MOON'S VOID OF COURSE
-------------------
John pazmino
NYSkies Astronomy Inc
www.nyskies.org
nyskies@nyskies.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.