HY DOES THE MOON SKIP AROUND?
-----------------------------
John Pazmino
NYSkies Astronomy Inc
www.nyskies.org
nyskies@nyskies.org
2015 August 14
Introduction
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One of the curious features of the solar-lunar motions around
Earth is the 'moon-skip' effect. Home astronomers commonly are shown
this when watching the perseid meteor shower, altho it occurs for any
annual event occurring on a given calendar date.
The Perseids happen to be one of the prime astronomy events that
take place on the same date each year. Almost all other astronomy
activity disregards the civil calendar or occur at irregular or random
instances. There are many meteor showers but the Perseids, for many
reasons, is the 'big one' for home astronomers. One reason is that it
can be counted on to give at least a pleasing fall of shooting stars,
at least a few tens per hour in the best years. Other showers are
more erratic, ranging form a good show to a dud, with only lousy
forecasts in advance.
One item emphasized for the Perseids is the location of the Moon
during the predawn hours of August 12 and 13, the days of the peak
downfall of shooting stars. In some years there is a large Moon in the
sky; on others, no Moon or a small one. The Moon adds her own luminous
graffiti to slash the number of meteors discernible. Only the brighter
ones are noticed, too few per hour to give the 'shower' effect.
The Perseids, with regard to the Moon's vicinity to them, have
favorable and unfavorable apparitions.
Lunar-3
-----
Meteor observers sometimes speak of this effect as the 'lunar-3'
or 'rule-of-3', the rough cycle of three years when the Perseids has
one good and two poor apparitions.
The rule is really crude because the Moon does NOT closely repeat
her location on a three-year cycle. In fact, the rule falls apart
after three round and has to reset by indexing one year for the next
set of rounds.
A more descriptive term, with no connotation of regularity, s the
'moon-skip' effect. Each year on the same date the Moon skips along
the zodiac to cause either a favorable or unfavorable influence on the
event on that date.
Lunar months
----------
The Moon takes one 'month' to circle Earth but there are many ways
to complete one lap of her orbit. The two that pertain to the Moon-
skip are the sidereal and synodic months. Other months, like the
draconic, tropical, and anomalistic months, play only a minor role for
this article.
I use here mean values for the parameters of the lunar orbit, which
is quite sufficient to show the Moon-skip effect.
The sidereal month is the interval between successive passings of
the Moon against the celestial sphere. Typicly it's the time between
conjunctions of Moon and a fixed star. This is 27.32 days.
The synodic month is the interval between successive instances of
a given phase or age of the Moon. Conventionally it's the period
between new Moons or full Moons. The synodic month is 29.53 days.
The synodic month is longer because after rounding the Earth once
for a sidereal month, the Sun moved downrange along the ecliptic. The
Moon must run for a couple more days to catch up and regain her next
new Moon phase and complete the synodic month.
Calendars
-------
Since the dawn of humankind we used the celestial activity to
regulate daily life. The day-night cycle is our day and the cycle of
seasons is our year. The latter works only for a temperate zone of
latitude, in which most of human culture flourished eons ago. much
later we learned that the seasons were tied to the apparent
circulation of the Sun around the Earth. When one cycle of season was
finished, the Sun made one lap around Earth.
There Moon gave us a third natural slice of time between the fay
and year. One cycle of phases was a handy span of 29 or so days.
Crudely there were 12 laps of phases in one lap of the Sun to make a
year.
It's the 'crudely' that throws the wrench into the neat order of
calendars. It would be wonderful os there was an integer count of
synodic months in a year! We would than count off synodic months,
cycles of phases, to keep track of the year.
This is far more secure than watching the seasons, like for first
frost or first bloom. Seasons do not repeat precisely year to year.
The Moon phases do. But not in step with the year.
Leftover days
-----------
One culture that wrestled with the Moon-Sun inequity of motion is
the Hebrew culture. Banking off of amazingly accurate work by
Babylonian astronomers, the hebrews figured out how to mesh the
synodic months into the solar year. They first count off 12 synodic
months and note that there were still about 10 days left over to
finish the solar year. This Hebrew year has 12 months and the 10 extra
days are put into a breadbox.
