Oleg Zabluda's blog
Thursday, May 24, 2012

Solar eclipse of May 20, 2012 was annular (magnitude 0.9431, width 237km, duration 5m 46s).
Solar eclipse of May 20, 2012 was annular (magnitude 0.9431, width 237km, duration 5m 46s). That why we didn't bother driving 4 hours north from San Francisco Bay Area to Reno/Shasta/Redding. We had Maker Faire to catch. It it were total, we would have gone.

It was Deja Vu all over again. Solar eclipse of May 10, 1994 also was annular (magnitude 0.9439, width 230 km, duration 6m 13s), and that's why, back then, we also didn't bother driving 4 hours north from Columbus, Ohio to, say, Toledo, Ohio.

What a, amazing coincidence?! Not really.

Both eclipses are from the same Saros 128 (http://en.wikipedia.org/wiki/Solar_Saros_128), #57 and #58 (of 73) respectively.

Saros is exactly 223 Synodic months or 223*29.530589=6585.32135 days. One saros after an eclipse, the Sun, Earth, and Moon return to approximately the same relative geometry, and a nearly identical eclipse occurs [2].

Saros repeats every 6585.32135 days, or 18 years, 11 days. This also checks out. The difference between

Tue, May 10, 1994 at 17:07 UTC
Sun, May 20, 2012 at 23:47 UTC

is 6585 days (=18 years, 10 days), 6 hours, 40 minutes or 6585.278 days [4]

By the amazing coincidence, and some resonances, saros divided by the following are [almost] whole numbers:

6585.3213/29.530588853 = 223.000000 Synodic months [1]
6585.3213/27.212220817 = 241.998672 Draconic months
6585.3213/27.554549878 = 238.992157 Anomalistic months
6585.3213/365.242189 = 18.0300127 Tropical years

Synodic month is critical, because it's got to be New Moon.

Draconic is a must because otherwise during the New Moon, the Moon will not be on the ecliptic, and, by definition, will not eclipse anything. The fact that it's 2 min short of 242 days, is responsible for the fact that the saros has beginning and end. Over 73 eclipses, 2min*73=2.3 hours, shifting the Moon too far from ecliptic and making the moon's shadow to miss the Earth altogether.

Almost exact whole number of Anomalistic months (11.3 min short of 239 days) is a bonus (due to some resonances) and causes the circumstances of the eclipse to be even more very similar. i.e if #57 was very annular, #58 surely will be too). In 11.3 min Moon moves by 700km, but Earth-Moon distance changes by at most 30 km. However, over 73 eclipses in a saros cycle, it slowly adds up to 2100 km, which is enough to change magnitude by 0.006.

Almost exact number of Tropical years is also a bonus, because since the saros is only 11 days longer then to 18 Tropical years, Sun-Earth geometry will also be nearly identical eclipse-to-eclipse in the saros, but the difference does accumulate (11*73)/365=2.2 years.

You can see similarity in type, magnitude, width, duration, latitude, etc..

Let's put our 2 eclipses from Saros 128 into some context:
#01 (first) Aug 29, 984
#57 May 10, 1994
#58 May 20, 2012#59 (next) Jun 1, 2030
#73 (last) Nov 1, 2282

http://en.wikipedia.org/wiki/Solar_eclipse_of_May_10,_1994 http://en.wikipedia.org/wiki/Solar_eclipse_of_May_20,_2012

More coincidences: San Francisco, Reno, Toledo, University Park, NYC, are all on I-80.

[1] http://en.wikipedia.org/wiki/Month

[2] But because 0.32135 is almost exactly 1/3 of a day (17 min less) the Earth turns almost 1/3 of the way around, so the eclipse is identical, except 116 degrees farther to the west. And what's 116 degrees west of Toledo, OH? Tokyo, Japan.

[3] There is a difference between New Moon (when Moon's ecliptic longitude is equal to Sun's and is what we really care about) and Max Eclipse (which is when Moon-Sun line passes closest to Earth center, and which we care about only approximately):
Tue, May 10, 1994 at UTC (17:12:27 max eclipse) (17:07 New Moon)
Sun, May 20, 2012 at UTC (23:53:54 max eclipse) (23:47 New Moon)
the two can differ by ~(1/360)*sin(5.145°)*29.5*24*60 = 10.5 minutes

[4] It's 10 calendar days instead of 11 because of 5 leap years. (.32135 - .2778)*24=1.0452 hours. Don't worry, heavens are not broken. 29.530588853 is an average Synodic month. Because of perturbations in the orbits of the Earth and Moon, the actual time between lunations is 29.18-29.93 days. So what if the in this saros cycle the average synodic month was (1.0452*3600)/223=16.9 seconds shorter.
http://en.wikipedia.org/wiki/Solar_eclipse_of_May_10,_1994

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