MOON'S VOID OF COURSE ------------------- John pazmino NYSkies Astronomy Inc www.nyskies.org firstname.lastname@example.org 2007 September 23
Introduction ---------- An old astronomy acquaintance recently returned to the stars and got to chatting with me about, uh, astrology. While I have little belief in the mumbo-jumbo of astrology, there are curious astronomy features in it. Well, we got to discussing the 'void of Moon'. No, this is NOT a function cared for in the restroom!
Void of the Moon -------------- 'Void' here means 'gap', 'hiatus'. It's the interval between the final aspect of the Moon with any other planet within the Noon's current zodiac sign and the Moon's departure from that sign to enter the next one. A diagram makes this concept easier to understand
0 G e m i n i 2 G e m i n i 1 G e m i n i 0 0 0 0 0 - | - - - - - - - - - : - - - - - - - - - : - - - - - - - - - | - - e d c b a Lun-dep-Gem Lun-60W-Mar Lun-cnj-Sun Lun-arr-Gem | | Lun-cnj-Jup |<----void of course--->|
The slice of ecliptic above is within the sign of Gemini, which for the astronomer is the same slice as ecliptic longitude 60 degree thru 90 degree. The previous sign to the right or west, is Taurus. The next sign, to the east or left, is Cancer. Within each sign the degrees are numbered 0 thru 29, but I hear of astrologers numbering them 1 thru 30. While astronomers hardly ever use the sign-degree notation, this method of expressing longitude along the ecliptic does indicate roughly a planet's location among the stars. The main caution is that the signs are slipped against the constellations by precession thru quite one full sign, 30 degrees. The SIGN of Gemini is more or less centered on the CONSTELLATION of Taurus. Gemini 10, for example, is near Aldebaran in Taurus. The Moon courses thru the zodiac, west to east, right to left in the diagram. She enters Gemini at point a ot such-&-such a day and hour. She continues downrange and attains an aspect with Jupiter at point b, then an aspect with the Sun at c, finally an aspect with Mars at d. She leaves Gemini, moving into Cancer, at d. The time spent between the aspect with Mars, d, and leaving Gemini, e, is when the Moon is 'void of course' or the period of the 'void of the Moon'. There is no objective significance to this interval but the usual astrological interpretation is that a person should avoid major decisions and critical actions during this period. it's a sort of 'rest' period, which is probably as good a way to enforce a periodic and frequent relaxation as any other I can think of.
Precession -------- To an excellent first order correction, precession slides only the ecliptic longitudes, increasing them about 50 min per year or 1d23m per century. This slow motion was discovered by Hipparchus in about 200BC. The ecliptic latitudes are not changed. Astrology of today is still based largely on the works of Ptolemaeus, who flourished in the 100s AD. His astrology book Tetrabilios is a companion to his astronomy treatise Almagestum. At that time, the ecliptic longitude scale, starting at the vernal equinox, was zeroed near gamma Arietis. The vernal equinox is sometimes called the gamma-point from this early location, as well as from the resemblance of the Aries symbol with the Greek letter. Since then, precession slided the vernal equinox, and the entire longitude scale, westward thru Aries, into Pisces, where it stands now. The shift over quite two thousand years is about 28 degrees. This is nearly a full zodiac sign. In the coming centuries, as precession continues, the drift will accumulate more closely to 30 degrees. The immediate result of precession is that the zodiac SIGNS, the 30-degree segments of the ecliptic, are one unit out of phase against their original constellations. The stars beyond a given sign are those of the preceding sign's constellation. The table here gives the sign-degree and longitude of many stars near the ecliptic for epoch 3000:
-------------------------- STARS NEAR THE ECLIPTIC -------------------------- | star | sign | lon | +---------+--------+-----+ | gam Peg | Ari 9 | 9 | | alp Psc | Ari 29 | 29 | | gam Ari | Tau 4 | 34 | | alp Ari | Tau 8 | 38 | | alp Cet | Tau 14 | 44 | | eta Tau | Gem 0 | 60 | | alp Tau | Gem 10 | 70 | | bet Tau | Gem 23 | 83 | | zet Tau | Gam 25 | 85 | | gam Gem | Cnc 9 | 99 | | lam Gem | Cnc 19 | 109 | | bet Gem | Cnc 23 | 113 | | eps Cnc | Leo 7 | 127 | | eps Hya | Leo 12 | 132 | | alp Leo | Vir 0 | 150 | | bet Vir | Vir 27 | 177 | | gam Vir | Lib 10 | 190 | | alp Vir | Lib 24 | 204 | | alp Lib | Sco 15 | 225 | | del Sco | Sgr 3 | 243 | | alp Sco | Sgr 10 | 250 | | eta Oph | Sgr 21 | 261 | | M 8 Sgr | Cap 1 | 271 | | sig Sgr | Cap 12 | 282 | | eta Sgr | Cap 16 | 286 | | bet Cap | Aqr 4 | 304 | | del Cap | Aqr 24 | 324 | | lam Aqr | Psc 14 | 342 | | gam Psc | Psc 21 | 351 | +---------+--------+-----+
Note the peculiar abbreviations for Cancer, Sagittarius, Pisces. There are other constellations beginning with 'can' and 'sag' and the obvious abbreviation for Pisces is a naughty word in French. Astrologers almost never deal with extrazodiacal constellations and they do deal with naughty topics occasionally, so there is no conflict. They use Can for Cancer, Sag for Sagittarius, and Pis for Pisces.
