WHY DOES THE MOON SKIP AROUND? ----------------------------- John Pazmino NYSkies Astronomy Inc www.nyskies.org firstname.lastname@example.org 2015 August 14 Introduction ---------- One of the curious features of the solar-lunar motions around Earth is the 'moon-skip- effect. Home astronomers commonly are shown this when eatching 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 actiivity distrgards the civil calendar or occur at irregular or andom instances. Ther 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 erakest 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 sunodic 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 preents both longitude and sign-degree. --------------- MOON-SKIP TABLE ------------------------------ yr | lon | sign | age | lap ---+--------+-----+------+- -- 00 | 030 | 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.