John Pazmino
 NYSkies Astronomy Inc
 2007 December 8 
    During summer of 2007 an old acquaintance, whom I lost track of 
years ago, returned to the stars. Sort of. This person ended up as a
astrologer for career, altho still keeps interest in astronomy. We got 
to catching up on news and all that. Any way, the dialog recalled to 
me the common roots of the two disciplines[!], before they diverged 
sometime in the Middle Ages. 
    I, as readers well know, have little belief in astrology. However, 
astrologers must first figure out where the planets are before they 
can do their mumbo-jumbo about them. Hence, there is some astronomy 
underlying the scented air and spacey music in the astrologer's 
    I got to inquiring. How much of the astrologer's computational 
tools are valid for astronomy? It turns out there's much that is, and 
perhaps a lot that has potential use, for the astronomer. 
Some history
    Before around 1600 AD there was no hard distinction between 
astronomy and astrology. The nature and forces of the solar system 
were at the time unknown and unknowable. The movements of the planets, 
including the Sun and Moon, were mysterious and their import, 
influence, impact, on Earth affairs was plausible. 
    There were two schools in the common astrology/astronomy studies. 
One had the duty to foretell the location and motion of the planets; 
the other, explain how these locations and motions impelled us on 
Earth. Many people were both astronomers and astrologers, calling 
themselfs the one or the other as the occasion required. 
    The foundation of astrology and astronomy in the western world 
(there were separate astrologies elsewhere in the world) was laid by 
Ptolemaeus. He in about 150 AD wrote (among other works) two grand 
books about the heavens. The Almagest details the calculations of the 
planets, The Tetrabiblos describes the interpretation of the planets. 
Right thru the Middle Ages, these two books were the basis for western 
astrology and astronomy. 
    These works, with innumerable others from the Classical era, were 
lost to the West during the Dark Ages. They were recovered during the 
Middle Ages, sometimes after multiple translations. 
    The Almagest, for example, was written originally in Greek. It was 
first recovered in Arabia and cast into Arabic. Then it was carried to 
Europe. to be translated into Latin. 
    One reason Europe kept hold of these books, tinkering with them in 
only minor ways, was the general collapse of education and culture in 
Europe during the Dark Ages. The ancient world, specially the Roman 
Empire, was highly revered as a former golden era. Artifacts and 
writings from the Roman era were preserved and handed down in more or 
less unmolested form. 
    Altho astrologers tried to invent newer schemes of planet 
influences, the Ptolemaeus system is still the core of modern western 
astrology. The Tetrabiblos is still a strong seller in the astrology 
litterature. It, and the Almagest, is available today as Latin or 
Greek reprints or in English and other modern languages. 
    On the other hand, the Almagest was put aside by the 1700s with 
newer knowledge and understanding, so that today it's only of 
historical interest. Never the less, astronomers still reed it for 
'finding their roots' and there is at least one computer program that 
calculates planet positions based on it. The results for dates in our 
time are ridiculous due to the millennia of accumulated tiny errors. 
    For the ancient astronomer, the heavens were a fixed fabric of 
stars, permanent and unchanging. In front of this backdrop a certain 
seven stars meandered. These were the planets. The Romans named them 
after deities: Luna, Mercurius, Venus, Sol, Mars, Jupiter, Saturnus. 
You may suss out the English names from these as yet an other 
tradition we keep from the Roman Empire. 
    The planet movements are confined to a narrow band in the stars, a 
great circle, crossing certain constellations. This zone is the 
zodiac, which has 12 constellations along it. I mean 12 classical 
constellations, not those based on the modern frontiers. I skip the 
Ophiuchus flap. 
    Eleven of the zodiac constellations are creatures. Only Libra is 
an artifact. Sagittarius and Capricornus are fanciful animals, a 
centaur (half-man-half-horse) and half-fish-half-goat. The earliest 
known depiction of the zodiac comes from Sumeria in the fourth 
millennium BC. Cultures since then were careful to preserve the 
constellations, so that today they are just about the most ancient of 
human writings. 
    Astrologers and astronomers in English use about the same names 
for the zodiac constellations. There is the tussle of 'Scorpius' 
versus 'Scorpio',  The English equivalent is 'Scorpion' and that in 
Spanish is 'Scorpio'n'. Both words are copasetic Latin words for the 
lobster-like creature. 
    Astronomers employ the Latin grammar cases in their vocabulary, 
which moves some astronomers to study latin in school, at least for a 
semester or two. American Astrologers do not decline their vocabulary. 
I don't know what overseas astrologers do. For the record, the 
genitive of 'Scorpio' is 'Scorpionis'. 
    The astrologer has slightly different 3-letter abbreviations. 
These come from dealing with only the zodiac constellations, avoiding 
conflicts with groups beyond the zodiac. Where room is tight, like in 
computer output, astrology has a set of 2-letter abbreves. Because 
astrologers often avail of astronomy databases and ephemerides, they 
also are fluent with the astronomy names and abbreves. 
    Keep in mind that the astrologer means the sign and never the 
constellation, as explained later. Astronomers intend only the 
constellation, never the sign. 
    Here is a comparison between the two systems: 
    astronomy          astrology 
    ---------------    -------------------
    name        3LA    name        3LA  2L 
    ----------  ---    ----------  ---  --
    Aries       ARI    Aries       ARI  AR
    Taurus      TAU    Taurus      TAU  TA
    Gemini      GEM    Gemini      GEM  GE
    Cancer      CNC    Cancer      CAN  CN
    Leo         LEO    Leo         LEO  LE
    Virgo       VIR    Virgo       VIR  VI
    Libra       LIB    Libra       LIB  LI
    Scorpius    SCO    Sxorpio     SCO  SC
    Sagittarius SGR    Sagittarius SAG  SA
    Capricornus CAP    Capricorn   CAP  CP 
    Aquarius    AQR    Aquarius    AQU  AQ
    Pisces      PSC    Pisces      PIS  PI
    Astrologers, as much as astronomers!, commonly mispronounce the 
zodiac names. This is a direct result of the vanishing classics 
education in America. 
    The symbols in astrology are the same as those in astronomy. There 
are variations due to typestyle but all are readily recognized. 
Astrology tracks certain other points besides the real planets and has 
several alignments not commonly used in astronomy. Symbols for these 
are new to the astronomer. 
    Astrologers keep symbols the astronomer abandoned 150ish years 
ago. When the asteroids were first discovered, New symbols were 
invented for them to follow the tradition of the main planet symbols. 
When the number of asteroids got too large by the mid 19th century, we 
stopped devising symbols and just used names and numbers. In time, 
astronomers lost memory of the original asteroid symbols. 
