Saturday, July 2, 2011

Welcoming Saros 156: July 1, 2011 Partial Solar Eclipse Pictures

A new Saros began yesterday at 08:39:11 UT. Even though nobody could see the eclipse (after all, 99% of the visibility was suspended over the ocean), nevertheless the moon blocked out 9.7% of the Sun. Taken by the Proba-2 satellite (by European Space Agency (ESA)), the below picture is a real picture of what happened yesterday. Although it does seen fake, it's the eclipse in a never-seen-before perspective.

Surprisingly, this was the only picture I could find on the eclipse. I guess it was the eclipse 'nobody could see!' By now, a few may be asking what Saros is? Starting a new Saros is rare - even though nobody could see the eclipse, it was still significant, but only under academic terms. As defined by a dictionary, Saros is simply:
The period of 223 synodic months, equaling 6585.32 days or 18 years, 11.32 days (or 10.32 days if 5 leap years occur in the interval), after which eclipses repeat but are shifted 120° west.
In Astronomical Events: Eclipses, Transits, Occultations, and Conjunctions, Matthew Winter writes this about Saros and the synodic (etc) months. Months will never be the same after reading this!
How are eclipsed formed? What are the requirements? There is a whole complex underlying structure that keeps eclipses in balance; where Saros comes into the picture. Saros determines when eclipses occur, where they occur, how they occur, why they occur, and much more. Despite this concept needs a paper for just it itself, Saros is easily understandable. Fred Espanak’s Glossary of Solar Eclipse Terms tells us what Saros is. ‘The periodicity and recurrence of solar (and lunar) eclipses is governed by the Saros cycle, a period of approximately 6585.3 days (18yr 11d 8h). When two eclipses are separated by a period of one Saros, they share a very similar geometry. The eclipses occur at the same node with the Moon at nearly the same distance from Earth and at the same time of year. Thus, the Saros is a useful tool for organizing eclipses into families or series. Each series typically lasts 12 or 13 centuries and contains 70 or more eclipses.’ 

First introduced by van den Bergh in 1955, numbering Saros cycles never appealed to anyone else before him. Currently, there are a total of 204 Saros cycles (thanks to van den Bergh) in use today with more than 20,000 eclipses (both solar and lunar) in a period of five-thousand years. Each of these eclipses happen during an eclipse season and in an eclipse season come types of periods (a fancy term for months). These four types of months (all with different day counts—a few are just by a matter of seconds!) all play their own role in Saros, which is what they are all comprised of. It’s not really mathematics, but numbers play a huge role in computing days and other essential matters. First, nodes and the nodical period play their part for eclipses to occur. A node is a general term which is used to express the intersection of two planes in space. The nodical period is the interval of time it takes the moon to make two successive crossings of either the ascending or descending nodes (ascending node: the moon crosses the ecliptic in the north, descending node is direct opposite—the south). The nodical period is 27.2122 days. After every year, the nodes move westward (which also referred to as lunar regression) on account of orbital motion, and must return to that same node before completing a complete orbit around earth. Nodes regress because the nodes result from the Sun’s gravity trying to pull the orbital plane of the moon into the plane of the ecliptic. As a result, the force causes the moon’s orbit to ‘wobble’ (nodical regression cycle) to the west. One ‘wobble’ takes 18.61 years. 

Secondly, the next month is the sidereal month. Although a strange name, its meaning is simple. A sidereal month is only the period of revolution of the moon around the earth, which is 27.321661 days. It’s not a perfect number of days; that’s why the phases of the moon shift a day on the regular calendar you have at your house. If a full moon’s on a Monday in January, then it will be on a Tuesday in February. Sometimes, two days will pass after the decimals (27.321661) build up to equal one day—every three to four months. 

The synodic period, another type of special astronomical month, is the length of time it takes for the moon to complete all its phases. This is from first quarter to first quarter of another month. Between the years 1600 to 2400 AD, the shortest synodic month is 29.27152 days and the longest, just a few hours later at 29.83262 days. But, on average the moon’s synodic month is 29.53059 days. Note that the synodic month is different from the sidereal month. The sidereal period does not include the time of phases, while synodic period does not determine the moon’s revolution alone. 

