Monday, November 28, 2005

Time Part One

As the earth turns on its axis, the sun appears to move across our sky. The shadows cast by the sun move in a clockwise (hence the definition of clockwise) direction for objects in the northern hemisphere.

Shadow sticks or obelisks are simple sundials. If the sun rose and set at the same time and spot on the horizon every day, they would be fairly accurate clocks. However, the sun's path through the sky changes every day because the earth's axis is tilted. On earth's yearly trip around the sun the North Pole is tilted toward the sun half of the time and away from the sun the other half. This means the shadows cast by the sun change from day to day.

In addition, because the earth's surface is curved, the ground at the base of the shadow stick or obelisk is not at the same angle to the sun's rays as at the equator. This means that the shadow does not move at a uniform rate during the day. That is, if you mark the shadow at sunrise and sunset, you cannot evenly divide the space between for the individual hours. Try changing the latitude in the applet to the right and see how the hour marks change.

There are several ways to overcome these problems. One is to build a horizontal sundial, where the base plate is level, and the "stick," called the style, is angled so it is parallel to the earth's axis. The hour marks can then be drawn by trigonometric calculations, correcting for the sundial's latitude.

Another solution is an equatorial sundial, where the base plate is titled at an angle equal to the latitude, and the style is perpendicular to the base, which will align it with the earth's axis. The base can then be marked with regularly-spaced hour marks.

Oh, yes, there's one more problem. Sundials only measure local solar time. If a friend had a sundial 5 degrees longitude to the west of your sundial, his sundial would read a different time than yours. This is a simple calculation: the earth turns 360 degrees in about 24 hours, therefore the sun's apparent position moves 360/24 = 15 degrees each hour. So your friend's sundial would read 20 minutes different (earlier) than yours. This difference is only affected by longitude, not latitude. To standardize things, the earth was divided into 24 time zones in the 1840's, each to be one hour different from the next.

More sundial info than you could possibly want here and here.

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