    Astronomers still use the more common symbols, altho most printed 
material since the late 20th century switched to plain text. Yet it is 
well to remember them for taking notes or other quick writing. 
    The paths of the planets were so varied year to year, that they 
never repeated exactly. The trace of a planet for many laps of the 
zodiac looks like a string winded around a ball. This added to the 
mystique of astrology in that it was beyond the layman to suss out the 
planetary behavior. It required a professional to work it out. 
    One planet, the Sun, did repeat its path year after year, to the 
extent that the year was defined as one circuit of the Sun thru the 
zodiac. The actual path is the ecliptic. The Sun's motion was regular 
enough to maintain a one-to-one calendar date for each step of the Sun 
along the ecliptic. Many starcharts mark these calendar dates on the 
    The ecliptic is inclined to the celestial equator by 23-1/2 
degrees and intersect it in two opposite points, the nodes. The node 
where the Sun crosses from south to north is the vernal equinox. That 
where the Sun crosses north to south is the autumnal equinox. 
    Where Sun is at its greatest north distance from the equator is 
the summer solstice. Its greatest southern deviation point is the 
winter solstice. These points are 23-1/2 degree declination, north and 
    The other planets, besides wandering thru the zodiac, deviate 
north and south a little from the ecliptic, always staying close to 
it. By convention, the zodiac is 16 degrees wide, centered on the 
ecliptic. This width bounds all of the planet motions. 
Longitude & latitude
    The distance downrange along the ecliptic is ecliptic longitude, 
longitude for short. The deviation north or south of the ecliptic is 
ecliptic latitude, latitude for short. 
    The origin of longitude is the vernal equinox, This is a 
boreocentric feature from the vernal equinox being near when winter 
turned over to spring. In times past, the vernal equinox was also the 
start of the new calendar year. 
    Latitude and longitude were the first celestial coordinate scheme 
from its extreme importance for following the planets. Right ascension 
and declination came much later and had to take new names to avoid 
conflict. As late as the 1700s, starcharts were dimensioned in lat-
lon, rather than or along with RA-DC. Only in the 1800s was lat-lon 
finally dropped from the usual starcharts.
    Ecliptic coordinates remains the easiest and preferred system in 
planetary computations. If RA-DC are required, a conversion is done, 
now a trivial chore with calculettes or computers. 
    The size of zodiac constellations ranges widely. To simplify 
calculation of ephemerides, the astronomer/astrologer schematized the 
zodiac into 12 zones of 30 degrees each. They are named for the 12 
zodiac constellations. The degrees are numbered 0 thru 29, like the 
hours of the day, NOT 1 thru 30 like the days of a month. Some 
astrologers count 1 thru 30, leading to mistakes in math and dialog. 
    The longitude of a planet can be given in the sign-degree 
notation, which the astrologer does routinely. Jupiter, if in longitude 
127d 23m, is also in 'Leo 7d 23m'. The sign of Leo occupies ecliptic 
longitude 120 thru 149 degree. 
    It's like giving a calendar date in month-day or in count-of-day. 
The latter is common for timekeeping in business and commerce. 
Astronomers use only the degree of longitude. Astrologers stay with 
sign-degree, turning to degree for special purposes.. 
    The connection between lat-lon, RA-DC, and the background stars is 
not an static rigid one. From the gravity effects of the Sun and Moon 
and the oblate shape of the Earth, the Earth's polar axis describes a 
wobbling-top motion in space. This motion migrates the north (and 
south) celestial pole thru the stars, shifting the 'north star' to one 
star after an other. It also slews the celestial equator against the 
ecliptic, pulling the equinoxes westward thru the constellations. 
    Since the vernal equinox is the zero of ecliptic longitude, the 
migration of this point pulls with it the longitudes coordinate. The 
longitudes of all stars is continuously increasing, returning to the 
original value after one precession cycle. 
    The latitudes are essentially unchanged, suffering only minute 
change from a tiny alteration of the ecliptic inclination, the 
obliquity, from the equator. Because of this obliquity variation, the 
precession cycle does not repeat exactly, as a mechanical planetarium 
    This motion was discovered by Hipparchus and confirmed by 
Ptolemaeus. It was -- and still is! -- an annoying feature of 
astronomy. Starcharts must be dated for the location of the vernal 
equinox they are plotted against. This is the epoch of the map. Epoch 
2000, the one in wide use now, means that the coordinate grid on the 
map is banked off of the vernal equinox for the year 2000. 
    From about 1940 thru about 1980 the epoch 1950 was in force. 
Before that, 1900. 2000 became the current epoch in about 1980, but 
1950 was still used thru about 1990. Probably by 2030 we may step to a 
2050 epoch. We have to revise our starcharts every couple decades to 
move to the next standard epoch. 
    It is crucial to understand that the stars are substantially fixed 
in space, their proper motions being minuscule to the bare eye in even 
a couple millennia. It's only the value of their coordinates that 
drifts with the ages. Imagine a photograph of the sky and overlay a 
transparent grid on it. Sliding this grid over the photo changes the 
x-y value of a star's position but the star itself does not move. 
    You can not actually observe a planet's position in the epoch 2000 
grid because it is no longer year 2000. You observe the position 
against the grid of the instant date. To make the measures useful to 
others on a consistent level, you must convert from the values of the 
date to those of 2000. By the same consideration, ephemerides are 
computed for a standard epoch, now 2000.. 
    The longitude of a point always increases at a uniform rate of 
about 1.4 degree per century or 1 degree every 72 years. I say 'about' 
because, believe or not, the precession period, the time to complete 
one lap, is uncertain by a couple decades. 
    The precession shift from 2,000 years ago to now is 27.7 degrees, 
for a 26,000 year precession period. This is close to one whole zodiac 
sign. When the Sun enters sign Leo, at Leo 0, it is more nearly 
entering constellation Cancer. Leo 0 = lon 120d -> next to mu Cancri. 
It also is where the Sun stands on October 21st of each year. 
    Applying the shift of one sign, the astronomer has a clue to where 
in the zodiac the Sun is. It's near the front, west, end of Cancer. 
    Very few astronomy programs report sign-degree positions. Yet it 
is tricky to quickly see from the longitude where a planet sits among 
the stars. The sign-degree method gives an clear picture of the planet 
in its constellation. This is a reasonable approximation considering 
that the constellations are of varied length along the ecliptic. 
    The correspondence of sign-degree to degree is: 
        sign-deg      ecl lon    sign degree        ecl lon 
        -----------   -------    ----------------   -------
        Aries 0-29  =   0- 29    Libra 0-29       = 180-209 
        Taurus 0-29 =  30- 59    Scorpius 0-29    = 210-239 
        Gemini 0-29 =  60- 89    Sagittarius 0-29 = 240-259 
        Cancer 0-29 =  90-119    Capricornus 0-29 = 270-299 
        Leo 0-29    = 120-149    Aquarius 0-29    = 300-329 
        Virgo 0-29  - 150-179    Pisces 0-29      = 330-359
    Just keep in mind that the astrological sign is one step AHEAD, 
EAST, of the constellation it now overlies. The constellation is one 
step BEHIND, WEST, of the sign sitting over it. 
