23 January 2017

Solar Eclipses and the Saros Cycle

Moon's Ascending and Descending Nodes
Eclipses are the outcome of a chance series of alignments between three bodies: the Sun, Moon and Earth. Orbital mechanics and the laws of Kepler ensure that these bodies circle each other in a beautiful series of harmonious ellipses, near perfect circles each with their own periodicity and in the case of the Moon, with its own orbital inclination. The interplay between the various cycles of the Moon orbiting the Earth, the Earth orbiting the Sun, and the Moon’s gradually changing orbital inclination lead to patterns that repeat over short, medium and long periods of time as these three bodies align.
Eclipses of Saros 145

One of the overall epicycles of these orbits is called the Saros Cycle. At any given time there are many Saros Cycles occurring coincidentally and the Great Eclipse on August 21st is a member of Saros 145. What does this mean? A Saros is an 18 year cycle in which three of the Moon-Earth cycles repeat nearly perfectly, the end effect of which is to create a near duplicate eclipse in this long period of time. The eclipse across Europe in August 1999 was a member of Saros 145, the most recent one of that Saros series until this coming August. In the intervening 6585 days there have been many other lunar and solar eclipses, but none with the exact geometry and timing that we saw in August 1999. So if you get a chance to see the eclipse in August 2017, know that it is virtually identical to the one experienced by observers in Europe 18 years ago. I was in Hungary for the 1999 eclipse and look forward to seeing the Great American Eclipse this summer, a chance to see an old friend again, a pleasant 2 minutes and 40 seconds where I am aligned with the Sun, Moon and Earth but not only just aligned, but in the specific geometrical arrangement that I witnessed 18 years prior. 

For a somewhat deeper look into the Saros Cycle, here are the basic three motions. (1) The Moon’s orbit around the Earth combined with the Earth’s orbit around the Sun leads to the well-known phases of the Moon that repeat every 29.5 days, the time from New Moon to New Moon, and we call that the Synodic Month. (2) At the same time, the Moon’s elliptical orbit around the Earth means we have a close approach and a more distant approach every month and the time between two successive closest approaches (Perigee) is 27.55 days, a time period that is called the Anomalistic (Perigee) Month. (3) Finally the Moon orbits the Earth on a slightly inclined orbit so at times the Moon is ascending from below to above the plane of the solar system (‘ascending node’) or descending from above to below the ecliptic plane (‘descending node’). The time period from one ascending node to the next is called a Draconic Month which is 27.21 days. If you combine all three of these time periods, they nearly perfectly repeat after 18 years and 10 or 11 days (depending on the number of Leap Years between the two years in question), constituting the repetition period of consecutive eclipses in a Saros Series. Saros 145 eclipses took place on August 11th 1999 and on August 21st 2017. And of course the next Saros 145 eclipse will arrive on September 2nd 2035, right on schedule!

For more on this subject, Wikipedia has an excellent write up

Images courtesy NASA. 

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