|MadSci Network: Astronomy|
1. "And even though solar and lunar eclipses occur with comparable frequency, it is still far more commonplace to experience a lunar eclipse. That's because the darkened full Moon can be seen from anywhere on the nighttime half of the Earth during the eclipse. To see a total solar eclipse, you have to be in the path of totality. This path, sometimes up to 200 miles wide, never covers more than roughly one-half of one percent of the Earth's surface and often traverses open seas or remote regions of the planet. With fewer than 70 total eclipses per century, the chance to see one is for most of us a once-in-a-lifetime event." This is from Brian Brewer, http://www.earthview.com/tutorial/causes.htm
Guy Ottewell in his annual publication, Astronomical Calendar, and his Astronomical Companion, available from Skypub.com, explains that most often a solar eclipse, when the moon lines right up between us and the sun, is paired either two weeks before or two weeks after, or even both, as happened in July, 2000, with a lunar eclipse because the 5 degree tilt of the moon's orbit doesn't take it completely out of our shadow.
Fred Espinak has compiled a 5,000 Year Catalog of Solar Eclipses: http://sunearth.gsfc.nasa.gov/eclipse/SEcat/SEcatalog.html You might do a statistical analysis with all that data!
2. You're right about the frequencies of eliptical orbits - that's just the way the primordial dust cloud condensed and there are a great many eccentricities NOT equal to 0 (a circle is just an ellipse with 0 eccentricity) for whirling bodies to choose. But that is just using vacuous math to avoid a physical explanation. I suggest the answer to your question lies in the fact that no body, planet, comet, asteroid or star, is perfectly uniform in itself and that all the orbiting bodies in a system perturb each other from day one. Perhaps the wonder is that our solar system is so well behaved compared to all but one of the rest we have observed where Jupiter-sized planets careen madly in orbits of .3 or even greater eccentricities just a fraction of an A.U. from their suns. See the cover story of the October 2001 issue of Scientific American: "Refuges for Life in a Hostile Universe" by Guillermo Gonzalez, Donald Brownlee and Peter D. Ward.
Congratulations on your wonderful, inquisitive student!
James C. Veen Observatory
Lowell, Michigan, USA
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