ASTROLOGY FOR ASTRONOMERS? ------------------------ John Pazmino NYSkies Astronomy Inc firstname.lastname@example.org www.nyskies.org 2007 December 8
Introduction ---------- 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 office. 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.
Zodiac ---- 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.
Symbols ----- 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.
Ecliptic ------ 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 ecliptic. 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 south. 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.
Signs --- 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..
Precession --------- 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 demonstrates. 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.
sign-degree --------- 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.
Lilith ---- 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 eclipse. 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.
Ascendent ------- 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.
Time -- 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.
Metrics ----- 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.)
Aspects ----- 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 planetarium.
Houses ---- 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 motion. 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.
Accuracy ------ 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 select. 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. ------------------- G:\swisseph\swetest
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) 23ø26'25.9944 Nutation 0ø 0' 6.4008 0ø 0' 8.2565 Sun 218ø10'38.1724 0ø 0' 0.4935 0.992666341 1ø0' 0.1136 Moon 117ø18'40.9676 3ø 6' 9.5385 0.002535603 13ø25'42.8825 Mercury 203ø26'45.2913 1ø23'24.6062 0.785686315 -0ø10'57.9589 Venus 171ø45' 0.2614 0ø27'13.9405 0.717408195 1ø 1'20.9851 Mars 101ø 5' 0.8855 0ø58'25.9449 0.769650827 0ø11' 3.2795 Jupiter 259ø36'25.9059 0ø16'28.1491 5.972590415 0ø11'47.8213 Saturn 156ø29' 6.2505 1ø26'31.5623 9.679517210 0ø 4'51.9877 Uranus 345ø 0' 7.3479 -0ø47'42.4089 19.483816163 -0ø 1' 8.1787 Neptune 319ø14'52.8496 0ø17'10.0314 29.837567740 0ø 0' 0.3180 Pluto 267ø 3'44.8491 6ø26'53.9729 32.004969210 0ø 1'36.0492 mean Node 333ø34'19.5497 0ø 0' 0.0000 0.002569555 0ø 3'10.5580 true Node 334ø51'55.1095 0ø 0' 0.0000 0.002425114 -0ø 1' 4.1971 mean Apogee 221ø56'44.0918 -4ø47' 5.7710 0.002710625 0ø 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) 23ø26' Nutation 0ø 0' 0ø 0' 01.07.2008 -4ø55' -0ø33' -7.749532207 0ø30' 02.07.2008 -4ø25' -0ø33' -7.756574056 0ø30' 03.07.2008 -3ø55' -0ø34' -7.763521706 0ø30' 04.07.2008 -3ø24' -0ø35' -7.770372433 0ø30' 05.07.2008 -2ø54' -0ø35' -7.777123553 0ø30' 06.07.2008 -2ø24' -0ø36' -7.783772428 0ø30' 07.07.2008 -1ø54' -0ø36' -7.790316470 0ø30' 08.07.2008 -1ø23' -0ø37' -7.796753142 0ø30' 09.07.2008 -0ø53' -0ø37' -7.803079959 0ø30' 10.07.2008 -0ø23' -0ø38' -7.809294485 0ø30' 11.07.2008 0ø 7' -0ø39' -7.815394331 0ø30' 12.07.2008 0ø37' -0ø39' -7.821377152 0ø30' 13.07.2008 1ø 8' -0ø40' -7.827240646 0ø30' 14.07.2008 1ø38' -0ø40' -7.832982550 0ø30' 15.07.2008 2ø 8' -0ø41' -7.838600641 0ø30' 16.07.2008 2ø38' -0ø41' -7.844092730 0ø30' 17.07.2008 3ø 8' -0ø42' -7.849456662 0ø30' 18.07.2008 3ø39' -0ø43' -7.854690316 0ø30' 19.07.2008 4ø 9' -0ø43' -7.859791596 0ø30' 20.07.2008 4ø39' -0ø44' -7.864758438 0ø30' ---------------------------------------------------- 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 -69ø19' -57ø44' 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 116ø10' -69ø27' 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 -37ø 0' -73ø39' 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 -151ø 9' -67ø10' 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 102ø25' -57ø44' 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 -15ø 3' -53ø40' 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 -152ø 1' -57ø46' 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 51ø39' -67ø21' 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 -113ø51' -75ø 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 105ø21' -73ø22' 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 -10ø47' -62ø55' 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 -121ø51' -52ø49' 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 120ø25' -50ø28' 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.
Conclusion -------- 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.