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The evolving eclipse map: nearly 400 years of fine-tuning have turned today's eclipse maps into works of art that predict cosmic alignments with exquisite precision.

Eclipse maps tell amazing stories. They combine space and time to instruct us how to station ourselves to observe a total eclipse of the Sun. Eclipse maps also weave together exploration, mathematics, astronomy, geography, culture, and artistry.

Eclipse maps arose four centuries ago and progressed in synchrony with advancements in scientific knowledge, eclipse calculations, and cartography. Today's eclipse maps present an audacious degree of precision, predicting where and when the Moon's shadow will fall on Earth with accuracies of tens of meters and tenths of seconds. With modern technology, we can predict the syzygies of the Sun, Earth, and Moon with such confidence that our current eclipse maps will still be reasonably accurate for centuries into the future. As eclipse chasers gather in Australia and the Pacific this November (see page 52), we'll know exactly where and when to go to witness the greatest show on Earth a total eclipse of the Sun.

Origins

Historians have traced the origin of eclipse maps back to the ancient Greeks and Claudius Ptolemy, who made rough eclipse predictions and diagrams. But mapping an eclipse's path on Earth required more detailed knowledge of the motions of the Earth, Sun, and Moon than these past astronomers possessed. The ancients found rhythms of the Moon and Sun (such as the saros cycle, see page 37) that they used to make predictions of when an eclipse might happen, but this knowledge was insufficient to predict the path of a solar eclipse on Earth.

It was not until the scientific revolution in Europe that eclipse predictions improved to a point when astronomers could produce the first true eclipse maps. The modern conception of the motions of solar system bodies arose in the 16th and 17th centuries, marked by Copernicus's heliocentric model, Kepler's laws of planetary motions, and Newton's theory of gravitation.

This scientific milieu was the setting for the earliest known eclipse map, created in 1654 by German mathematician, astronomer, and philosopher Erhard Weigel. Weigel was a key figure in the German Enlightenment, a mentor to Gottfried Liebniz, and a leader of calendar reform in Germany. Weigel's eclipse map had been long forgotten until its recent recognition by German historian of astronomy Klaus-Dieter Herbst.

Weigel's calculations were based on the Rudolphine Tables, an early ephemeris calculated by Johannes Kepler, who applied his discovery of elliptical planetary orbits to Tycho Brahe's extensive observations of planetary motions. Remarkably, Weigel prepared his eclipse map on the day before the total solar eclipse of August 12, 1654. Weigel's map is fairly accurate and compares reasonably well with a reconstructed map of this eclipse. The point of greatest eclipse on Weigel's map matches the modern calculated position to an accuracy of about 100 kilometers (60 miles), quite impressive for the earliest effort!

More eclipse maps followed. In 1676 Johann Christoph Sturm, professor of astronomy, mathematics, and physics at Altdorf University in Bavaria, published a 34-page almanac. In a similar fashion to Weigel's map, he also depicted eclipses as a series of circles representing the Moon's outer (penumbral) shadow. But unlike Weigel, Sturm more accurately portrays the eclipse path as curved rather than as a straight line, which results from the combination of the passage of the Moon's inner (umbral) shadow, Earth's rotation, and the tilt of Earth's axis.

While at the Paris Observatory, Jean Dominique Cassini created a map for the path of the annular-total solar eclipse of September 23, 1699. Cassini's map is significant not for its greater accuracy but because it begins to resemble modern eclipse maps with features such as curves representing the maximum magnitudes of eclipse. At Denmark, the eclipse path on Cassini's map is about 150 km south of the true location and at the Crimean Peninsula, it improves to about 50 km south of the true path.

The May 12, 1706, solar eclipse crossed Europe and motivated many observations by astronomers of the day. Historian Robert van Gent has documented several maps produced in the Netherlands and Germany for this eclipse. In Amsterdam, Symon van de Moolen published a predictive eclipse map in 1705, and in Rotterdam, Andreas van Lugtenburg published a map in 1705 or 1706 with a rough path for the eclipse and detailed descriptions of eclipse circumstances for various places in Europe. Van Lugtenburg's map shows only three points with two connecting lines. The three points each seem to be accurate to within 300 km, but it's difficult to judge this map because the eclipse's path could be determined to a greater accuracy than the location of the continents on maps of this era.