Shift the signs?
    It may be tempting to index the signs to better line up with the 
current constellations. In fact, some astrologers do this in a 
'sidereal' zodiac, as opposed to the normal 'tropical' zodiac.
    I see this as a rather bad idea. The signs are merely names for 
zones of the ecliptic like the names of our calendar months. Even tho 
now we start the year in January rather than in March, we left the 
month names alone. 'September', once the 7th month, is now the 9th. 
    Besides that, the bulk of computational methods work with ecliptic 
longitude based on the vernal equinox and not the fixed stars. Hence, 
when we figure out that Jupiter is in lon 127d 42m, it is in Leo 7d 
42m, regardless of what star group that degree is within. 
    The sign system isn't really broken, so let's not try and fix it. 
Fixed stars
    Only rarely does astrology work with the fixed stars. Each star 
does have its own longitude, in degree and sign-degree, by which it can 
be aligned with the planets. Astronomers routinely check these 
alignments for possible occultations. 
    Here is a list of stars brighter than 3.0 in the zodiac with their 
ecliptic coordinates. Like astronomy, astrology has erratic spelling 
of star names. 
        star     sign    lon  lat  magn  name 
        -------  ------  ---  ---  ----  --------
        bet Ari  Tau  4   34   +8  +2.6  Sheratan
        M45 Tau  Gem  0   60   +4  +1.2  Pleiades
        eta Tau  Gem  0   60   +5  +2.9  Alcyone
        alp Tau  Gem 10   70   -5  +0.9  Aldebaran
        bet Tau  Gem 23   83   +5  +1.7  Alnath
        zet Tau  Gem 25   85   -2  +3.0  Al Hecka
        mu  Gem  Cnc  5   95   -1  +2.9  Tejat Posterior
        gam Gem  Cnc  9   99   -7  +2.0  Alhena
        eps Gem  Cnc 10  100   +2  +3.0  Mebsuta
        bet Gem  Cnc 23  113   +7  +1.1  Pollux
        M44 Cnc  Leo  4  124   +2  +3.7  Praesepe
        alp Leo  Vir  0  150    0  +1.4  Regulus
        alp Vir  Lib 24  204   -2  +1.0  Spica
        alp Lib  Sco 15  225    0  +2.8  Zuben Elgenubi
        bet Lib  Sco 19  229   +8  +2.6  Zuben Elschemali
        del Sco  Sgr  3  243   -2  +2.4  Dschubba
        pi  Sco  Sgr  3  243   -5  +2.9  ---
        bet Sco  Sgr  3  243   +1  +2.6  Graffias
        sig Sco  Sgr  8  248   -4  +2.9  Alniyat
        alp Sco  Sgr 10  250   -5  +1.0  Antares
        tau Sco  Sgr 12  252   -6  +2.8  ---
        eta Oph  Sgr 18  258   +7  +2.4  Sabik
        M8  Sgr  Cap  1  271   -1  +6.0  Spiculum
        gam Sgr  Cap  1  271   -7  +3.0  Nash 
        del Sgr  Cap  5  275   -6  +2.7  Kaus Meridionalis 
        lam Sgr  Cap  6  276   -2  +2.8  Kaus Borealis
        M22 Sgr  Cap  8  278   -1  +5.1  Facies
        sig Sgr  Cap 12  282   -3  +2.0  Nunki
        zet Sgr  Cap 14  284   -7  +2.6  Ascella
        pi  Sgr  Cap 16  286   +1  +2.9  Albadah
        del Cap  Aqr 24  324   -3  +2.9  Deneb Algedi 
        bet Aqr  Aqr 24  324   +9  +2.9  Sadalsuud        
    Astrology has odd proper names for bright deepsky objects! 
Astronomy comes up with whimsical names, too, for many DSOs. 
Sidereal time
   Sidereal time is the right ascension standing on the upper meridian 
at a given moment. Both astronomy and astrology had a steamy fetish for 
sidereal time in former decades because it fixed the celestial sphere 
in its east-west motion. In fact, older mechanical planetaria had dials 
for geographic latitude and sidereal time to show how the projector 
was oriented. 
    In astrology the sidereal time for a given latitude determined the 
ascendent, medium coeli, and house cusps. These are concepts detailed 
later. For astronomy the sidereal time was an ingredient for setting 
the equatorial mount of a telescope on a given target. 
    Note quite well that sidereal time and ecliptic longitude are 
zeroed at the vernal equinox. For every sidereal time there is a 
unique ecliptic longitude on the upper meridian, which is the medium 
coeli. This one-to-one match is fixed. Precession does not affect it. 
    In the 1980s thru 1990s, with the spread of electronic calculating 
devices, the need to figure out sidereal time rapidly waned. Today, 
early 21st century, this topic is just about absent from both the 
astronomer's and astrologer's education. 
    The astrologer's concept of a fake planet called Lilith actually 
has value. Astrologers define Lilith two ways. One is the empty focus 
of the Moon's elliptical orbit. This point is about 36,000Km from 
Earth, near the geosynchronous satellites. The other is the apogee 
of the Moon's orbit, around 406,000Kn from Earth. 
    In a given astrology case only one or the other Lilith is in 
force. Astrology computer programs let you set Lillth as you want. 
    When Lilith is the lunar apogee, many astrologers call it apogee. 
The Lilith of the empty focus is also called Dark Moon or Dark Earth. 
There is no obvious astronomy reason to know where the empty focus is. 
    The apogee is a very handy parameter. When the Moon is near apogee 
it moves angularly slowest thru the zodiac. The opposite point in the 
sky is the perigee, where the Moon moves fastest. The Moon's angular 
distance from its apogee, the elongation from it, is a measure of how 
fast the Moon is moving. The Moon's mean angular speed relative to the 
stars is 13.2 degree/day. At perigee it's 14-1/2; apogee, 11-1/2. 
    The distinction is sometimes made for the mean or true apogee. Use 
the true apogee. The mean apogee is based on a rigid lunar orbit.
Ascending node 
    The Moon's ascending node, also called North Node and Dragon's 
Head (Caput Draconis), is the one of two places a lunar or solar 
eclipse can occur. The other node is the descending, south, node or 
Dragon's Tail (Cauda Draconis), 180 degrees or 6 signs away. Most 
astronomy programs do not output the nodes. The node location helps 
gauge the possibility of an eclipse at a given new or full Moon. 
