I'm hoping some of the math geeks can help me out with this. I'm too lazy to do it the convoluted Sarah way, and I know some of you get off on formulas. On Winter Solstice 1995, we had not only the shortest day of the year, but also the darkest, as the new moon began that night. I was wondering how often this happens, given that a year has 365.25 days (allows for leap years) and the lunar cycle is 28 days with four stages (new, first quarter, full, last quarter). In other words, when will we have another Winter Solstice on the start of the new moon?28 responses total.
Tommorow, believe it or not.
http://www.google.com/search?hl=en&ie=UTF-8&oe=UTF-8&q=%22winter+solstice%2 2+%22new+moon%22&btnG=Google+Search (more specifically, http://itss.raytheon.com/cafe/qadir/q315.html ) (of course, the problem with his answer is that it doesn't use the calendar length [usually three 365-day years followed by a 366-day year; ignoring the "century rule"], but rather the actual length of 365.24 days. I don't know about you, but my calendar doesn't use fractional days. ditto for the lunar period, although I suppose that's more negotiable.) (that said, it's difficult to answer without knowing what time of day the moon rose on 1995's winter solstice. hrm. it's possible that the two events will again coincide in 2007, but the .56 day drift might be enough to push it off to the next day.) (plus, there's the matter of how precise you want the answer to be. is your new moon 7.3825 days long? how long is your solstice? which time zones are you willing to visit?)
To safely calculate this, you'd have to know the exact moment of the solstice and the exact moment of the new moon. But, in general, it should happen about 1 in every 29.5 years, since the length of a lunation (29.5 days) isrelatively prime to the length of a year (365.2425 days).
Carson slipped in, and raises a good point. I think the question is, "when will the solstice and the new moon occur on the same calendar day?"
(on December 21, 1995, in Gwinn, Michigan, a new moon rose into the morning sky at 6:38am EST, setting at 4:11pm EST. on the same day, in Chicago, Illinois, the same moon rose at 5:26am CST and set at 3:26pm CST.) (accepting that both moons on that day were actually new moons [factoid: the Islamic calendar does not consider a moon "new" until the first sliver of moon shows, whereas Hebrew calendars use the predicted new moon. these both can differ from an astronomical new moon.] and given the length of time that the new moons remained in the sky on that particular day, I feel safe in saying that, on December 21, 2014, a new moon will appear over both locations at some point during the day. I figure the moons will rise the evening before, but will remain in the sky throughout the morning. granted, I can't verify that either location, nor the moon itself, will still exist at that time, but otherwise I think the prediction is reasonable.) (how did I come up with that estimate? I divided the length of a year [365.2425 days] by the length of a lunar cycle [29.53 days], which worked out to roughly 12.3685, or how many lunar months there are per year. I then checked multiples of this number until I found a nearly whole number, which was about 235.002. by using a "whole" number, in theory, I would minimize the deviation from the actual day. next, I determined the actual scalar, or 19, that would correspond to years. and, finally, I used that number to determine roughly when the moons would be in the sky, given a regular lunar cycle, on that day [about 9.42 hours earlier].) (of course, none of the above actually answers the question either, but it's a lead.)
(addenda: I considered checking to see if the solstice would occur on the same day, despite leaping days, but quickly realized that, even if I could figure out that a new moon would happen on a particular day, I'm out of my league when it comes to determining a solstice. I found a neat NOAA site at http://www.crh.noaa.gov/ind/seasons.txt which shows the solstice as happening after the new moon sets. however, http://w3c.ct.astro.it/calendario/almanacco/2014almaeng.html suggests the solstice will take place before the new moon. of course, that's in Italy, and it may be different here in the States.)
Well, if you or someone else is interested in doing the math, AADL's Main branch has a book, Astronomical Algorithms by Jean Meeus, call number 520.212 ME that has formula for the solstices and the new moon dates. It is available to be checked out, but is sitting on my desk right this minute. I'll go return it to the proper shelf by 6:00pm. :)
Carson's right, 19 years is very close to exactly 235 months. So it will probably happen again in 19 years. But over the long haul, it should still happen about once every 29.5 years. (I guess I have to think about how to prove that...)
(the only problem with happening every 29.5 years is that the winter solstice would have to happen in the summer.) ;)
Yes, that does seem like a bit of a problem.
No, no. *On average*, meaning that in the next million years or so, it will happen about 1000000/29.5 times.
(hmm. still seems to me like the average would only be half that, i.e., 1000000/59. I admit that I haven't thought that approach through yet.)
The argument is this: the winter solstice happens on some say every year. On average, one out of every 29.5 days contains a new moon. Since the periods of the moon's orbit around the earth and the earth's orbit around the sun have no common factor, the day of the month that the solstice falls on is essentially random. Therefore on average, it should fall on the day of the new moon about once in every 29.5 trials. But, I haven't proved the part about the day of the month being essentially random.
Ah. That makes more sense. So really what carson has proved is that there have to be some irregularities in when it happens, since the solstice couldn't _regularly_ fall on the new moon every 29.5 years. Yes?
My head hurts, but you guys rock. :)
(I hesitate to say that I've proved anything [especially since my 2014 guess was off by one day!]; rather, I just extrapolated from known dates and rhythms. I haven't quite figured out how to work with a "set" time [solstice] and a "squishy" time [new moon], so I'm reasonably positive that there may be a new moon/solstice combo outside of the 19-year rhythm where the deviation from a whole year actually self-corrects and makes the two events coincide; I'd expect those times to be somewhere in the middle of the 19-year cycle. it's also entirely possible that what happens are "dry periods" where the two coincide every 19 years for a period of time, then drift before coinciding again. this would allow for Mark's predicted 29.5-year average.) (on a side note... http://w3c.ct.astro.it/calendario/almanacco/2033almaeng.html Dec 21/2033 13h46m53s Winter Solstice Dec 21/2033 18h48m New Moon http://w3c.ct.astro.it/calendario/almanacco/2052almaeng.html Dec 21/2052 4h17m New Moon Dec 21/2052 4h18m52s Winter Solstice ...so we can probably count on 2052 as the next time the two events actually occur simultaneously. Sarah, can you wait that long?) ;)
I didn't need them to coincide on the hour... just the day. :) I guess I wasn't specific enough. The cool thing about having a new moon the same day as Winter Solstice is that it becomes the shortest and darkest day of the year. :) Thanks for the work.
(I wasn't thinking so much that they occur in the same hour as I was that the moon actually be in the sky when the solstice happens. really, if the moon isn't in the sky, it's going to be a dark night anyway.) ;)
Oh shut up. ;)
If it's a new moon, the moon won't be up for most of the night anyway.
Baby moons have early bedtimes. Otherwise they're really cranky the next day.
Cute and funny all at once. :) "Baby moons"... I like that.
Re #13: Nothing is random, if you believe in Chaos Theory.
Re #23: Chaos and randomness are two very different things.
Chaos Theory isn't something you believe or don't believe - it's just a way of describing the behavior of certain systems. By "essentially random", in #13, I mean that the day of the month is on which the solstice falls is uniformly distributed over all possibilities.
>Chaos Theory isn't something you believe or don't believe - it's just a way >of describing the behavior of certain systems. On the contrary. That's why it's called a "theory." Not everyone subscribes to it.
Uh, no. That's not how mathematicians use the word theory.
Re #26: That is not a proper description of a scientific theory. We have theories of gravity, but you'd have to be an idiot not to believe that gravity exists. To confuse randomness and chaos only requires ignorance, thank goodness. (Chaos has been observed in putatively deterministic systems; a random system is not deterministic.)
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