Edmond Halley made a famous map for the total solar eclipse of May 3, 1715. Although not the earliest eclipse map as is often believed, Halley's map was nonetheless a significant advance. He applied Newton's laws of motion to create a map that predicted the eclipse path with an accuracy of about 30 km. Moreover, Halley solicited observations from the interested public to note where totality was actually observed, along with eclipse durations. Using reports from observers, he made a post-eclipse map with a corrected path that had an accuracy of about 3 km. Halley created additional maps with similar accuracy for the total solar eclipse of May 11, 1724.

Several British cartographers published maps for the solar eclipses of 1715, 1724, 1737, 1748, and 1764, a rare and fortuitous series of eclipses crisscrossing the British Isles within a relatively short time span. This was a golden era of eclipse mapping because of innovations such as the inclusion of the northern and southern limits of totality, lines of equal eclipse magnitude, and ovals representing the Moon's shadow at an instant of time.

The Next Step

A major breakthrough came in 1824, when German astronomer Friedrich Wilhelm Bessel developed an improved theory that simplified eclipse-path calculations. Bessel selected a frame of reference (the fundamental plane) through the center of Earth facing the Sun. This simplified the number of values needed to calculate the motion of the Moon's shadow and enabled faster computations of an eclipse path, which was advantageous in an era when calculations were done manually. Bessel's approach proved so successful that it remains the standard method of computing eclipse predictions today.

Around 1830 eclipse maps started to appear in three of the main annual ephemerides of the 19th century: the French nautical almanac Connaissance des Temps, the British Nautical Almanac and Astronomical Ephemeris, and the American Ephemeris and Nautical Almanac. Eclipse maps are just about the only illustrations that appear within these ephemerides, each of which contain hundreds of pages of numerical tables for the motions of the Sun, Moon, and planets, along with star positions.

Early ephemeris eclipse maps began as half-page graphics, then expanded to full-page maps, then as maps across a two-page spread, and finally as fold-out maps at the dawn of the 20th century. The map projections began with ill-considered choices such as the Mercator projection and were later replaced by map projections better suited for eclipses, such as the stereographic and orthographic projections. Early maps were spare in eclipse details, meaning they did not include features such as curves of equal magnitude or contact times. But more of this information appeared over the next several decades.

Although eclipse maps still appear in national ephemerides, most eclipse chasers turn to the NASA eclipse bulletins produced by Fred Espenak and Jay Anderson as the authoritative reference for eclipse predictions and maps. This series has been recently concluded, but Espenak and Anderson are launching a series of privately published eclipse bulletins, and Espenak provides many detailed predictions at his website, MrEclipse.com.

Canons of Solar Eclipses

Eclipse canons are collections of eclipse maps and tables spanning many years. Franz Ignatz Cassian Hallaschka published the first substantial canon of eclipses in Prague in 1816. The first volume of his book Elementa eclipsium contained eclipse maps from 1816 to 1860, and a second volume followed with eclipse maps through 1900. Hallaschka made a careful study of eclipse calculation techniques by luminaries such as Leonhard Euler, Joseph-Jerome LeFrancais de Lalande, and Joseph Louis Lagrange and developed a new method that anticipated Bessel's standard theory of eclipses.

In 1868 Austrian astronomer and mathematician Theodor von Oppolzer observed a total solar eclipse, and like many first-time eclipse observers, was deeply moved by the experience. He was inspired to organize a team to calculate the circumstances for a prodigious series of solar and lunar eclipses from 1200 BC to 2161 AD. These results were published in 1887 as the Canon der Finsternisse ("Canon of Eclipses"), which contained tables and maps of 8,000 solar and 5,200 lunar eclipses.

For each solar eclipse, von Oppolzer's team of 10 people calculated three points; the beginning, middle, and ending. Since each eclipse was mapped as an arc through these three points, the paths are not very accurate. Errors in estimates of the Moon's motion created inaccuracies for eclipse paths in the distant past. Still, the Canon was a groundbreaking feat of computation, and it became a vital resource for astronomers studying eclipse cycles and for historians identifying eclipses recorded in historical chronicles.

In the 20th century, several eclipse canons were built on improved methods of calculation and on computer technology. Jean Meeus, Carl Grosjean, and Willy Vanderleen published the Canon of Solar Eclipses in 1966 using IBM computers. In 1987 Fred Espenak produced the Fifty-Year Canon of Solar Eclipses: 1986-2035, which is still widely used by today's eclipse chasers. Canons have recently become available on the internet, such as Meeus and Espenak's Five Millennium Canon of Solar Eclipses.