    An example for three dates shows how this works: 
        date         EST  Sun     Moon    AscN    lunar eclipse? 
        -----------  ---  ------  ------  ------  --------------
        2007 Aug 28  04h  Vir  5  Psc  5  Psc  7   possible 
                                |       | 
                              oppos   asc node 
        2007 Oct 26  00h  Sco  2  Tau  2  Psc  4   too far from node 
                                |       | 
                              oppos  no node 
        2008 Feb 20  23h  Psc  2  Vir  2  Aqu 28   possible 
                                |       | 
                              oppos   dsc node 
    In all three cases the Moon is quite 6 signs from the Sun, in 
opposition, in its full phase. For the 2007 October 26 case, the Moon 
is 2 signs or 32 degrees away from the ascending node. There is no 
    Lunar eclipses are possible at the ascending node on 2007 August 
28 and at the descending node on 2008 February 20. In the latter case, 
the ascending node is near the Sun, so the descending node, 6 signs 
away, is near the Moon. 
    The elongation of the Moon from the ascending node is a measure of 
the Moon's latitude from the ecliptic. The maxima are +5.5 deg for 90 
deg east elongation and -5.5 deg for 90 deg west elongation. 
    Tabulations may list the mean or the true node. Prefer the true 
node. The mean node assumes a rigid lunar orbit. 
Medium coeli 
    The medium coeli, or mid heaven, is the ecliptic longitude on the 
upper meridian at a given moment. It tells which zodiac stars are due 
south. The ecliptic degrees pass over the meridian roughly at 15 
degree/hour, but there is an other parameter than better tracks the 
pass of the ecliptic across the meridian. That is the meridian house, 
explained below. Some astrologer mistake medium coeli with zenith, the 
direction up from the Earth's center, at altitude +90 degree. 
    The ecliptic longitude on the lower meridian is the imum coeli, 
'bottom of the heaven'. Some astrologers mistake this point for the 
nadir, which is the direction down to the Earth's center, opposite the 
zenith, at altitude -90 degrees. 
    The ascendent, or ascendant from French, is the ecliptic longitude 
rising at a given moment. It tells which zodiac stars are in the east. 
Unlike medium coeli, the speed of the rising degrees varies widely 
along the ecliptic. The rate of passing depends on the inclination of 
the ecliptic against the horizon near the ascendent. In the north 
temperate zones, signs Leo, Virgo, Libra (constellations Cancer, Leo, 
Virgo) are slowest to rise. Aquarius, Pisces, Aries (constellations 
Capricornus, Aquarius, Pisces) are the quickest. 
    The point where the ecliptic is setting is the descendent. It is 
usually not separately stated because it is opposite the ascendent by 
180 degrees or 6 signs. 
    Half of the ecliptic is above the horizon at any moment, from the 
descendent, eastward thru medium coeli, to the ascendent. The other 
half is below the horizon at that moment. 
    Both astronomy and astrology prefer UT, UTC, GMT, all treated as 
synonyms. Both have computer programs that convert input and output to 
and from a local time. The timezone in a computer program is either 
part of the observer location or a separate setting. 
    Both camps deprecate daylight savings time. i could not learn how  
asttrologers are dealing with the new American rules that started in 
2007. Individual astronomers let their clocks do their thing on the 
old dates, but hold back a special clock to show correct local time. 
    There is one glitch some astrologers suffer occasionally. They 
adjust GMT (UT, UTC) for daylight savings time when that's in force in 
Europe. Wrong. GMT does NOT shift for daylight savings time. Europe 
leaves GMT alone. Other, different, local times are used during the 
daylight savings period, whose names vary among countries. A time in 
Europe stated in GMT is pura mente 0th meridian time. 
    Like astronomers, there is a love-hate thing with the deviation of 
atomic time from GMT, This deviation, delta-T, in 2007 is about 66 
seconds. This is a full minute, a possible gross error for astrologers 
but a minor one for general astronomy functions. 
    Depending on the accuracy required at the instant, astrologers and 
astronomers correct for the observer's offset from the timezone 
central meridian. The offset can be substantial. In the western parts 
of the Eastern Standard timezone clocks are a half hour or so earlier 
than local mean time. 
    Astrologers and astronomers prefer the 24-hour notation, which 
keeps you out of trouble near midnight and noon. They do, once a 
while, lapse to the oldstyle AM/PM notation. By the late 20th century, 
most lay folk knew the 24-hr system, so the need to translate back to 
AM/PM went out of practice. 
    I have no idea how astrologers treated the leapsecond in 1998 or 
2005. The astrologers I spoke with knew nothing about it. 
    There is little need for weights and measures in astrology. It 
works almost exclusively with angular directions along sightlines of 
indefinite length. Astrologers, like the rest of world, moved to 
metrics in their talks and texts decades ago. 
    Many astrology programs include mainstream astronomy information 
for the planets and stars. These, copied from regular astronomy 
references, is in metrics. 
    Sometimes, like astronomers, they backslide into oldstyle 
measures. For instance, a text explaining Lilith as the Moon's second 
focus may say it is about 22,000 miles from Earth rather than 36,000 
kilometers. (A 'mile' is 1.61 kilometer.) 
    Besides the absolute longitude of a planet, the astrologer works 
out the angular elongations among the planets. Unlike in astronomy, 
where elongations are overwhelmingly against the Sun, astrology 
considers elongations among any pair of planets and points. 
    Elongations is the difference of ecliptic longitude between the 
two planets. Depending on the order of the subtraction, this may be 
positive or negative. The signum indicates, with other factors in the 
instant case, that the far planet is east or west of the home one. 
    Astrologers treat certain elongations, called aspects, as 
specially important. They are laid out in the Tetrabiblos and are 
based on the points of a hexagon and a square fitting into the 
ecliptic circle. These two shapes, with the triangle, are the only 
ones that tesserate a plane. Other shapes have gaps between the tiles. 
    The aspects for astronomy (A) and astrology (a) are: 
    A/a  aspect          elongation 
    ---  --------------  -------------- 
    A/a  conjunction     0 degree, also called conjunct 
    A    greatest elong  +/- 29 deg for Mercury; +/- 47, Venus 
      a  sextile         +/-60 degree 
    A/a  quadrature      +/-90 deg, also called quadrate & square 
      a  trine           +/-120 degree 
    A    station         enter and leave retrograde loop 
    A/a  opposition      180 degree, also called opposite 
    Altho all the planets have retrograde loops, those of Mercury and 
Venus occur in twilight or daylight, when they are difficult to 
observe. Astronomers generally skip the stations for them while 
astologers keep track of them. 
    There are many minor aspects. Astrologers are at odds about which 
of these, beyond the major ones of Ptolemaeus, are legitimate.. 