After sa second solar year there is a second 10 extra days. This
year also has 12 months and the extra days are put aside.
In the third year there is a third 10 extra days, amounting
closely to a full extra synodic month. This is handled by adding a
13th month to the year to bring the solar and lunar cycles back in
step.
In the actual Hebrew calendar the insersion of a leap month is NOT
every three years. The synodic month is 29-1/2 days and the leftover
days each year is more like 10-1/2 days. Three of these is 32-1/2
days, which is too much for a good fit by a synodic month.
The addition of leap-months follows a schedule that jiggers the
29-1/2 days and 31-1/2 days so that after 19 years the Moon and Sun
are almost exactly back in step. This account is NOT close to an clear
explanation of the Hebrew calendar but is meant to show one effort to
get the Sun and Moon to cooperate in calendar management.
Why 19 years?
-----------
Home astronomers are shown an other lunar rule, the 'rule-of-19',
when they study lunar and solar eclipses. The rule states, in its
simplest level, that given an eclipse, either kind, on a calendar
date, there is an other of the same kind on the same date 19 years
later and 19 years earlier. Eclipse chasers often mark their endurance
in astronomy by the number of 19-year cycles.
When an eclipse takes place the Moon, for a lunar eclipse, is
full. She also stands at a certain longitude along the ecliptic, that
opposite from that of the Sun for that day. On the next, later or
earlier, instance she again is full and occupies the same place in the
sky. Remember that the calendar date in the civil calendar is
essentially congruent with the longitude of the Sun.
There must be an integer number of sidereal months fitting into 19
years for the Moon to regain her longitude. There is also an integer
number of synodic months for the Moon to regain her phase in that 19-
year span.
We have for the sidereal months in 19 years
sidereal cycles = (19yr) * (365.25 day/yr) / (27.32 day/sid)
= 254 sidereal months
For the synodic cycles in the same 19 years we have
synodic cycles = (19yr) * (365.25 day/yr) / (29.53 day/syn
= 235 synodic months
The rule-of-19 is more general than only for eclipses. If the Moon
is observed at a given phase at a given longitude on a certain date,
that apparition repeats 19 years apart. The rule is not perfect. After
a few rounds it falls apart. At the same time a new 19-year cycle is
assembling to replace it for several more rounds. There is a break in
the sequence of years between the two cycles.
Within the 19 years
-----------------
Altho the longitude and phase come together after 19 years, they
are way out of step year to year. The offset is amazingly regular, one
that can be tabulated for foretelling where the Moon is in future
years. This a like the table of Hebrew leap months, which is used for
each 19 year span thru the ages with a calculated adjustment to jump
between closing and opening cycles two or three times per century.
We start with the sidereal months. There are 13 cycles of months
in a calendar year with part of the 14th month left to fill out the
year. The next year starts with this offset, the Moon running ahead of
its place since the previous year. Her place in the ecliptic is
displaced these extra days all thru this next year.
The extra days movement of the Moon into her 14 sidereal month is
excess movement = (360 deg/sid) * ((10.09day) / (27.32 day/sid)
= 132.96 deg
= 4 sign, 13 deg
This excess, the 'head start' for each successive year, is roughly
1/3 of the sky downrange in the zodiac. After three years the Moon
more or less returns to the same sign, producing the 'lunar-3'. After
three years the Moon actually moved along three times the 4sign, 13
degree, or 5 sign, 9 deg, The lunar-3 trick is really a poor one to
live by.
Moon phase
--------
An exactly parallel calculation is done to find the shift in Moon
phase within the 19-year period. We don't need the angular
displacement because it's simpler to state the phase as 'age' in days
since the preceding new Moon. Full Moon, halfway thru the 29.53 day
synodic cycle, is age 14.7 days.
excess age = )365.25 day/yr) - (12 syn) * (29.53 day/syn)
= 10.89 day
Each year on the same date the Moon is 10.89 days 'older'. The age
wraps around new several times in 19 years, eventually returning to
the same age at the end of the 19-year cycle.
