anti-blue moon?

As many of you know, the interpretation of a blue moon as the second
Full Moon in a month arose as a misinterpretation of a passage from an
old farmer's almanac. The correct reading of that almanac is, evidently,
that a blue moon is the third Full Moon in a season that has four (as
occasionally happens).

My question is, does the opposite ever happen? The usual course of
affairs is for there to be three in a season, but four happens rather
routinely. But is there ever a season with only *two* Full Moons?
Could there be a missing Full Moon--an anti-blue moon, if you will?

Consider: A year has about 365.24 days, and thus each season is about
91.31 days in length, on average. The Moon's synodic period, on the other
hand, is the average period between Full Moons, and is about 29.53 days.
If you multiply 29.53 by 3, you get only 88.59 days. That would seem
to eliminate the possibility of there being only two Full Moons in a
season.

However, as the ancient Greeks knew, the lengths of the season are not
all equal. Nor are the periods between Full Moons. In Hipparchus's
time, autumn (if we define it in the modern sense as the time between
the autumnal equinox and the winter solstice) was the shortest month,
lasting about 88-1/8 days.

Assuming that the synodic period of the Moon was about the same then as
it is now, there *could* have been an autumn now and then with only two
Full Moons. Imagine that the last Full Moon of summer occurred just 0.13
days before the autumnal equinox. Then the next Full Moon occurs 29.40
days after the equinox, the next one 58.93 days after, and the next one
after that at 88.46--enough to put it into winter.

The possibility of all this is increased if we take into account the
elliptical orbit of the Moon. The synodic period of the Moon is longer
than the sidereal period because as the Earth goes around the Sun in
its orbit, the Moon has to make a bit more than a complete revolution
around the Earth, as seen from the distant stars, in order to come
back in line with the Sun and Earth. That extra bit takes longer if
the Moon happens to be at apogee (when it revolves the slowest) when
Full Moon rolls around. I estimate that this would add about another
tenth of a day to each synodic period around Full Moon.

The catch to this is that the lengths of the seasons has not stayed
constant since the time of Hipparchus. In his day, perihelion took
place during autumn; now, it happens during winter. However, the date
of perihelion is less than two weeks after the winter solstice, meaning
that autumn and winter last almost equally long (with winter, I suppose,
being a tad shorter). They might both be too long to be able to stretch
out only two Full Moons to the season--but I haven't done all the math
to find out.

At some point, perihelion will take place in the middle of winter, and
it will then be the shortest season by a good margin. It seems almost
inescapable to me that there would be an anti-blue moon at some point
in time, even if it isn't possible in our epoch.

If any Sky and Telescope editors are reading this, I'd love to write
an article on this. Wink, wink.

Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.txt

"Brian Tung" wrote in message
...
As many of you know, the interpretation of a blue moon as the second
Full Moon in a month arose as a misinterpretation of a passage from an
old farmer's almanac. The correct reading of that almanac is,
evidently,
that a blue moon is the third Full Moon in a season that has four (as
occasionally happens).


If anyone is interested in the story of the misinterpretation -
http://skyandtelescope.com/observing...icle_127_1.asp

(Brian Tung) wrote:

It seems almost inescapable to me that there would be an anti-blue moon
at some point in time, even if it isn't possible in our epoch.

$ diary -r 120 19611220.0 | \
sed -n -e '/FULL MOON/p' -e '/Equinox/p' -e '/Solstice/p'
1961 Dec 22 00:41:18 FULL MOON
1961 Dec 22 02:19:29 Southern Solstice
1962 Jan 20 18:16:18 FULL MOON
1962 Feb 19 13:17:53 FULL MOON (Penumbral Eclipse)
1962 Mar 21 02:29:33 Northern Equinox
1962 Mar 21 07:55:24 FULL MOON

There are three other instances post 1AD, prior to 2000, and probably
a few more prior to 1AD (I only searched the DE 406 for 1-2000); I'll
leave those for you to publish in your article.