    It may help to imagine every planet and point on its own ring 
sliding around the zodiac. This ring is dimensioned in degrees of 
elongation east and west from its planet. As each other planet lines 
up with appropriate degrees, the aspects are hit. 
Useful aspects 
    Except for conjunction and opposition, the astrology aspects at 
first seem useless in astronomy. However, they can have a possible 
function. It can be that the Moon must be more than 30 degrees from a 
certain target, else observation of the target is too difficult by 
close moonlight. It would be nice if we could find when the Moon is 
+/-30 degrees elongation from the target to avoid moonlight. 
    Astronomy computer program do not directly calculate elongations 
other than against the Sun. Other elongations must be manually figured 
by subtracting appropriate solar elongations. 
    Astrology computer programs build a table of aspects among all of 
the planets. However, astrology sometimes omits the polarity of the 
elongation, whether east or west. You may have to work a planetarium 
program to clarify the sense. A western elongation is also called a 
dexter or right elongation; eastern, left or sinister. 
Planet orbs 
    Ths ia a term left over from when planets were aurae of spirit 
with power over a several degree radius around them, the 'sphere of 
influence' or orb of the planet. Given that the nature and function of 
planets were a mystery before the telescope era, maybe it wasn't all 
that terrible to concoct such a bizarre idea. 
    Today, the orb allows for a reasonable period of time before and 
after the aspect is exact. This span can be what astronomers loosely 
call an apparition. The concept has no standard definition now. 
    The apparition of two planets (almost always a conjunction( can 
begin when their orbs first touch together. The apparition continues 
while the orbs overlap. It ends when the orbs last touch, break apart. 
    Each planet has its own orb. There seems to be no standard orb 
values. Astrology programs generally allow you to establish them. Orbs 
are a few degrees, to form an apparition of many days to a week. 
    Astronomers have a vestigial orb for the Sun. This is a zone 
within which it may be too hard to discern an other planet or star. 
It's really a recognition value, with little attempt to vary the 
radius with season or other factor. The Sun's orb, called exclusion or 
twilight zone, is 15 degrees. 
    We could use orbs like an eclipse with 'contacts'. The apparition 
begins when the planet orbs first touch at '1st contact'. The prime 
part of the apparition comes between '2nd contact' and '3rd contact'. 
The apparition ends when the orbs break apart at '4th contact'. In the 
case where the planets bypass too far apart for their orbs to merge, 
we got a 'partial' apparition with no 2nd or 3rd contact. In extreme 
casrs the orbs never touch, like a new Moon missing the Sun to cause 
no eclipse, and we may skip mention of that apparition. The 
conjunction is too loose, the planets being too many degrees apart.. 
Sign crossings
    Astrologers follow the crossing of a planet from one sign into the 
next, called ingrees. This statistic seems of little use to astronomy, 
but in fact it can be. The boundaries of the signs, 30 degrees apart 
along the ecliptic, are meterposts by which the planet movements can 
be tracked. A table of sign crossings makes it easier to visualize the 
relative speeds of the planets. 
    Astrology programs either have the ingress function built in or 
you must manually set the ones you need. In essence, you're finding 
when a planet is in conjunction with the 30, 60, 90, &c degree point 
along the ecliptic. In a program I played with I asked for when the 
planets are in aspect with the vernal equinox at 30 degree intervals! 
    However it's done, you get an interesting output. For the faster 
planets, the ingresses are closely spaced in time. The slower planets 
hang around in a sign for months or years. When a planet goes into 
retrograde, it 'backs up' into the previous sign!
    Here's a table of sign crossings for Mars in 2007-2008:: 
        date         sign     deg/day  da/dg  constellation 
        -----------  -------  -------  -----  --------------------
        2007 Sep 28  Gem-Cnc  +0.4572  +2.13  prograde, enters Gem 
        2007 Dec 31  Cnc-Gem  -0.3649  -2.74  retrograde, enters Tau 
        2008 Mar  3  Gem-Cnc  +0.3168  +3.16  prograde, enters Gem 
        2008 May  9  Cnc-Leo  +0.5354  +1.87  enters Cancer 
        2008 Jul  1  Leo-Vir  +0.5950  +1.68  enters Leo 
        2008 Aug 19  Vir-Lib  +0.6356  +1.57  enters Virgo 
        2008 Oct  4  Lib-Sco  +0.6756  +1.48  enters Libra 
        2008 Nov 16  Sco-Sgr  +0.7146  +1.40  enters Scorpius 
        2008 Dec 27  Sgr-Cap  +0.7493  +1.33  enters Sagittarius 
    Ingresses are based on the signs. The correspondence with the stars 
is only approximate due to the varied lengths of constellations. 
    Astrology programs commonly output the speed of the planet in both 
degree/day and day/degree. Note how Mars scoots along the zodiac after 
leaving its retrograde loop. 
Stellar conjunctions
    A few astrology programs allow you to specify ANY ecliptic 
longitude to make an aspect against. Input the longitude of a star 
from the table above. You then figure the aspects with that star! You 
can get a list of dates to examine with your astronomy program for 
possible occultations. 
    For the Moon, you learn that the sidereal month is not precisa 
mente constant. The interval between adjacent conjunctions with a star 
varies. Not much, but enough to throw off a mechanical increment of 
downrange angle. 
    Here's a table of Venus conjunctions with Alcyone, ecliptic 
longitude 60 degree (Gem 0), in 2007-2010.
        date         GMT    deg/day  hr/dg
        -----------  -----  -------  -----
        12 Apr 2007  02:15  +1.1720  20.48
        24 May 2008  22:52  +1.2290  19.53
        05 Jul 2009  08:23  +1.0903  22.01
        25 Apr 2010  05:05  +1.2174  19.71
    It was orders easier to get this tabulation at once from an 
astrology program and then examine more closely each event with the 
planetarium. The alternative is hunt by trial-&-error with just the 
    The concept of houses is one of the most argued topics in 
astrology. Not only now but since the Dark Ages. The idea is to 
divvy up the ecliptic into 12 segments by a construction on the 
observer's horizon. Signs, planets, points drift thru them in diurnal 
    Houses have proper names, after human experience and character, 
and also numbers #1 thru #12. Just about all schemes of house number 
the houses eastward, downrange, in the zodiac. The numbers are by far 
the more common way in astrology to designate the houses. 
    Thus, the interpretation of a planet would be in part from its 
location in a sign and its location in a house. In this way, both the 
celestial and terrestrial influence of the planet are factored into 
the observer's case. 
    The boundaries between the houses are the cusps, the front or 
western edges. To say that house #5 is in Aries 22 means the 5th house 
cusp is at Aries 22. The house extends east to the cusp of house #6. 