Elongation -------- The difference in longitude between two planets -- including the Sun and Moon -- is the elongation of the one against the other. The 'base' planet is the zero mark and other planets are banked off of it. In astronomy just about the only elongations calculated are those against the Sun. This is for giving a clue to the planet visibility. If the planet is too close, too small elongation, to the Sun, it is lost in daylight or twilight. For recognition's sake, because visibility near the Sun is a compound of many, often unpredictable, factors, we allow an exclusion zone of 15 degrees elongation, to either side. Such considerations of close elongation for the Moon play a major role in some calendar keeping in some cultures. The star of months are declared by the first visual sighting of the Moon after new Moon. Elongation is counted either way, from planet A to B or B to A. It is important to state which sense is given. There seems to be no generally accepted algebraic signum for elongations. A weak standard is that elongations to the east, downrange, along the ecliptic, are positive; uprange to the west, negative. The calculation of elongations from the Sun is a common feature of planetarium and ephemeris computer programs. On the other hand, just about none offer elongations banked off of any other planet. To find, say, the elongation of Mars from Jupiter on a given day, you have to subtract the two solar elongations, thusly
ecliptic Mar Jup Sun - - - - - - - - - - - - * - - - - - - - - - * - - - - - O - - - -- | |<-Jup/Sun--| |<--Mar/Sun---------------------| |<--Mar/Jup---------|
The elongation of Mars from Sun and of Jupiter from Sun are taken from an astronomy program. The elongation of Mars from Jupiter is figured by manual subtraction. The diagram is a linear one: the sky is circular. This makes linear arithmetic on elongations a bit tricky. You MUST mind the crossing of the zero point, the Sun in almost all cases. Making a circular diagram will help avoid silly mistakes of signum and direction. It's amazing how easy it is to cross east & west, prograde & retrograde, positive & negative.
Latitude ------ For run of the mill stargazing, the latitude of a planet from the ecliptic is ignored. With the grosser portion of a planet's motion being in longitude, parallel to the ecliptic, this is fine. In critical situations, latitude is important, like a close convention of several planets and stars or an occultation of a star or planet by the Moon. Under the geocentric model of the solar system, the longitudes were reasonably well replicated in the calculations. Latitudes were a killer. No decent method could get them right. It was only with the heliocentric model, where the planets run in orbits tilted against Earth's orbit, that the latitudes fell into place.
Aspects ----- The Moon is always in SOME elongation relative to each other planet at any instant. However, certain elongations are specially important. In astronomy, the chosen special elongations indicate the visibility of the planet relative to the Sun. The most common ones are ----------------------- aspect elongation ----------- ---------- conjunction 0 degree grtest elong ~27 deg for Mercury, ~47 deg for Venus station range of values for each superior planet quadrature 90 degree opposition 180 degree ------------------------
The excentric orbits cause the greatest elongation and stations to range several degrees from instance to instance. The astrologer has several aspects, based on a square and hexagon fitting inside the circle of the ecliptic. With one point of the square or hexagon anchored on a planet, the major aspects are:
aspect elongation -------- ---------- conjunct 0 degree sextile 60 degree square 90 degree trine 120 degree opposite 180 degree
Actually, each 15 degrees of elongation can be an aspect. Most of these are seldom considered in astrology. The astrologer's square is the astronomer's quadrature when the base planet is the Sun. Both sets of aspects are symmetrical east-west around the base planet. Trine, as example, may be an eastern or western, positive or negative, sinister or dexter trine. Conjunct and opposite are treated as coincident aspects according as they are approached from the east or west. The astrologer misses the stations and greatest elongations, even tho these are critical points in the path of a planet. The astronomer misses the aspect for 15 degrees from the Sun, even tho it is a handy index of when the planet enters and leaves the Sun's exclusion zone. These aspects are counted from the location of ANY planet, not just the Sun. You can imagine that EACH planet carries with it a ring or band for its OWN elongation scale as it wanders thru the zodiac. Thus, each fixed point of the ecliptic, like 10 Gemini, is at the same time a degree of elongation, all different, for each of the seven planets. Sort of like:
0 G e m i n i 2 G e m i n i 1 G e m i n i 0 0 0 0 0 - | - - - - - - - - - : - - - - - - - - - : - - - - - - - - - | - - Sun - - - - -120- - - - - - - - - : - - - - - - - - - : - - - - - - Lun - - - - - - - - - : - - - - - - - - -030- - - - - - - - - : - - Mer - -120- - - - - - - - - : - - - - - - - - - : - - - - - - - - - Ven - - - - - - - -120- - - - - - - - - : - - - - - - - - - : - - - Mar - - - : - - - - - - - - - : - - - - - - - - -030- - - - - - - - Jup - - - - - - : - - - - - - - - - : - - - - - - - - -150- - - - - Sat - - - - : - - - - - - - - -060- - - - - - - - - : - - - - - - -
In this instance, the 10th degree of Gemini is also the 106th degree of elongation from the Sun; 30th, Moon; 103rd, Mercury; 109th, Venus; 34th, Mars; 157th, Jupiter; 55th, Saturn. (I simplified the chart by letting all elongations be positive.) As the planets move, their 'ring' of elongations slide along the ecliptic, altering the arrangement of elongations in an endless dance, never repeating the exact set again.