Once you catch the eclipse bug, a canon becomes an essential expedition-planning guide for the remainder of your life. Eclipse chasing is a fascinating interest because you will visit distant and exotic places that you would probably never otherwise consider, and the journeys can be as remarkable as the eclipses themselves (July issue, page 36).

Extreme Precision Eclipse maps are currently being produced with even higher levels of accuracy and cartographic quality. I'm developing new maps by integrating eclipse calculations into geographic information systems (GIS) using calculations by Bill Kramer and Xavier Jubier and eclipse elements from Espenak and Meeus (a GIS performs sophisticated spatial analysis on a mapping database). I'm applying detailed base-map layers such as satellite imagery, terrain relief, and street networks within the GIS software. I use state-of-the-art cartographic techniques so that the eclipse maps are not only precise, but also display the appropriate level of geographic detail.

The mathematical models for each eclipse (the Besselian elements) are based on extremely accurate measurements of the motions of the Sun, Earth, and Moon. For example, the Moon's distance is now known to a precision of several centimeters due to measurements made from laser reflectors left by the Apollo astronauts. Using customized eclipse calculators, I process several tens of millions of gridded points within the path of each eclipse. I input these points with eclipse circumstances into a geographic model to derive eclipse features such as lines of equal eclipse duration. In 1887 von Oppolzer had to rely on the efforts of his team of 10 human calculators to find three points for each eclipse; we can exploit today's computer technology to quickly calculate many millions of data points.

Previous eclipse maps assumed a perfectly round shape for the Moon. In 2009 I collaborated with Kramer to make the first maps that account for the Moon's irregular profile due to lunar mountains and valleys. We used lunar profiles derived by David Herald from digital elevation models captured by the altimeter on Japan's Kaguya lunar orbiter. By comparing our prediction with a timing derived from a video recording of the July 22, 2009 eclipse, we estimate that our eclipse predictions and maps now have an accuracy of about 0.1 second.

Recently, I began to apply calculations by Jubier to take into account the effects of atmospheric refraction. This correction is important if you plan to witness an eclipse at sunrise or sunset because the refraction of the Sun's apparent disk will extend the eclipse path by several tens of kilometers. Jubier and I are currently working on incorporating surface elevations for every point on Earth for even higher accuracy. We are truly in the era of high-precision eclipse predictions and mapping.

We're also starting to see dynamic eclipse maps on smartphones and tablets. I envision this scenario for the August 21, 2017, total solar eclipse in the U.S.: It's two hours before the eclipse and you're driving in Wyoming to intercept totality. Because of widespread thunderstorms in the area, you abandon your planned viewing location. Your phone displays a map showing the eclipse path, topography, roads, and real-time traffic and weather data. Through a voice interface, you'll ask your map to provide an optimized driving route to dodge the predicted clouds at eclipse time as well as to avoid traffic congestion caused by other eclipse chasers. When you arrive at your destination near the centerline, you'll view a glorious total eclipse, upload the video you made with your phone, and then watch pictures and videos from others by tapping icons overlaid on the map.

RELATED ARTICLE: SAROS CYCLES

Astronomers as far back as about boo BCE could predict lunar eclipses with at least crude precision because of their knowledge that eclipses repeat themselves with a periodicity known as the soros cycle. In more recent times, Edmond Halley discovered that solar eclipses also follow saros cycles. This is a cycle that repeats every 6,585.33 days (about 18 years, 11 days). It's governed by three elements of the Moon's orbit: its 29.53-day period from New Moon to New Moon, its 27.55-day period from perigee to perigee, and its 27.21-day period from a node to the same node (a node is one of two points where the plane of the Moon's orbit around Earth intersects Earth's orbit around the Sun). Two consecutive eclipses belonging to the same saros sequence will occur 18 years apart, on the same calendar date plus 10 or 11 days, when the Moon is at the same node and at the same distance from Earth.

Michael Zeiler (michael.zeiler@yahoo.com) sits on the International Astronomical Union's Working Group on Solar Eclipses. He is an author of several books on geographic data modeling for his employer, Esri (www.esri.com). Zeiler operates www.eclipse-maps.com, which contains more than 1,500 historical eclipse maps and hundreds of new eclipse maps.
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Title Annotation:Astronomical Advances
Author:Zeiler, Michael
Publication:Sky & Telescope
Geographic Code:1USA
Date:Nov 1, 2012
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