e-------- wrote:
$ diary -r 120 19611220.0 | \
sed -n -e '/FULL MOON/p' -e '/Equinox/p' -e '/Solstice/p'
1961 Dec 22 00:41:18 FULL MOON
1961 Dec 22 02:19:29 Southern Solstice
1962 Jan 20 18:16:18 FULL MOON
1962 Feb 19 13:17:53 FULL MOON (Penumbral Eclipse)
1962 Mar 21 02:29:33 Northern Equinox
1962 Mar 21 07:55:24 FULL MOON

There are three other instances post 1AD, prior to 2000, and probably
a few more prior to 1AD (I only searched the DE 406 for 1-2000); I'll
leave those for you to publish in your article.

Cool! Thanks for the tip. Do you have a pointer to "diary"? I'll look
for it via Google, but it's a sufficiently common word that I'm not sure
I'll be able to find it in a reasonable length of time...

Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.txt

One calculation shows 41 months that have 2 full moons @ per century.
Once each 2 1/2 years? Its technical definition differs from the various
colloqueal meanings applied to it over the years, since Shakespeare's time
at least. Its an old concept. Today I suppose it means "not very often"
implying rare occurrence of something as in "once in a blue moon". But
it has had ominous implications as in: "Never marry under a blue Moon.
Your marraige will be full of travail or Your first child willk be still born"

or "Children born under a blue moon are excpetional".

Personally Ive never seen what I would actually call a "blue" moon. Ive
seen several moons tending to violet, under cold dusty conditions. And
I wish my computer icon would stop flashing blue moons every two weeks!

Mark


Brian Tung wrote:

As many of you know, the interpretation of a blue moon as the second
Full Moon in a month arose as a misinterpretation of a passage from an
old farmer's almanac. The correct reading of that almanac is, evidently,
that a blue moon is the third Full Moon in a season that has four (as
occasionally happens).

My question is, does the opposite ever happen? The usual course of
affairs is for there to be three in a season, but four happens rather
routinely. But is there ever a season with only *two* Full Moons?
Could there be a missing Full Moon--an anti-blue moon, if you will?

Consider: A year has about 365.24 days, and thus each season is about
91.31 days in length, on average. The Moon's synodic period, on the other
hand, is the average period between Full Moons, and is about 29.53 days.
If you multiply 29.53 by 3, you get only 88.59 days. That would seem
to eliminate the possibility of there being only two Full Moons in a
season.

However, as the ancient Greeks knew, the lengths of the season are not
all equal. Nor are the periods between Full Moons. In Hipparchus's
time, autumn (if we define it in the modern sense as the time between
the autumnal equinox and the winter solstice) was the shortest month,
lasting about 88-1/8 days.

Assuming that the synodic period of the Moon was about the same then as
it is now, there *could* have been an autumn now and then with only two
Full Moons. Imagine that the last Full Moon of summer occurred just 0.13
days before the autumnal equinox. Then the next Full Moon occurs 29.40
days after the equinox, the next one 58.93 days after, and the next one
after that at 88.46--enough to put it into winter.

The possibility of all this is increased if we take into account the
elliptical orbit of the Moon. The synodic period of the Moon is longer
than the sidereal period because as the Earth goes around the Sun in
its orbit, the Moon has to make a bit more than a complete revolution
around the Earth, as seen from the distant stars, in order to come
back in line with the Sun and Earth. That extra bit takes longer if
the Moon happens to be at apogee (when it revolves the slowest) when
Full Moon rolls around. I estimate that this would add about another
tenth of a day to each synodic period around Full Moon.

The catch to this is that the lengths of the seasons has not stayed
constant since the time of Hipparchus. In his day, perihelion took
place during autumn; now, it happens during winter. However, the date
of perihelion is less than two weeks after the winter solstice, meaning
that autumn and winter last almost equally long (with winter, I suppose,
being a tad shorter). They might both be too long to be able to stretch
out only two Full Moons to the season--but I haven't done all the math
to find out.

At some point, perihelion will take place in the middle of winter, and
it will then be the shortest season by a good margin. It seems almost
inescapable to me that there would be an anti-blue moon at some point
in time, even if it isn't possible in our epoch.

