "standard time") will differ from sundial time, because it is usually kept uniform across "time zones"; each time zone differs from its neighbors by one full hour (more in China and Alaska). In each such zone, sundial time matches clock time at only one geographical longitude: elsewhere a correction must be added, proportional to the difference in longitude from the locations where sundial time is exact.
Note on LatitudeThe angles listed above are intended for a latitude of 38 degrees. If your latitude is L, √ denotes "square root of" and K (=cotg2L) is
then the angle between the fin and the line corresponding to the hour N+6 (N going from 0 to 6) satisfies Here 15N (=15 times N) is an angle in degrees, ranging from 0 to 90, and of course, the afternoon angles are mirror reflections of the morning ones. If your calculator has a button (sin-1), if you enter (sin A) and press it, you will get the angle A. For an explanation of sines and cosines, look up the math refresher. And don't forget to adjust the angle of your fin to L, too!
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And by the way...The sundial described here, with a gnomon pointing to the celestial pole, is a relatively recent invention, probably of the last 1000 years. Yet sundials were used long before, often with unequal hours at different times of the day. The bible--2nd book of Kings, chapter 20, verses 9-11 (also Isaiah, ch. 38, v. 8) tells of an "accidental" sundial, in which the number of steps covered by the Sun's shadow on a staircase was used to measure the passage of time. In that story, the shadow miraculously retreated ten steps on the staircase built by King Ahaz.
Exploring Further"Sundial Bridge," with a unique design which may well make it the largest sundial anywhere, opened July 4, 2004 in Turtle Bay Park in Redding, California, at the foot of Mt. Shasta. Designed by the innovative Spanish architect Santiago Calatrava, it resembles his stunning 1992 bridge erected in Seville, Spain. It is a pedestrian bridge, connecting two parts of Turtle Bay Park, and it also operates as a sundial, using plaques set in a semicircular upper plaza.For a more detailed article about this bridge, see Sundial Bridge at Turtle Bay You may also be interested to know that a North American Sundial Society (NASS) exists, with its home page at http://sundials.org. From the main page, the visitor can click on "About NASS", and/or access the many other features the site offers. And in case you wonder about the creatures drawn at the bottom of the "About NASS" page, they are toves, the whimsical invention of Lewis Caroll in his poem Jabberwocky. Concerning what toves are, see Humpty Dumpty's explanation, also reachable by clicking the winking sun icon on the top of the NASS home page. The reference is from the 6th chapter of Lewis Carrol's Through the Looking Glass. The British Sundial Society also has its sundial page. A sundial was included as part of the Mars lander mission and is shown in "Astronomy Picture of the Day" for 28 April 1999. It has a thick vertical gnomon, so that its readings may need some extra corrections . For those with serious interest in history (and access to a good library): "The Material Culture of Astronomy in Daily Life: Sundials, Science and Social Change" by Sara Schechner (History of Sci. Dept., Harvard) Journal for the History of Astronomy Vol. 32, part 3, August 2001, p. 189-222, with many illustrations. From the 1.1.2000 book catalog of Willman-Bell in Richmond, Virginia (www.willbell.com):
Sundials: History, Theory and Practice by Rohr, 230 pp, $12.95. Sundials: Their Theory and Construction by Waugh, 19 chapt., $8.95 Questions from Users: What is the Analemma? *** The equation of time |
Next Stop: #3 Seasons of the Year
Timeline Glossary Back to the Master List
Author and Curator: Dr. David P. Stern
Mail to Dr.Stern: stargaze("at" symbol)phy6.org .
Last updated: 9-17-2004