    Unlike a universal acceptance of the signs of the zodiac, there is 
just no consensus regarding the way to slice up the ecliptic into the 
12 houses. I found at least 20 methods of doing this, all yielding 
different cusps and houses of varying length. Each method has its 
fervent promotors and demotors. 
    Among astrologers, the Placidus method is the most popular scheme. 
This comes fro the historical fluke that cheap, widely available, 
tables of Placidus houses were published before calculettes and 
computers. Publications for other house systems were hard to find and 
too costly. 
    The Placidus scheme is useless for astronomy because it uses an 
arbitrary construct that produces irregularly spaced cusps that migrate 
in the local sky during the diurnal rotation. 
Meridian houses
    Of the 20-odd schemes of house, I found only two of sensible value 
for astronomy. Many astrology programs include both in the selection 
of system to calculate. 
    The meridian, also called the axial, polar, and equatorial. houses 
are spaced 30 degree, or 2 hour, of hour angle around the sky, The 
cusps are where the hour angle lunes cut the ecliptic. The cusp of 
house #10 is at the medium coeli, HA = 0h. The cusp of the 4th house 
is at the imum coeli on the lower meridian, HA = 12h. 
    In astronomy the hour angle is counted west or east from the upper 
meridian, thru 24h, back to the meridian. In the west count, the hour 
angle of a point in the sky is the time since that point's previous 
meridian pass, or culmination. For the east count, the hour angle is 
the time before the next culmination. 
    By getting a table of meridian houses, you have the timetable of 
the ecliptic culminations at 2-hour intervals! Thus, the astrology 
houses become a movie of the sky to assess the visibility of various 
parts of the zodiac. 
    Be careful. Altho all 12 houses are specified, the cusps of 
certain houses are down at the instant. Only cusps from the descendent, 
eastward to the ascendent are up. 
    The correspondence of meridian house and hour angle is: 
        H#  eastward   westward     H#  eastward   westward 
        --  ---------  ---------    --  ---------  ---------
        10  00h-01:59  22h-23:59     4  12h-13:59  10h-11:59 
        11  02h-03:59  20h-21:59     5  14h-15:59  08h-09:59 
        12  04h-05:59  18h-19:59     6  16h-17:59  06h-07:59        
         1  06h-07:59  16h-17:59     7  18h-19:59  04h-05:59 
         2  08h-09:59  14h-15:59     8  20h-21:59  02h-03:59 
         3  10h-11:59  12h-13:59     9  22h-23:59  00h-01:59 
    As time rolls on, the houses index lune by lune from east to west 
in numerical order across the meridian. The ecliptic longitude of the 
11th house will clulminate in 2 hours. That of the 8th house passed 
the meridian 4 hours ago. 
    The nice feature of this house system is that you get the 
timetable at once for the entire 24 hours from the one calculation. 
You do not have to do the calcs again at 2-hr (or 1-hr as long as 
you're going thru this trouble) increments. 
Horizontal houses 
    The other house method I find helpful to astronomers is the 
horizontal, zenithal, or azimuthal scheme. The sky is divided into 
lunes of 30 degree azimuth. Where the lunes cut the ecliptic are the 
house cusps. House #10 is on the medium coeli, azimuth 180d. House #4 
is at the imum coeli, azimuth 0d 
    This set of houses is a snapshot only for the instant. There is no 
easy way to figure out the cusps for other hours. You have to recalc 
the whole set all over again. 
    The horizontal houses give the direction of various points of the 
ecliptic. Bear in mind that certain cusps will be down. Only cusps 
from the descendent eastward to the ascendent are above the horizon. 
     The horizontal house-azimuth correlation is: 
         H#  azimuth    H#  azimuth    H#  azimuth 
         --  -------    --  -------    ------------
         10  180-151     2   60- 31     6  300-271 
         11  150-121     3   30-  1     7  270-241 
         12  120- 91     4  360-331     8  240-211 
          1   90- 61     5  330-301     9  210-181 
    Note that in the horizontal and meridian systems the ascendent or 
descendent is NOT at a house cusp. Some other house systems force 
these points to be house cusps. 
Astronomy information
    Astrology programs commonly offer glatt astronomy! This is in 
boxes, panels, tags that open when a planet or star is selected. The 
data are the facts & figures for the target, physical specs, and 
ephemeris data relative to the observer's location and time. 
    The calculated parts of astronomy data is mostly a derivative of 
the main ephemeris computations. Hence, it is overall of good quality. 
The facts & figures stuff comes from regular astronomy references, but 
they could ediurnate from lax review and revision. 
    Because astrologers have no direct need for this material, it may 
be buried several layers deep in the program. However, it can save the 
need to open an astronomy program to obtain the same information. 
    Depending on the program, the astronomy data can be output, along 
with the astrology items, or can only be viewed or captured on screen. 
    The accuracy of computation is pretty good among astrology 
programs I played with. That's because they are based on the Swiss 
Ephemeris engine, which in turn banks off of the JPL ephemeris engine. 
Because Swiss Ephemeris offers its source code for free to incorporate 
into your own program, there's no reason for an astrology author not 
to use it. In fact, you can get Swiss Ephemeris, as I discuss below, 
for pure astronomy purposes and skip most of the astrology dressing. 
    Astrologers sometimes include minor wobbles, like nutation and 
aberration and Chandler polar migration. Some factor in gravity 
deflection of starlight by the Sun. Astrology programs may allow you 
to turn these extra corrections off, but they are so minor that it's 
easier to leave them alone. 
Swiss Ephemeris 
    While astrologers can avail of the same computational tools as the 
astronomers, they favor the Swiss Ephemeris machinery. This generates 
planetary positions, and other astrological parameters, elaborated 
from the JPL ephemeris engine in its HORIZONS application. 
    There are three quick and simple ways to benefit from Swiss 
Ephemeris. One is to download prepared tables of parameters for the 
specific years you need. These are in PDFs looking like printed 
booklets, with geocentric data for each day at 0h GMT in Greenwich, 
England. Linear interpolation is valid for other timezones and hours. 
    The ecliptic longitudes are given in sign-degree. This makes it 
easy to spot the major aspects, their angles being 0, 2, 3, 4, and 6 
signs. The node and apogee are either the mean or true points, as you 
    These tables are prepared for several thousand years in the past 
and future, covering most of human history. Account is taken of the 
calendar change in 1582 but do know that many countries kept Julian 
dates for long after 1582. 
Computer programs 
    The other two ways to reap Swiss Ephemeris (SE) value is to 
download a ready-to-run computer program for DOS or Windows. For the 
astronomer the DOS program is far and away the better choice. The 
Windows version is surprisingly limited, offering only a small 
selection of stock outputs. 