If any Sky and Telescope editors are reading this, I'd love to write
an article on this. Wink, wink.

Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.txt

(Brian Tung) wrote:

Do you have a pointer to "diary"?

"diary" is member of a suite of unpublished programs of my own making
that use the JPL ephemerides. It produces output similar to the
"Diary of Phenomena" that is printed in the Astronomical Almanac(*).
The actual search was conducted through two other programs called
"phases" and "seasons" and a simple unix shell scipt using the usual
suspects -- awk, sort, sed, etc; diary was used only for the nifty
display.

I don't know if anything like this stuff exists elsewhere. It's kind
of specialized to the point of arcane. I don't publish it because of
this, but also because even 15 years later(**), I am still finding
silly bugs or misfeatures or the need to make necessary enhancements
in the code whenever I use it for some new problem(**). Most people
seem to like GUI-based planetarium software anyways. Can't they do
this sort of thing by now?

(*) with some differences
(**) initial versions used the van Flandern (et al) trigonometric
series
(***) thankfully, none required this time

e--------- wrote:
I don't know if anything like this stuff exists elsewhere. It's kind
of specialized to the point of arcane. I don't publish it because of
this, but also because even 15 years later(**), I am still finding
silly bugs or misfeatures or the need to make necessary enhancements
in the code whenever I use it for some new problem(**). Most people
seem to like GUI-based planetarium software anyways. Can't they do
this sort of thing by now?

I suppose some of them can, but I've always preferred using ordinary
text tools.

Thanks again for the lead, though--I might contrive something of my
own.

Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.txt

...is there ever a season with only *two* Full Moons?
Could there be a missing Full Moon--an anti-blue moon, if you will?
If any Sky and Telescope editors are reading this, I'd love to write
an article on this.

There are three other instances post 1AD, prior to 2000, and probably
a few more prior to 1AD (I only searched the DE 406 for 1-2000); I'll
leave those for you to publish in your article.

Sounds interesting.
The circumstances and rarity alone make it a worthy article.
But there would really be nothing to 'see'. They would only
be 'anti-blue moon', 'delinquent moon', or 'missing moon' seasons.
Maybe the status of one or both of the two
remaining Full Moons that are pulling the 'extra' seasonal shift
could be recognized as well (for public attention especially) e.g.,
the first could be the Late Moon, or the second: the Long Moon.
If you get my drift.

SSX

(SaberScorpX) wrote:

The circumstances and rarity alone make it a worthy article.

You can invent any number of 'rare' events though. This sort of thing
has an air of numerology to it...

But there would really be nothing to 'see'. They would only
be 'anti-blue moon', 'delinquent moon', or 'missing moon' seasons.

Over the 6000 year span of the DE-406 (3000BC to 3000AD), there are 50
defective seasons, 2260 (~10%) abundant seasons ("blue moons"), and
the remainder are normal. Defective seasons were much more common
prior to 1AD, and will again be common probably around 4000AD (hard to
say - I need a longer ephemeris). The one I reported in 1962 was the
first in over a thousand years, and there won't be another for a few
hundred more, when the old pattern begins to re-assert itself again.

Another way of looking at this is to ask: what is the shortest
interval between two successive blue moons? The answer is: ~177
days. In between such a pair is a defective season. The spectrum has
sharp peaks at (roughly):

177, 826, 914, 1003, 1090

days. (There appears to be no blue-moon pair in the same calendar
year though. Time for a new calendar if you ask me.)

If you plot the season length, the 3-Full Moon period, along with the
times of these defective and abundant moons, you get an interesting,
albeit cluttered, plot that basically tells you the entire story. It
even points out the "near misses".

e--------- wrote:
(There appears to be no blue-moon pair in the same calendar
year though. Time for a new calendar if you ask me.)

Nothing to do with the calendar, except for the accident that the
perihelion falls close to the end of the old year and beginning of
the new. Thus the deficient seasons are going to be autumn or winter.
Ten thousand years from now, the deficient seasons will be spring or
summer.

Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.txt