Predicting Eclipses: How Does the Saros Cycle Work?

Boy, how about that total solar eclipse last Friday? And there’s more in store, as most of North America will be treated to yet another total lunar eclipse on the morning of April 4th. This eclipse is member three of four of a quartet of lunar eclipses, known as a tetrad.

Solar and lunar eclipses are predictable, and serve as a dramatic reminder of the clockwork nature of the universe. Many will marvel at the ‘perfect symmetry’ of eclipses as seen from the Earth, though the true picture is much more complex. Yes, the Sun is roughly 400 times larger in diameter than the Moon, but also about 400 times farther away. This distance isn’t always constant, however, as the orbits of both the Earth and Moon are elliptical. And to complicate matters, the Moon is currently moving 3 to 4 centimetres farther away from the Earth per year. Already, annular eclipses are more common in the current epoch than are total solar eclipses, and about 1.4 billion years from now, total solar eclipses will cease to happen entirely.

This has an impact on lunar eclipses as well. The dark inner umbra of the Earth is an average of about 1.25 degrees across at the distance from Earth to the Moon. The Moon’s orbit is inclined 5.1 degrees relative to the ecliptic plane, which traces out the Earth’s path around the Sun.  If this inclination was equal to zero, we’d be treated to two eclipses — one solar and one lunar — every 29.5 day synodic month.

This inclination assures that we have, on average, two eclipse seasons year, and that eclipses occur in groupings of 2-3.  The maximum number of eclipses that can occur in a calendar year is 7, which next occurs in 2038, and the minimum is 4, as occurs in 2015.

A solar eclipse occurs at New Moon, and a lunar eclipse always occurs at Full — a fact that many works of film and fiction famously get wrong. And while you have to happen to be in the narrow path of a solar eclipse to witness totality, the whole Moonward facing hemisphere of the Earth gets to witness a lunar eclipse. Ancient cultures recognized the mathematical vagaries of the lunar and solar cycles as they attempted to reconcile early calendars. Our modern Gregorian calendar strikes a balance between the solar mean and tropical year. The Muslim calendar uses strictly lunar periods, and thus falls 11 days short of a 365 day year. The Jewish and Chinese calendars incorporate a hybrid luni-solar system, assuring that an intercalculary ‘leap month’ needs to be added every few years.

But trace out the solar and lunar cycles far enough, and something neat happens. Meton of Athens discovered in the 5th century BC that 235 synodic periods very nearly equals 19 solar years to within a few hours. This means that the phases of the Moon ‘sync up’ every 19-year Metonic cycle, handy if you’re say, trying to calculate the future dates for a movable feast such as Easter, which falls on (deep breath) the first Sunday after the first Full Moon after the March equinox.

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A unique ‘moondial’ in front of the Flandrau observatory on the University of Arizona Tucson campus. Image credit: David Dickinson

But there’s more. Take a period of 223 synodic months, and they sync up three key lunar cycles which are crucial to predicting eclipses;

Synodic month- The time it takes for the Moon to return to like phase (29.5 days).

Anomalistic month- The time it takes for the Moon to return to perigee (27.6 days).

Draconic month- the time it takes for the Moon to return to a similar intersecting node (ascending or descending) along the ecliptic (27.2 days).

That last one is crucial, as eclipses always occur when the Moon is near a node. For example, the Moon crosses ascending node less than six hours prior to the start of the April 4th lunar eclipse.

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The evolution of a solar saros. Image credit: A.T. Sinclair/NASA/GSFC/Wikimedia Commons

And thus, the saros was born. A saros period is just eight hours shy of 18 years and 11 days, which in turn is equal to 223 synodic, 242 anomalistic or 239 draconic months.

The name saros was first described by Edmond Halley in 1691, who took it from a translation of an 11th century Byzantine dictionary. The plural of saros is saroses.

This also means that solar and lunar eclipses one saros period apart share nearly the same geometry, shifted 120 degrees in longitude westward. For example, the April 4th lunar eclipse is member number 30 in a cycle of 71 lunar eclipses belonging to saros series 132. A similar eclipse occurred one saros ago on March 24th, 1997. Stick around until April 14th, 2033 and you’ll complete a personal triple saros of eclipses, known as an exeligmos.