Moon-skip table
-------------
We here step year by year and note the position of the Moon. We
start with the Moon in the zero degree of Aries, at the vernal
equinox. On the same date in the next year the Moon is 133 degrees or
4 signs, 13 degrees downrange, in Leo 13. We continue this for each
year for 19 years. Because the displacement is not exactly 132
degrees, we must hitch a degree once in a while, which I do here every
four years to spread the correction more evenly thru the 16-year span.
I start the age at new Moon, ae 00.0 days. This does NOT mean
there is or was an actual year when the new Moon was at the vernal
equinox. The two columns should be worked separately, once for the
displacement and an other for the age, from which so ever values for
each were in force at the instant starting date. A calculette is handy
for this chore, minding the rollover after each 30 degrees for the
sign and 29.53 days for each phase cycle.
It can be easier to imagine the Moon's movement with the sign-
degree notation. The table presents both longitude and sign-degree.
---------------
MOON-SKIP TABLE
------------------------------
yr | lon | sign | age | lap
---+--------+-----+------+- --
00 | 000 | Ari 00 | 00.0 | 0
01 | 133 | Leo 13 | 10.9 | 0
02 | 266 | Sgr 26 | 21.8 | 0
03 | 039 | Tau 09 | 03.1 | 1
04 | 171 | Vir 21 | 14.0 | 1
05 | 304 | Aqr 04 | 24.9 | 1
06 | 077 | Gem 17 | 06.2 | 2
07 | 210 | Sco 00 | 17.1 | 2
08 | 342 | Psc 12 | 28.0 | 2
09 | 115 | Cnc 25 | 09.3 | 3
10 | 248 | Sgr 08 | 20.2 | 3
11 | 021 | Ari 21 | 01.6 | 4
12 | 153 | Vir 03 | 12.4 | 4
13 | 285 | Cap 15 | 23.3 | 4
14 | 058 | Tau 28 | 04.7 | 5
15 | 191 | Lib 11 | 15.6 | 5
16 | 323 | Aqr 23 | 26.4 | 5
17 | 095 | Cnc 05 | 07.8 | 6
18 | 227 | Sco 17 | 18.7 | 6
19 | 000 | Ari 00 | 00.0 | 0
------------------------------
Use of the table
--------------
It is usually not feasible to tell just where in the zodiac the
Moon is, by her sign and degree or longitude. This is specially true
for twilight, large Moon, hazy sky. It is also usually not feasible to
tell the age of the Moon, particularly when she is near full.
These factors make the table impractical as an absolute cycle,
starting from a known location and age of the Moon. It is easiest to
employ it as a relative cycle. It is zeroed or homed at the 'year #0'
for the situation of the instant Moon.
For the position and age of the Moon in future years, read the
figures as positive, so many degrees downrange and so many days older
than now. For past years, the figures are negative, for uprange
position and younger age. As a sanity check, the Moon odes -- roughly
-- skip 1/3 way round the zodiac and 183 phase cycle per year with an
The typical application is to find if the Moon interferes with an
event on the same ate in various years. If, say, the Moon on the
instant occasion is nearly full in the east, she will be well below
the horizon, many hours before rising on the next year's event. She
also will be a waning crescent when she does rise. For this event
there is no Moon in the sky.
Do mind well that diurnal rotation can displace the Moon in the
sky, even tho during a night she moves only a few degrees thru the
zodiac and ages only a few hours. The displacement of position and age
are applied to the aspect of the Moon for a particular hour, like a
predawn hour for the Perseids. Assessing the Moon's aspect by the
Moon-skip table for the evening of an other year on the same date
yields nonsense results.
Conclusion
--------
While the Moon's movement seems at first complicated, there is a
cycle to it. The skipping of the Moon around the sky year by year has
a regularity that starts over again in 19-year blocks. Like other
astronomy cycles, this Moon-skip unravels after several rounds, long
enough to satisfy a person's lifespan but not to cover several
generations.
Most of us don't keep to hand almanacs for historical and future
years. The lunar position and age could be looked up in them for the
given calendar date. The Moon-skip table is a handy substitute in case
of wanting such almanacs.
Keeping this Moon-skip table handy helps to appreciate the lunar-
solar interactions and better bond you to the heavens. This is
specially true if you in fact observe the Moon annually, like at a
garden party each year to watch the 4th-of-July fireworks.