Lastly, comes the tropical month. Although seven seconds shorter than the sidereal month (27.32158 days), the tropical month is completely different than a sidereal month. The tropical month is the time taken for the moon to return to the same celestial longitude where it started its orbit. The sidereal month encompasses time of revolution—not the time to return to celestial longitude. So, both periods are totally different, yet so close to each other in time!

Once these terms are understood, then it is also necessary to understand Saros further by knowing what circumstances are necessary for the repetition of two eclipses; note they may not be similar. For one thing, the moon must be new (for solar eclipses) or full (for solar eclipses), and because the synodic period of the moon takes us about one-twelfth around the Sun; the earth, moon, and sun are not in the same alignment. To repeat the alignment, the moon must continue orbiting for two and one-sixth day. When this interval is added to the sidereal period, it turns out to be the synodic period—which you could also be called ‘the elongated sidereal period.’  While that is occurring, the moon must be at one of its node (either ascending or descending). So the chance that the moon is at one of its nodes and the correct position in the sky is rare. That’s why eclipses happen so rarely (and not every time it is at its nodes). So, 47 synodic months (1387.938 days) equals 51 nodical months (1387.822 days) which equal eclipse repetition! “In order for the repetition of an eclipse to occur, the same number of days must be contained within integral numbers of synodic and nodical months. Integers are whole or counting number such as -2, -1, 0, 1, 2, etc.” tells us about the repetition of two eclipses. “The numbers 47 and 51 are integers, while the numbers of whole days within 47 synodic months equals the same number of days in 51 nodical months.” The period of that time equals 3.8 years, and represents an eclipse cycle. It does not mean the eclipse will be similar, though. But, because different Saros series are currently running, eclipses occur more than one every 3.8 years! 

Circumstances for the repetition of similar eclipses are another matter. Even though this section is mainly towards solar eclipses, it may apply to lunar eclipses as well. Along with cemented, known facts about the repetition of similar eclipses (the moon must be at one of its nodes, it must be new/full, etc.), to repeat similarly, the moon must be at a similar distance from the earth. This makes an eclipse repeat itself. Then we are introduced to another period: the anomalistic month. The anomalistic month is the time interval between the moon’s apogee (farthest) and perigee (closest); it takes the time of 27.555 days and is longer than the sidereal month, with only 27.321661 days. The line of apsides, ‘which is the major axis of the moon’s elliptical orbit...and...Is the longest line segment that can be placed within the boundary of an elliptical orbit’ as defines, for the moon, the line of apsides finishes one revolution around the sky in the time interval of 8.85 years. Therefore, because the line of apsides completes one revolution in 8.85 years, the perigee and apogee continuously change their positions, creating uncertainty where the next apogee or perigee will be next, but we know that it will be ahead of its last location. Occasionally, the line of apsides will cause the moon to orbit faster on account of solar tidal forces, but this is not a dramatic effect; it is just thought of as another part of the moon’s orbit.

Finally, Saros enters the picture in full force. In order to meet conditions of similar solar eclipses, these things must occur: integral numbers of the synodic period, integral numbers of the nodical period, and integral numbers of the anomalistic month must all contain the same number of whole days. The result is Saros! Saros is a period of eighteen years, ten or eleven days (depending on whether it’s leap-year) and eight hours. 233 synodic months equal 6586.312 days which equal Saros! 247 nodical months equal 6585.375 days which equal Saros! (And) 239 anomalistic months equal 6585.538 days which equal Saros! So in conclusion, similar eclipses will repeat themselves in approximately 6585 days. However, the occurrence of the eclipse will be one-third day later (which is 0.321 day), shifting the location about 120 degrees west across the globe. That’s why we can get an eclipse in Antarctica in one year, and get another the next year (note that it’s part of another Saros cycle) we can get one over Alaska. More mathematics is required to go fully in-depth, but that is just too advanced for now. Saros is in incredible method!

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