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A tale of three eclipses spanning 1997-2033 from lunar saros 132. Credit: Fred Espenak/NASA/GSFC

Dozens of saros series — both solar and lunar — are underway at any particular time.

But there’s something else unique about April’s eclipse. Though saros 132 started with a slim shallow penumbral eclipse way back on May 12th, 1492, this upcoming eclipse features the very first total lunar eclipse of the series. You can tell, as the duration of totality is a short 4 minutes and 43 seconds, a far cry from the maximum duration of 107 minutes that can occur during a central eclipse.

Created by author.
The evolution of lunar saros 132, showing five key eclipses out of the 71 in the series. Created by author

This particular saros cycle of eclipses will continue to become more central as time goes on. The final total lunar eclipse of the series occurs on August 2nd, 2213 AD, and the saros finally ends way out on June 26th, 2754.

Eclipses, both lunar and solar, have also made their way into the annuals of history. A rising partial eclipse greeted the defenders of Constantinople in 1453, fulfilling a prophecy in the mind of the superstitious when the city fell to the Ottoman Turks seven days later. And you’d think we’d know better by now, but modern day fears of the ‘Blood Moon‘ seen during an eclipse still swirl around the internet even today. Lunar eclipses even helped mariners get a onetime fix on longitude at sea: Christopher Columbus and Captain James Cook both employed this method.

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The rising partial eclipse as seen from Constantinople on May 22nd 1453. Image credit: Stellarium

All thoughts to ponder as you watch the April 4th total lunar eclipse. This eclipse will be visible for observers across the Pacific, the Asian Far East, Australia and western North America, after which you’ll have one more shot at total lunar eclipse in 2015 on September 28th. The next total lunar eclipse after that won’t be until January 31st 2018, favoring North America.

Welcome to the saros!

Read Dave Dickinson’s eclipse-fueled sci-fi tales Exeligmos and Shadowfall.

The Birth of a Saros – This Weekend’s Hidden Eclipse

As the first eclipse season of 2013 comes to an end this weekend, an extremely subtle lunar eclipse occurs on the night of Friday, May 24th going into the morning of Saturday, May 25th. And we do mean subtle, as in invisible to the naked eye… this eclipse only lasts 34 minutes in duration and less than 2% of the disk of the Moon enters the bright outer penumbra of the Earth’s shadow!

So, why talk about such a non-event at all?

Great things come from such humble beginnings. And while this weekend’s eclipse is one mostly for the almanacs and astronomical tables rather than a true observational event, it also marks the start of a new lunar saros cycle.

This weekend’s eclipse is one of five for 2013, a year which contains two solars and three lunars. This eclipse marks the end of the first “eclipse season” of the year, a time when the intersection of the Moon’s orbit (known as nodes) and the ecliptic nearly coincide with the position of the Sun (for a solar eclipse at New Moon) and the Earth’s shadow (for a lunar eclipse at Full Moon).

The current season began with a very slight partial eclipse on April 25th, followed by an annular eclipse on May 10th. It will last only 33 minutes and 45 seconds in duration starting at 03:53:11 UTC on May 25th. The Moon will be high over the Americas at the time, but again, shading on the southern limb of the Moon will be too slight to be seen.

Curiously, SLOOH will be providing live coverage of the eclipse, although again, it will be too slight to see.

Starry Night
The Full Moon just nicks the Earth’s penumbra in the early morning hours of May 25th. (Created by the author in Starry Night).

What is a saros? A saros is a period of 18 years 11 days and 8 hours after which an eclipse cycle lines up, producing a similar eclipse to the one that preceded it 18 years before. Note that due to its 8 hour offset, the Earth will have rotated 120° and the visibility region will have shifted westward.

In said period, three lunar cycles very nearly line up;

The Anomalistic month (the period the Moon takes to go from one perigee to another) = 27.555 days.

