Solstices and the Solar Analemma

Infinity is the bane of navigators — you’re nowhere when there’s no beginning or end to time and space. Yet in one of Nature’s better jests, an infinity symbol ( \infty  ) tells us about our movement through time and space. Click the Thom Matheson video below to see the sun’s position, its declination, in 26 noons over the course of a year.  It loops through the New Jersey sky from the bottom Winter Solstice to the top Summer Solstice and back again. This revelation of the our celestial course is called the solar analemma.

One might expect our annual view of the sun to trace a simple circle, but Earth’s orbit is elliptical and tilted on its axis. Those two factors combined result in this figure published by Ethan Siegel of ScienceBlogs. Orientation of the figure 8 depends on one’s location on the globe.

Or in a real-world example is from the Greenwich Observatory. Notice that the Winter and Summer biases are removed from the following chart. Instead, neutral “Northern” and “Southern” designations are used, because the seasons are reversed between northern and southern hemispheres.

From the Wikimedia Commons: This is a plot of the position of the sun at 12:00 noon at the Royal Observatory, Greenwich (latitude 51.4791° north, longitude 0°) during 2006. The horizontal axis is the azimuth angle in degrees (180° is facing south). The vertical axis is the altitude in degrees above the horizon. The first day of each month is shown in black, and the solstices and equinoxes are shown in green. It can be seen that the equinoxes occur at an altitude of \begin{smallmatrix}\phi\end{smallmatrix} = 90° ∼ 51.4791° = 38.5209°, and the solstices occur at \begin{smallmatrix}\phi\end{smallmatrix} ± ε where ε is the axial tilt of the Earth, 23.439°. This plot was constructed using altitude and azimuth data generated by JPL Horizons. This data is listed below. The analemma is plotted with width highly exaggerated, which permits noticing that it is very slightly asymmetrical (due to the two-week misalignment of the apsides of the Earth’s orbit and its solstices).

How is this useful to navigation? HarborLAB will request an article called “Resurrecting the Analemma,” published by the Institute of Navigation for greater details. The article notes that fewer and fewer maps and globes have included the analemma in recent years as GPS has overtaken traditional low-tech navigation. According to the abstract:

“It provides the user with values of declination and equation of time for every day of the year. In the first half of the twentieth century, it was a standard feature on any globe or map of the world. In recent years, however, the analemma has all but disappeared. This paper resurrects the analemma. The construction and use of the analemma is explained and some modern source materials are provided. Using the analemma in conjunction with other low-tech methods, a complete scheme for navigating by the sun is outlined. The analemma is a figure eight shaped graphic representation of the Earth’s annual path around the sun. It provides the user with values of declination and equation of time for every day of the year. In the first half of the twentieth century, it was a standard feature on any globe or map of the world.”

Old globes commonly included the analemma as a navigational aid. Some cartographers still include them. Detail of an analemma, on a globe by Gilman Joslin, Boston, 1890, in the collection of the Library of Congress. (By Lawrence W. Jackson Jr./Washington Post)

As for the relationship between the infinity symbol and the analemma, it seems to be coincidental. Some consider it a pictograph based on the mobius strip, but its origins have been traced to the ancient Greek final letter of the alphabet, Omega (ω), or the Roman symbol for 1,000 ( CIƆ or CƆ ).

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