    The DOS edition is a versatile and manipulable program with lots 
of options and settings. You must be versed in DOS operations, a skill 
rapidly evaporating among today's computerists. Without such fluency 
with DOS you may find Swiss Ephemeris a wickedly frustrating software. 
    The DOS edition runs in a Windows DOS or 'command-prompt' panel. 
This facility in the newer versions of Windows is deeply buried and 
not obvious to the casual computerist. Just firing up the EXE file 
under Windows brings up a constrained mode with only a few options. 
Get to the DOS panel, then work with DOS operations. 
    The DOS SE is an excellent astronomy tool that outputs parameters 
missing from the usual astronomy applications. You can send the output 
to a file to import into a wordprocess, graphing, spreadsheet program. 
    The program does its work with 'switches', letters and numbers 
appended to the EXE filename on the command prompt. These are tough to 
remember or figure out. Print out the help pages and keep them handy. 
Pay close attention to typing. SE, like other DOS programs, is bruta 
mente unforgiving of typos. It throws out the first wrong character 
and aborts the run. 
    As you work with SE, you'll find certain switches which you want 
to include in all or most runs. You can package the whole lot into a 
textfile to avoid typing the chars every time. You do this by coding 
the command and switches into a BAT, for 'batch', file and running 
that file. This requires a fluency with the BAT machine. Maybe it's 
time to dust off that old DOS command reference manual? 
Swiss examples
    I give here a few examples of Swiss Ephemeris DOS runs. 
    Without any switches, just the EXE filename, you are asked for a 
date. This is 'day.month.year' with delimiter dots. SE delivers a 
standard table of planets and points for a geocentric observer at 0h 
GMT. I compacted the columns to fit within the page width here. 
 Date ? 1,11,2007    ['1.11.2007' is keyed in as input] 
 date (dmy) 1.11.2007 greg.   0:00:00 ET ET: 2454405.500000 
 Epsilon (true) 2326'25.9944 
 Nutation       0 0' 6.4008  0 0' 8.2565  
 Sun          21810'38.1724  0 0' 0.4935  0.992666341  10'  0.1136 
 Moon         11718'40.9676  3 6' 9.5385  0.002535603 1325'42.8825
 Mercury      20326'45.2913  123'24.6062  0.785686315 -010'57.9589 
 Venus        17145' 0.2614  027'13.9405  0.717408195  1 1'20.9851
 Mars         101 5' 0.8855  058'25.9449  0.769650827  011' 3.2795
 Jupiter      25936'25.9059  016'28.1491  5.972590415  011'47.8213
 Saturn       15629' 6.2505  126'31.5623  9.679517210  0 4'51.9877
 Uranus       345 0' 7.3479 -047'42.4089 19.483816163 -0 1' 8.1787
 Neptune      31914'52.8496  017'10.0314 29.837567740  0 0' 0.3180
 Pluto        267 3'44.8491  626'53.9729 32.004969210  0 1'36.0492
 mean Node    33334'19.5497  0 0' 0.0000  0.002569555  0 3'10.5580
 true Node    33451'55.1095  0 0' 0.0000  0.002425114 -0 1' 4.1971
 mean Apogee  22156'44.0918 -447' 5.7710  0.002710625  0 6'42.8713 
    The columns are ecliptic longitude in degree, ecliptic latitude, 
distance from Earth in AU, angular speed (longitude only, no latitude) 
in deg/day. Note that on 2007 November 1, Mercury and Uranus are in 
retrograde; their speeds are negative. The lunar node retrogrades thru 
the ecliptic while the apogee progrades. 
    Altho SE was built for astrologers, the normal output for 
longitude is degree. There is a sign-degree switch. 
    Here is a run for conjunction of Mars with Saturn in 2008 July 1-
20. I wanted the elongation between Saturn and Mars, the latitude 
difference, the distance between the two in AU, and the relative speed 
of Mars against Saturn in deg/day. To be realistic, I rounded the 
angles to the minute. I let the place be geocentric; hour, 0h GMT. 
 G:\swisseph\swetest -roundmin -p4 -d6 -fTLBRS -n20 -b1.7.2008 
 date (dmy) 1.7.2008 greg.   0:00:00 ET ET: 2454648.500000 
 Epsilon (true)    2326'
 Nutation           0 0'    0 0' 
 01.07.2008   -455'   -033'   -7.749532207    030' 
 02.07.2008   -425'   -033'   -7.756574056    030'
 03.07.2008   -355'   -034'   -7.763521706    030'
 04.07.2008   -324'   -035'   -7.770372433    030'
 05.07.2008   -254'   -035'   -7.777123553    030'
 06.07.2008   -224'   -036'   -7.783772428    030'
 07.07.2008   -154'   -036'   -7.790316470    030'
 08.07.2008   -123'   -037'   -7.796753142    030'
 09.07.2008   -053'   -037'   -7.803079959    030'
 10.07.2008   -023'   -038'   -7.809294485    030'
 11.07.2008    0 7'   -039'   -7.815394331    030'
 12.07.2008    037'   -039'   -7.821377152    030'
 13.07.2008    1 8'   -040'   -7.827240646    030'
 14.07.2008    138'   -040'   -7.832982550    030'
 15.07.2008    2 8'   -041'   -7.838600641    030'
 16.07.2008    238'   -041'   -7.844092730    030'
 17.07.2008    3 8'   -042'   -7.849456662    030'
 18.07.2008    339'   -043'   -7.854690316    030'
 19.07.2008    4 9'   -043'   -7.859791596    030'
 20.07.2008    439'   -044'   -7.864758438    030'
    See how Mars closes in to Saturn from the west and moves along 
eastward? The change of signum, when Mars crosses zero longitude 
offset, is the conjunction. This occurred during July 10. 
    An astronomy program gives the conjunction at July 10th, 18h GMT, 
in good agreement with the position of Mars at the previous and next 
0h GMT. Mars passes 39 arcmin south of Saturn at 30 arcmin/day. 
    The distance is from Saturn to Mars, NOT to Earth. The minus sign 
comes from the signum of the calculation, which doesn't matter. 