Void of course ------------ Look again at the first chart, with the Moon's path thru Gemini. The interval between the last aspect, d, and the departure from Gemini, e, may of any duration, from a second to quite the full 2-1/2 day traverse of the sign. That's because the aspect points are disposed in the sign according as the locations of the other planets thruout the zodiac. Thus, that final aspect could occur a second before the Moon leaves the sign or there could be no aspect at all within that sign. There is no average duration due to the complex overlapping of planet motions, but a few hours to a day is typical. I suppose, but do not know for sure, that an astrology computer program can calculate the void of course periods. No astronomy does this. It could be trivially included in an astronomy program. It amounts to subtracting the Moon's solar elongations from that of each other planet and finding when this result is on a square or hexagon point. Then finding when the Moon crosses a 30-degree point of ecliptic longitude. A table of these moments reveals the span between the last aspect occurring within a zodiac sign of the Moon against other planets and the crossing over to the next sign. With current offerings in astronomy programs, this calculation must be done in pieces with human intervention.
Example ----- A little fiddling showed me that it was easiest to find when the Moon ENTERS a given sign, then backtrack her to the first PRECEDING aspect. For 2007 August 18, Moon enters Scorpius at 11:14 EST (12:14 EDST). That's when she attains longitude 210d, the 0th degree of Scorpius, taken from a computer ephemeris program. All numbers here are rounded to the minute of time and degree of angle. For this hour I generated a table of planet elongations from the Sun, from the same program.
PLANETS AT 11:14 EST 18 AUGUST 2007 =========================================== Planet Sun Moon Aspt Diff Time Hour ------- ---- ---- ---- ---- ---- ---- Sun 0 -65 -60 -5 -10h --- Mercury +3 -62 -60 -2 -4h 07:09 Venus -1 -66 -60 -6 -12h --- Moon +65 0 -- --- -- --- Mars -78 -143 -120 -23 -46h --- Jupiter +105 +40 -- --- -- --- Saturn +3 -62 -60 -2 -4h 07:23
The first column is the other planets, including Sun. 'Sun' is the elongation of the planet from the Sun. '+' is east; '-', west. 'Moon' is the elongation relative to the Moon in the sense (planet) - (Moon). East and west are relative to the Moon, not Sun. 'Aspt' is the major aspect nearest the actual lunar elongation of the planet. 'Diff' is the degree difference in the sense (elongation) - (aspect). '-' means the Moon already passed the aspect. If there were any '+' entries, they mean the Moon didn't reach the aspect yet. Remember! I'm looking UPRANGE from the Scorpius frontier to run the Moon BACK in time. 'Time' is the approximate time needed for the Moon to get from the actual elongation to the aspect while moving at the average rate of 1/2 deg/hr. '-' means the Moon must run backwards to reach the aspect, she being ahead of it at 11:14. If there were any '+' entries, they mean she isn't yet at the aspect. She will reach the aspect AFTER crossing the sign boundary, so such hits can not be candidates for the instant void of course. These aspects fall into the void of Moon computation of the NEXT sign Sagittarius. 'Hour' is the actual hour when the Moon achieves the aspect. I found this by a search around the approximate hour from the previous column. I did this only for the aspects most recently passed before 11:14, those for Mercury and Saturn. Aspects passed earlier are not the last one within Scorpius and can not be the beginning of the void of course period. From this computation, it appears that the last aspect of the Moon prior to a sign crossing was on 18 August 07:23 EST and the Moon crossed into Scorpius at 11:14 EST, same day. Between these times, for 3h 51m, she was in her void of course.
Topocentric view -------------- The Moon's place among the stars is altered substantially by parallax when viewed from various places on Earth. That's how occultations and solar eclipses are affected. The aspect should be computed for the actual location of the observer to accommodate the parallactic displacement of the Moon. A good ephemeris program offers the topocentric lunar position and motion. Hence, for observers widely separated, specially in longitude, the start and stop times of the current void of course will differ. Some astrology tables give a geocentric view, which is OK for sloppy work, like a geocentric lunar ephemeris for casual stargazing.