One Exeligmos Unites Dec. 21, 2010, and Nov. 18, 1956, Lunar Eclipses

Summary: One exeligmos unites the Tuesday, Dec. 21, 2010, and Sunday, Nov. 18, 1956, total lunar eclipses in the Saros lunar 125 series of 72 similar eclipses.

Total lunar eclipse of Tuesday, Dec. 21, 2010, frames an exeligmos cycle (approximately 54 years 34 days) with total lunar eclipse of Sunday, Nov. 18, 1956, in lunar Saros 125 series: "Permission is freely granted to reproduce this data when accompanied by an acknowledgment, Eclipse Predictions by Fred Espenak and Jean Meeus (NASA's GSFC)," via NASA Eclipse Web Site

One exeligmos unites the Tuesday, Dec. 21, 2010, total lunar eclipse with the Sunday, Nov. 18, 1956, total lunar eclipse in the Saros lunar 125 series of 72 similar eclipses.

The Saros series of lunar and solar eclipses is based upon the Saros cycle. A Saros cycle approximates 6,585.3 days (18 years 11 days 8 hours). A Saros series comprises 70 or more eclipses, with each eclipse separated from its predecessor by one Saros cycle. A Saros series typically spans 12 to 15 centuries.

A Saros series recognizes similarities in occurrence in the series’ component eclipses. Every eclipse in a specific Saros series shares the geometry of association with the same one of the lunar orbit’s two nodes.

The lunar orbit’s ascending and descending nodes demark the two intersecting points of the lunar orbit around Earth with Earth’s orbital path around the sun. The nodes arise from the approximately 5.1 degree tilt of the moon’s orbit with respect to Earth’s orbit.

Even numbers are assigned to those Saros series with lunar eclipses occurring at the ascending node. Eclipses in even-numbered Saros series experience southward lunar movement with respect to the ascending node.

Those Saros series composed of lunar eclipses associated with the descending node receive odd numbers. Eclipses in odd-numbered Saros series exhibit northward lunar movement with respect to the descending node.

Every triple Saros cycle, a Saros series approximately revisits the same geographic region. The Saros cycle’s equivalence, at 18 years 11 days 8 hours, to less than a whole number of days accounts the cycle’s ending before Earth has completed a full rotation. The cycle’s ending on one-third of a day (eight hours) expresses as the Earth’s rotation of 120 degrees. The cycle’s 120-degree increments with each succeeding eclipse occasions the series’ return to the same geographic region every triple Saros cycle.

Three Saros cycles within a Saros series approximates 54 years 34 days. Greco-Roman astronomer and mathematician Claudius Ptolemaeus (ca. 100-ca. 170 CE) noted in chapter 2, On the Periods of the Moon, in Book 4 of his Almagest that ancient astronomers designated the triple Saros cycle with the term exeligmos. Astronomy historian Gerald James Toomer (born Nov. 23, 1934) explained in his annotated translation of Ptolemy’s astronomical treatise that exeligmos (Ancient Greek: ἐξέλιγμος) means “turn of the wheel.”

The total lunar eclipse of Sunday, Nov. 18, 1956, was centered on the northeastern Pacific Ocean, off the coast of northwestern Mexico. Visibility of the entire eclipse was available to North America, northwestern and parts of western central South America, northernmost Europe (Iceland, Norway’s Svalbard archipelago, parts of northwesternmost Russia) and northernmost Asia (Russian Far East). The Arctic Ocean, parts of the northwestern Atlantic Ocean and the Pacific Ocean (northeastern; northwestern Pacific’s marginal Bering Sea; parts of the southeastern Pacific) comprised the oceanic regions of entire eclipse visibility for the November 1956 total lunar eclipse.

The total lunar eclipse of Tuesday, Dec. 21, 2010, centers on the northeastern Pacific Ocean, west of the Baja California Peninsula. Entire eclipse visibility is available to North America, parts of northwestern South America (western parts of Venezuela, Colombia, Ecuador and Peru), northernmost Europe (Iceland; Norway’s Svalbard archipelago; northern Scandinavian Peninsula; northwestern Russia) and northern Asia (northern Russia). The oceanic regions of entire eclipse visibility comprise the Arctic Ocean, parts of the northwestern Atlantic Ocean and the Pacific Ocean (northeastern; parts of the northwestern; parts of the southeastern).

Ecliptic occurrence at the descending lunar node characterizes Saros 125, the Saros lunar series to which the November 1956 and December 2010 total lunar eclipses belong. Each successive lunar eclipse in the lunar Saros 125 series displays lunar movement northward of the descending node.

Lunar Saros series 125 requires 1,280.14 years to produce its 72 similarly occurring lunar eclipses. Saros 125 began with the 12th century’s penumbral eclipse of Wednesday, July 17, 1163. Saros 125 will end in the 25th century with the penumbral eclipse of Wednesday, Sept. 9, 2443.

The takeaway for the one exeligmos that unites the Tuesday, Dec. 21, 2010, and Sunday, Nov. 18, 1956, total lunar eclipses in the Saros lunar 125 series of 72 similar eclipses is that an exeligmos cycle of approximately 54 years 34 days explains the return of the December 2010 lunar eclipse to approximately the same visibility regions as those favored by the November 1956 lunar eclipse.