The Draconic month (the period the Moon takes to return to the same node) = 27.212 days.

The Synodic month (the most familiar one, the period between similar phases) = 29.531 days.

Note that:

239 Anomalistic months = 239×27.555= 6585.645 days.

242 Draconic months = 242×27.212=6585.304 days.

223 Synodic months = 223×29.531=6585.413 days.

There’s that mis-alignment of a third of a day again (8 hours) for every 18 years and 11 days. This also causes the node of each eclipse in the cycle to drift eastward by 0.5° along the ecliptic. Thus, each eclipse isn’t exactly the same. A lunar saros series starts with a very brief penumbral like this weekend’s, becomes deeper and deeper every 18+ year period until partial and total eclipses begin centuries down the road. Thereafter, the cycle reverses, until a final faint penumbral marks the end of the lunar saros.

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The progression of selected eclipses of the same saros cycle. (Credit: Matthew Zimmerman. Wikimedia Commons graphic in the Public Domain).

After this weekend’s eclipse, the next start of a lunar saros won’t occur until November 8th 2060 with the start of saros 156. The last new saros series (number 149) began on June 13th, 1984.

There are numbered saros series for both lunar and solar eclipses. There are currently 41 saroses (the plural of saros) active with the inclusion of this weekend’s start of lunar saros 150.

Saros 150, of which this eclipse is the 1st of 71, will last for just over 1,262 years. It will begin to produce partial eclipses on August 20th, 2157 and produce its 1st total on its 32nd lunar eclipse on April 29th, 2572.

It amazes me that ancient cultures such as the Chaldeans new of saros cycles and could predict eclipses. Being geographically isolated, lunar eclipse cycles would have been easier to decipher than solar ones, as you only have to be on the Moonward facing hemisphere of the Earth to witness the eclipse. They may well have stumbled upon the saros while attempting to calculate a slightly longer 19 year period known as a Metonic cycle to align ancient luni-solar calendars.

And yes, that 8 hour offset also means that after a triple saros period, lunar and solar eclipses of the same saros series do return to roughly the same longitude every 54 years & 34 days. This is known as an exeligmos, and if you get this on a triple-word score in Scrabble, you can safely retire from the game.

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The theoretical visibility circumstances for this week’s penumbral eclipse. (Credit: F. Espenak/NASA/GSFC).

And while this eclipse is more of academic than observational interest, you can always enjoy the light of a brilliant Full Moon. The May Full Moon is referred to as the Flower, Milk, and Corn Planting Moon by the Algonquian Indians of North America, alluding the latent season of Spring.

Also, keep an eye out for several conjunctions and occultations this week by the Moon with bright stars and planets.

The first up is the bright star Spica (Alpha Virginis) which gets occulted by the waxing gibbous Moon around ~11:00 UT on Wednesday, May 22nd for viewers across northern Australia, southern Asia and the South Pacific. Spica is one of four stars brighter than magnitude +1.5 that the Moon can occult, the others being Antares, Aldebaran and Regulus. This is the 6th occultation in a cycle of 13 of Spica by the Moon spanning 2013.

The planet Saturn will lie about 4° north of the waxing gibbous Moon on the following evening of May 23rd.

Also, watch for an occultation of the +2.6th magnitude star Beta Scorpii on the evening of May 24th around the time of the lunar eclipse. This will be a difficult one, as the Moon will be near 100% illumination. Conjunction of the Moon and Beta Scorpii in right ascension occurs at 3:04 UT on May 25th, about 2.5 hours after Full. The occultation will span the southeastern US, Caribbean, northern South America and western Africa.

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Visibility path of the occultation of Beta Scorpii by the Moon. (Credit: Occult 4.1.0.2).

2013 isn’t a grand year for eclipses. We’ve got two more in the late season of the year, another slightly deeper penumbral on October 18th and a hybrid solar eclipse on November 3rd. And when, may you ask, will we FINALLY have another total lunar eclipse? Stick around ‘til U.S. Tax Day next year (April 15th 2014) for a total lunar eclipse spanning the Americas!