Boreal B[l]og

Next annular solar eclipse, 15 January 2010.  I hope to be in Kenya for it.

Next total solar eclipse, 11 July 2010.  I hope to fly it from El Calafate, Argentina, viewing it over the Chilean fjords.

Three things are necessary for an eclipse of the Sun.

1. The Moon has to be new; that is, between the Earth and the Sun.  This is the familiar  29 1/2 day cycle, which is 29.53059 days in length on average (it varies from cycle to cycle).
2. The Moon has to near one of the nodes of its orbit.  The Moon and Earth’s orbits are very nearly in the same plane, but not quite.  The Moon can be 5.1 degrees above or below the Earth’s plane.  That being the case, the two planes intersect in two places called nodes.  The Moon is large enough that it doesn’t have to be exactly at a node but just near enough to cause an eclipse.  The cycle of the nodes. called the draconic (the dragon eating the Sun) averages 27.21222 days.
3. The Moon and Earth’s orbit vary in distance from the Earth and Sun respectively.  The Moon can be close to the Earth and appear up to 7% larger than the Sun.  It can be far from the Earth and appear 10% smaller than the Sun.  The Sun varies within a narrower 3% in size, the Earth being closest in January and furthest from the Sun in July.  This anomalistic cycle is  27.54555 days long.  This determines whether an eclipse is total, with the Moon’s completely covering the Sun, or annular, where the Moon is inside the Sun so to speak, with a ring or annulus of sunlight around it.

223 synodic (typical) lunar months are 6585.3216 days.

242 draconic months are 6585.3572 days

239 anomalistic months are 6585.5375 days

18 years are 6574.365 days.

Put in 11 days more (and we have the 18 years 10 or 11 days (leap years) are almost exactly 6585.xxxx days above.  This means that the eclipses will repeat in similar fashion, but that extra 0.3 days moves the next member of the family about a third of the way west around the world.

I hoped this would be explained on one of the eclipse trips I went on but was told by a Sky and Telescope editor that people would think it was too nerdy.  (As if astronomers don’t already suffer that perception).  Frankly, anybody who goes to the effort of seeing one of these spectacles ought to be fascinated by the simple mathematics above!

Eclipses occur, therefore, in what is known as a SAROS cycle.  Each cycle is 18 years and 10 or 11 1/3 days depending upon leap years.  Eclipses are born near the poles as partials, become annular or total (or hybrid, where they are total in the middle and annular at each end), become partial and then disappear.  Each family of eclipses lasts about 70-75 cycles or about 1300 years.  An eclipse that begins at the ascending node of the orbit will start at the North Pole and move south with each family.  A descending node eclipse does the opposite.  The long eclipse of last July (and Baja in 1991, and Kenya in 1973) is Saros 136, a descending node eclipse now past its prime.  It will continue to give use total solar eclipses for the next couple of centuries, but the length of totality will be significantly shorter with each successive eclipse.

On the other hand, the eclipse of 29 Mar 06 has yet to reach its prime.  It will be the American eclipse of 10 April 2024 and will be extremely long in the 22nd century.

Hybrid eclipses mean that the Moon and Sun’s angular size are so closely matched that only at local noon, when the Earth’s curve bulges toward the Moon a few thousand miles, can there be totality.  The 8 April 2005 eclipse was one of those.

Many view eclipses without knowing or caring about all this stuff.  I think it is interesting, so I throw it in for those who are interested!

Tags: Total Solar eclipses

This entry was posted on September 13, 2009 at 12:45 and is filed under ECLIPSE CHASING. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.