>For example, remember how Keith Ramsay and Phillip Helbig pointed >out the existence of two kinds of day? There's the 24-hour >"solar day" and the 24-hour, 56-minute and 4-second "sidereal >day", depending on whether you watch the sun or the stars going >around.But note: The "sidereal" day is really reckoned with respect to the vernal equinox, which moves relative to the stars! It's dependent upon the precession rate. None of the other sidereal periods are so reckoned. (e.g., the tropical year is reckoned with respect to the vernal equinox, not the sidereal year, which is really reckoned with respect to the stars, as best as we know how).
>1) The SIDEREAL MONTH is the time it takes for the moon to orbit >360 degrees around the earth as viewed from the fixed stars. It's >27.321661 days long. (Don't ask me if these are solar or sidereal days - >I assume the former, but the thing I'm reading doesn't say.)Your assumption is correct. Days of 86,400 SI seconds are the standard unit for timekeeping in astronomy when "days" are mentioned without qualifier.
>This means that eclipses occur in a pattern which depends >on how the synodic and draconic months drift in and out of >phase. > >And *this* means that to predict eclipses, you need to find >a number which gives you something close to an integer when >you divide it by 27.321661 and also when you divide it by >27.212220.Except that you've used sidereal and draconitic months in your calculation here. Interestingly enough, the number 6585 + 1/3 is what you get for all three months (sidereal, synodic, draconitic), as well as for the anomalistic month! This means that the Saros duplicates not only the fact of an eclipse (Sun at node, Moon and Sun in conjunction) but also the kind of eclipse (annular or total in the case of solar eclipses). The Moon will be nearly the same distance from the Earth after one Saros period.
It's nice to point out that these near-integers are conveniently calculated using continued fraction expansions. I do this for my "TIME" course (for Freshmen nonscience students). Also, the 1/3 day means that the eclipse happens 1/3 of the way around the world. Eclipses are wonderful, just knowing the fact that an ancient eclipse occurred at a particular place gives very accurate information about earth rotation and the loss of spin angular momentum of the Earth.
>Q: Hmm, I'll have to think about it. But here's another question: >why do they call it the "draconic month"? Is this an allusion to >the Athenian lawmaker Draco or to the dragon-shaped constellation >of the same name? > >A: Hmm, good question - I don't know.The ancient idea was that a dragon ate the Sun or Moon, causing an eclipse. There are two nodes, the ascending node and the descending node. They are the "head of the dragon" and the "tail of the dragon", respectively. The symbol for the node looks like the Greek letter Omega; (except that the serifs are replaced by one or two little circles in the old-style symbol). That's for the ascending node. To get the symbol for the descending node ("tail of the dragon"), turn the symbol upside down!
>Q: Okay, one more: Though there officially 12 months in a year, >there are about 12.36 synodic months in a year - i.e., 12.36 new >moons per year. Doesn't this make life even more complicated? > >A: Sure! It means that the phases of the moon keep drifting out >of synch with the passage of the seasons. They loop around back >about once every 19 years - this is called the Metonic cycle. > >Q: Why's it called that? > >A: It was discovered by the Greek astronomer Meton in the 5th >century BC. The Babylonians may have discovered it earlier - >I don't really know - but Meton got his name on it.The Babylonians indeed knew the cycle. If you look at the development of the Babylonian calendar--see Parker and Dubberstein's book--you see that they gradually regularized the intercalations of the 13th month over the centuries. By the 3rd century BCE the intercalation scheme was the same same sequence as in the modern Hebrew calendar (and of course, the Hebrew calendar was derived from Jewish experience during the Babylonian captivity).
>Q: Hey! The Metonic cycle is pretty close to the Saros cycle: >19 years versus 18 years plus a bit. And these are both close to the >period of the nutation of the earth - 18.6 years. Is there something >interesting going on here? > >A: Hmm, that's a *very* good question. Coincidence, phase-locking, >or some sort of mathematical a priori relationship?Just a coincidence, I fear. As the Moon moves further from the Earth, the year stays about the same length and the synodic month gets longer, so the Metonic cycle, at least, will disappear when the fraction 7/19 is no longer a good approximation to the continued fraction.
The node regresses at a rate -0.75 m2 n, where m is the ratio n/N of mean angular motion of Moon to Sun (1/12.36 approximately) and n is the mean motion of the Moon. That's an n3 dependence, whereas the synodic motion goes as n. So as n changes, there's no reason to suspect that the relationship between synodic and draconitic month will be preserved as a simple fraction either.
>In the meantime, check these out for more info: >Different kinds of month: >http://www.hermit.org/Eclipse1999/why_months.html >Babylonian planetary theory and the development of heliocentrism: >http://www.hermit.org/Eclipse1999/why_months.html >Saros cycle versus Metonic cycle: >http://www.arval.org.ve/metonic.htmI'll look at these. Perhaps useful for my course. You might want to look at the pages I constructed:
http://quasar.as.utexas.edu/ast309.html
Cheers, Bill