An exeligmos cycle (approximately 54 years 34 days) accounts for the similar geographic region visibility that the total lunar eclipse of Sunday, Nov. 18, 1956, shares with the total lunar eclipse of Tuesday, Dec. 21, 2010, in lunar Saros 125 series: "Permission is freely granted to reproduce this data when accompanied by an acknowledgment, Eclipse Predictions by Fred Espenak and Jean Meeus (NASA's GSFC)," via NASA Eclipse Web Site

Acknowledgment

My special thanks to talented artists and photographers/concerned organizations who make their fine images available on the internet.

Image credits:

Total lunar eclipse of Tuesday, Dec. 21, 2010, frames an exeligmos cycle (approximately 54 years 34 days) with total lunar eclipse of Sunday, Nov. 18, 1956, in lunar Saros 125 series: "Permission is freely granted to reproduce this data when accompanied by an acknowledgment, Eclipse Predictions by Fred Espenak and Jean Meeus (NASA's GSFC)," via NASA Eclipse Web Site @ https://eclipse.gsfc.nasa.gov/5MCLEmap/2001-2100/LE2010-12-21T.gif

An exeligmos cycle (approximately 54 years 34 days) accounts for the similar geographic region visibility that the total lunar eclipse of Sunday, Nov. 18, 1956, shares with the total lunar eclipse of Tuesday, Dec. 21, 2010, in lunar Saros 125 series: "Permission is freely granted to reproduce this data when accompanied by an acknowledgment, Eclipse Predictions by Fred Espenak and Jean Meeus (NASA's GSFC)," via NASA Eclipse Web Site @ https://eclipse.gsfc.nasa.gov/5MCLEmap/1901-2000/LE1956-11-18T.gif

For further information:

Espenak, Fred. “2010 Dec 21: Total Lunar Eclipse.” NASA Eclipse Web Site > Eclipses During 2010.
Available @ https://eclipse.gsfc.nasa.gov/OH/OH2010.html

Espenak, Fred. “Key to Catalog of Lunar Eclipse Saros Series." NASA Eclipse Web Site > Lunar Eclipses > Catalog of Lunar Eclipse Saros Series > Saros Series 125.
Available @ https://eclipse.gsfc.nasa.gov/LEsaros/LEsaroscatkey.html

Espenak, Fred. “Penumbral 1163 Jul 17.” NASA Eclipse Web Site > Lunar Eclipses > Catalog of Lunar Eclipse Saros Series > Saros Series 125.
Available @ https://eclipse.gsfc.nasa.gov/5MCLEmap/1101-1200/LE1163-07-17N.gif

Espenak, Fred. “Penumbral 2443 Sep 09.” NASA Eclipse Web Site > Lunar Eclipses > Catalog of Lunar Eclipse Saros Series > Saros Series 125.
Available @ https://eclipse.gsfc.nasa.gov/5MCLEmap/2401-2500/LE2443-09-09N.gif

Espenak, Fred. “Total 1956 Nov 18." NASA Eclipse Web Site > Lunar Eclipses > Lunar Eclipse Links > Catalog of Lunar Eclipse Saros Series > Saros Series 125.
Available @ https://eclipse.gsfc.nasa.gov/5MCLEmap/1901-2000/LE1956-11-18T.gif

Espenak, Fred. "Total 2010 Dec 21." NASA Eclipse Web Site > Lunar Eclipses > Catalog of Lunar Eclipses: Catalog of Lunar Eclipse Saros Series > Lunar Eclipses of Saros Series 1 to 180: Summary of Saros Series 101 to 125: 125 > Saros Series 125: 48 11 2010 Dec 21.
Available via NASA Eclipse Web Site @ https://eclipse.gsfc.nasa.gov/5MCLEmap/1101-1200/LE1163-07-17N.gif

Espenak, Fred. “Total Lunar Eclipse of 1956 Nov 18.” EclipseWise > Solar Eclipses > Six Millennium Catalog of Lunar Eclipses -2999 to +3000 (3000 BCE to 3000 CE) > 1901 to 2000 (1901 CE to 2000 CE).
Available @ http://eclipsewise.com/lunar/LEprime/1901-2000/LE1956Nov18Tprime.html

Espenak, Fred. “Total Lunar Eclipse of 2010 Dec 21.” EclipseWise > Solar Eclipses > Six Millennium Catalog of Lunar Eclipses -2999 to +3000 (3000 BCE to 3000 CE) > 2001 to 2100 (2001 CE to 2100 CE).
Available @ http://eclipsewise.com/lunar/LEprime/2001-2100/LE2010Dec21Tprime.html

Espenak, Fred; Jean Meeus. "Saros Series 125." NASA Eclipse Web Site > Lunar Eclipses > Catalog of Lunar Eclipse Saros Series.
Available @ https://eclipse.gsfc.nasa.gov/LEsaros/LEsaros125.html

Freeth, Tony. “Eclipse Prediction on the Ancient Greek Astronomical Calculating Machine Known as the Antikythera Mechanism.” PLOS ONE. July 30, 2014. DOI: doi.org/10.1371/journal.pone.0103275
Available via PLOS @ https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0103275#references

Toomer, G.J. [Gerald James]. Ptolemy’s Almagest: Book IV, page 175, note 8. London, England: Gerald Duckworth & Co. Ltd., 1984.
Available via Internet Archive @ https://archive.org/details/PtolemysAlmagestPtolemyClaudiusToomerG.5114/page/n182