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The planetarium sundial

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A sundial, based on the design and calculations of physics professor and associate provost

Brandt Kehoe, will be etched into the Downing Planetarium lobby floor. (See diagram on page 2.) A slender window - all of dark glass except for a small circular clear area four feet above the lobby floor - is mounted in the center of the front wall.

Kehoe says that sunlight coming through that circle will form a spot on the floor that moves from west to east along one of the long curves shown in the figure. Which curve depends upon the date: the curve farthest from the front is the path on Dec. 22, the time of the winter solstice when the sun is lowest in the sky; the curve closest to the front is the path on June 21, the time of the summer solstice when the sun is highest in the sky. Intermediate paths are for intermediate dates a month apart. The pattern on the floor is not symmetric because the building is oriented with its centerline 18 degrees east of north.

In order to use the sundial to tell time, we need to mark the position of the spot at each hour. Kehoe explained that except at the solstices, there are two dates for each long curve and two spot locations for a given hour. Connecting the locations of the spots corresponding to a particular time on June 21 through the fall months to Dec. 22 and then through the spring months back to June 21 forms the figure eight patterns you see in the drawing. These curves are called analemas. Shown in the figure are the analemas for the hours 8 a.m. to 5 p.m.

The pattern is the result of the rotation of the Earth, the tilt of the Earth's axis at 23 degrees from the perpendicular to the plane of the orbit, and the shape of the Earth's orbit around the Sun. The rotation causes the passage of the Sun across the sky and the spot across the floor. The tilt, and the fact that the orbit is not quite a circle, make the length of a "solar day" (the time it takes for the sun to go from directly south on one day to directly south on the next) change throughout the year. Our 24-hour day is the length of an average solar day. The difference between the true solar day and the average solar day gives rise to the analemas.