   A final example outputs the occultations of Antares by the Moon 
during 2007: 
 G:\swisseph\swetest -occult -pf -xfAntares -b1.1.2007 -n13 
 total   15. 1.2007      12:51:21.8    -3485.269562 km 100.000000 o/o 
          10:49: 9.9    10:49: 9.9    14:53:24.1    14:53:24.1
         -6919'         -5744'        75 min 17.48 sec
 total   11. 2.2007      22: 3:20.2    -3485.359172 km 100.000000 o/o
          20: 9:43.1    20: 9:43.1    23:56:48.6    23:56:48.6
         11610'         -6927'        68 min 28.30 sec
 total   11. 3.2007       6: 0:38.1    -3485.460805 km 100.000000 o/o
           4:10: 5.5     4:10: 5.5     7:51: 2.8     7:51: 2.8
         -37 0'         -7339'        66 min 27.36 sec
 total    7. 4.2007      12:28:28.9    -3485.507846 km 100.000000 o/o
          10:31:11.2    10:31:11.2    14:25:38.2    14:25:38.2
        -151 9'         -6710'        71 min 6.97 sec
 total    4. 5.2007      18:15: 5.2    -3485.497901 km 100.000000 o/o
          16:10:17.2    16:10:17.2    20:19:45.4    20:19:45.4
         10225'         -5744'        77 min 27.25 sec
 total    1. 6.2007       0:25:44.3    -3485.461833 km 100.000000 o/o
          22:18:40.7    22:18:40.7     2:32:39.7     2:32:39.7
         -15 3'         -5340'        79 min 54.58 sec
 total   28. 6.2007       7:39:28.5    -3485.437396 km 100.000000 o/o
           5:35:26.7     5:35:26.7     9:43:21.2     9:43:21.2
        -152 1'         -5746'        76 min 53.09 sec
 total   25. 7.2007      15:51:39.9    -3485.454722 km 100.000000 o/o
          13:55: 5.0    13:55: 5.0    17:48: 5.4    17:48: 5.4
          5139'         -6721'        70 min 39.78 sec
 total   22. 8.2007       0:20: 2.5    -3485.513405 km 100.000000 o/o
          22:30:14.3    22:30:14.3     2: 9:42.6     2: 9:42.6
        -11351'         -75 8'        66 min 3.41 sec
 total   18. 9.2007       8:10:12.7    -3485.574265 km 100.000000 o/o
           6:17:47.4     6:17:47.4    10: 2:30.0    10: 2:30.0
         10521'         -7322'        67 min 46.95 sec
 total   15.10.2007      14:53:13.7    -3485.604938 km 100.000000 o/o
          12:50:44.5    12:50:44.5    16:55:35.2    16:55:35.2
         -1047'         -6255'        75 min 16.94 sec
 total   11.11.2007      20:50:24.6    -3485.601681 km 100.000000 o/o
          18:40:42.3    18:40:42.3    23: 0: 0.1    23: 0: 0.1
        -12151'         -5249'        82 min 28.84 sec
 total    9.12.2007       2:57:45.1    -3485.578864 km 100.000000 o/o 
           0:47: 0.0     0:47: 0.0     5: 8:22.8     5: 8:22.8
         12025'         -5028'        83 min 55.52 sec
    SE treats occultations like solar eclipses and outputs the same 
parameters. I spaced the output records here for clarity. 
    The first row has the word 'total' since the occultation does take 
place. If it didn't, there would be no record for it. Then the date 
and hour of the middle of the occultation, diameter of the Moon's 
shadow at Earth, ratio of Moon/star diameter. 
    The ratio pins at 100 because the star is a point. The shadow is 
quite the same as the Moon's own size because it is a cylinder cast by 
the star from infinity. In a solar eclipse the shadow tapers toward 
the Earth to only a hundred or so kilometer diameter. 
    The second row has the four contacts. The 1st and 2nd are nearly 
the same for the point size of the star. So are 3rd and 4th equal. 
    The third row gives the geographic lon-lat where the occultation 
is central and the duration of the event at that place. This location 
has nothing to do with the observer's actual location. 
Other programs
    I examined three other astrology programs of potential value for 
astronomy: the DOS version of Astrolog, Windows version of Astrolog, 
and ZET in only Windows version. All three are free for the download, 
with ZET the largest at 11Mb. 
    The DOS Astrolog is like Swiss Ephemeris for requiring fluency in 
DOS. It is far more complex than Swiss Ephemeris with an instruction 
printout of some 130 pages. After careful study and lots of 
experimenting, Astrolog can deliver an amazing variety of good 
astronomy information. 
    The Astrolog Windows version is flexible and gives pleasing 
amounts of astronomy information. In the absence of a solid DOS 
grounding, you'll do quite well with this program for starts.
    ZET is a very strong program that has many astronomy features of 
little interest for astrologers. There's a solar system orrery that 
can be tilted and zoomed. It has a tolerably adequate planetarium! 
This even has the zodiac signs marked along the ecliptic to show 
directly how they align (or misalign) with the stars. The orrery and 
planetarium are linked so you can flip between the two and see the 
relation of the planets in the sky to their orbital position. 
    One great feature is an event-hunter. With this you can key in a 
query for just about any scheme of planet locations and motions and 
get the dates they occur on! You get first a timeline of event 
occurrences. This is good for spotting cycles and patterns among the 
planets. Then there is a list that gives details for each occurrence. 
This is a range, based on the planet orbs, being the period of the 
whole apparition. 
    For example, I recall a convention of Mars, Jupiter, and Regulus 
in the early 1980s. When? I gave the query to ZET, and, bingo!, it 
turned up TWO instances in the 1980s:
    Range of search: 31.12.1979 - 31.12.1984 In steps of: 24h 0m 
    Search for...: mars.regulus & mars.0.jupiter 
    Realization intervals (begin - end): 
    11.03.1980 19:00 (GMT-5) - 14.03.1980 19:00 (GMT-5) 
    30.04.1980 20:00 (GMT-4) -  3.05.1980 20:00 (GMT-4) 
    A planetarium program showed that the March 1980 event was a loose 
triangle many degrees on a side. The April-May one was the event I 
recalled, a tight triangle of the three bodies. 
   The instruction book is a 200ish page printout. It's worth a close 
read for the background details and worked out examples. This book 
also gives crucial insight to many astrological topics. 
    Astronomers have for many centuries railed and sallied against 
astrologers for their quack science. Despite this antagonism, there 
are features of astrology that can be handy, useful, valuable for the 
astronomer. By setting aside the impulsions and influence attributed 
to the positions and motions of the planets, the astronomer can make 
good use of many astrology concepts. 
    The astrology softwares mentioned here will not supplant the 
mainstream astronomy applications. They can live in peaceful 
coexistence with them. You have to crosswalk between astrology and 
astronomy vocabulary, suss out obtuse astrology features, precess 
signs to constellations, and all that. 
    Because they use an astronomy ephemeris generator, astrology 
programs should produce results of acceptable quality. I did spot 
check assorted output from these program against regular astronomy 
computations. I find that they agree within minutes fo time, 
    The differences are just about always negligible for the usual 
astronomy chores where the angles or times are not critical. Their 
price (free!) for the the ones here make them all the more appealing 
    I allow,that the results can be merged into those from astronomy 
programs to build a fuller description of various celestial events.