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| Author |
Message |
michaela
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Math Problem
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Jun 26 17:27 UTC 2003 |
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?
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| 28 responses total. |
polytarp
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response 1 of 28:
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Jun 26 18:47 UTC 2003 |
Tommorow, believe it or not.
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carson
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response 2 of 28:
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Jun 26 19:07 UTC 2003 |
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?)
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aruba
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response 3 of 28:
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Jun 26 19:07 UTC 2003 |
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).
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aruba
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response 4 of 28:
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Jun 26 19:13 UTC 2003 |
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?"
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carson
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response 5 of 28:
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Jun 26 20:09 UTC 2003 |
(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.)
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carson
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response 6 of 28:
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Jun 26 20:22 UTC 2003 |
(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.)
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kip
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response 7 of 28:
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Jun 26 21:27 UTC 2003 |
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. :)
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aruba
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response 8 of 28:
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Jun 27 00:51 UTC 2003 |
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...)
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carson
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response 9 of 28:
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Jun 27 01:47 UTC 2003 |
(the only problem with happening every 29.5 years is that the winter
solstice would have to happen in the summer.) ;)
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orinoco
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response 10 of 28:
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Jun 27 03:09 UTC 2003 |
Yes, that does seem like a bit of a problem.
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aruba
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response 11 of 28:
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Jun 27 05:05 UTC 2003 |
No, no. *On average*, meaning that in the next million years or so, it will
happen about 1000000/29.5 times.
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carson
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response 12 of 28:
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Jun 27 05:24 UTC 2003 |
(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.)
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aruba
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response 13 of 28:
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Jun 27 12:38 UTC 2003 |
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.
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orinoco
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response 14 of 28:
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Jun 28 16:26 UTC 2003 |
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?
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michaela
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response 15 of 28:
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Jun 29 09:22 UTC 2003 |
My head hurts, but you guys rock. :)
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carson
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response 16 of 28:
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Jun 30 12:24 UTC 2003 |
(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?) ;)
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michaela
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response 17 of 28:
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Jun 30 18:02 UTC 2003 |
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.
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carson
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response 18 of 28:
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Jun 30 18:25 UTC 2003 |
(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.) ;)
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michaela
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response 19 of 28:
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Jun 30 22:20 UTC 2003 |
Oh shut up. ;)
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orinoco
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response 20 of 28:
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Jul 1 00:56 UTC 2003 |
If it's a new moon, the moon won't be up for most of the night anyway.
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other
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response 21 of 28:
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Jul 1 05:41 UTC 2003 |
Baby moons have early bedtimes. Otherwise they're really cranky the next
day.
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michaela
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response 22 of 28:
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Jul 1 19:34 UTC 2003 |
Cute and funny all at once. :) "Baby moons"... I like that.
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gregb
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response 23 of 28:
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Jul 8 02:01 UTC 2003 |
Re #13: Nothing is random, if you believe in Chaos Theory.
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russ
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response 24 of 28:
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Jul 9 02:12 UTC 2003 |
Re #23: Chaos and randomness are two very different things.
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