ECLIPTIC CYCLORAMA ---------------- John Pazmino NYSkies Astronomy Inc www.nyskies.org email@example.com 2008 September 7
Introduction ---------- My article 'Astrology for astronomers' generated a LOT of comment, much of it, uh, deprecative. However, many readers took a fancy to the fact that there is much in astrological calculation of good value for astronomers. On the other hand I sure did not win over any 'converts' to regulation astrology. If you missed that piece, it's in the articles section of 'www.nyskies.org' under John Pazmino. To fully visualize how astrological calculation can assist the astronomer, I include HERE a classical 'wheel' chart done up for 0h EST on 24 December 2007 in New York. That's the night before the 2007 Mars opposition. It turns out that, by happy chance!, this night has major significance for astrologers. For us as astronomers, it presents a most curious and interesting arrangement of planets in the sky that can enhance our skywatching. The astrologer plots the planets on a circular chart, commonly called a wheel for its obvious shape with rim, hub, and spokes. The one we'll explore was generated by ZET, a standard astrology computer program that has some really handy features for astronomers. I do not here discuss the workings of this program but merely explain this particular output from it. If you're interested, ZET is a free download. It's large for a dialup Internet connection, 11Mb. Please note that I in this article give only brief descriptions of the astrological concepts. You really better read 'Astrology for astronomers?'.
Equatorial chart -------------- If you recall the equatorial chart usually shown in astronomy magazines, that's a big, really big, head start in understanding the wheel. In that diagram the equator and ecliptic are unrolled from the sky and spread out flat. east is on the left; west, right. In southern hemisphere magazines, this chart is inverted to better match the stars in the local sky. The seam is usually at the vernal equinox, but a close second choice is to put it at the Sun. That way the entire night sky, from dusk to dawn, in in one piece. In this method, a new base map is prepared for each magazine issue. The equator is the horizontal centerline of the chart and the ecliptic is the 'sine wave' trending left to right. It is rare to see this chart aligned with the ecliptic with a sinuous equator. Stars, to some modest depth of magnitude, are sprinkled over the map field. The declination width is about +/- 40 degrees north and south to make sure all the planet motions are contained within it. Planets are plotted for the instant or coming month by symbols or icons, including the Sun and Moon. The Moon may be plotted for her cardinal phases. A quickly moving planet may be plotted for the 1st and last days of the month. No other solar system bodies are marked, like asteroids or comets. Other parts of the magazine deal with them. This equatorial chart can be elaborated by fancy art with a daylight glowball around the Sun, phase discs of the Moon, tinted stars, air brushed Milky Way, and so on. To some astronomers, the more jazzed up is the chart, the harder, not easier, it is to read. In the old days, such charts were simple black-&-white maps with hand-drawn dots and labels for the planets. The chart presents at a glance the locations of the planets relative to the Sun and stars by which you then assess their visibility in your local sky. You have to mentally sketch in the local horizon for the instant hour or refer to a regular allsky map. I do see, once in a long while, an accompanying template to copy and cut out. Placed over the chart, lined up with certain index marks, it masks off the part of sky below the horizon.
Wheel chart --------- HERE is the astrologer's version of the equatorial chart. It is not unrolled, left circular, and centered on the Earth at its hub. You can compare this to the equatorial chart curled around, taped at the seam, and somehow squashed flat into a broad circular band. The wide- screen view becomes a cyclorama of the ecliptic zone of the sky. To be a bit more careful, this is a natal chart, one cut for a person's moment of birth. For the record, according to one astrologer I know, the moment of birth is NOT, as commonly thought, that of seeing the light. It's when the child first interacts independently with the cosmos. This is signaled by its first cry, completing its first breath by which it ingests the mix of celestial inducements at the instant. These inducements imprint the child with the general qualities of life it will live thru. There's an other chart, the horary chart, compiled for a moment within a person's life. Such may be for buying a house, moving out of town, getting divorced, &c. The mechanics of generating a horary chart are the same as for the natal chart, only the processing of the information in the chart differs. By skipping the astrology function of the chart, you may use either type. Most astrology computer programs cut a natal chart in the lack of other instruction. Hence, you can create a 'natal' chart for any moment you want, like I did here for the Mars opposition.. Everything is predicated on the geocentric solar system, which, of course, is invalid for dynamical and physical astronomy. However, for us staying on Earth and looking into space, the geocentric model is quite handy and adequate. Just don't push its envelope too far. No, I have no idea how astrologers deal with the planets and zodiac as seen from other places in the solar system. The horizontal line thru Earth in the center (smothered by overlying lines in this chart) is your horizon. The left side is at the rising point of the ecliptic; right, setting. Because of the obliquity of the ecliptic against the equator, the rise and set points are generally NOT at the east and west points of the horizon. The rising point of the ecliptic is the ascendent, 'Asc' on the chart. Where the ecliptic sets is the descendent, 'Dsc'. The tow are always exactly six zodiac signs, 180 degrees, apart. Both words are also spelled with '-dant' from a French derivation. The astronomer prefers the Latin base with '-dent'. 'Ascendere' is a 3rd conjugation verb; feel better now? The rim is the circles of the zodiac and of the houses. The signs are labeled by their traditional symbols and the houses are labeled by Roman numerals. Houses have fanciful names but most astrologers prefer the numbers. Both houses and signs progress eastward, Aries thru Pisces and house #1 thru house #12. Near the top of the chart is the medium coeli, 'MC', where the ecliptic crosses the upper meridian. This point is the astrologer's equivalent of the astronomer's sidereal time. Near the bottom is the imum coeli, 'IC', the crossing of ecliptic and lower meridian. The planets are plotted by their symbols at their places in the zodiac. The little numbers next to them are the degree within the sign where they sit. In this particular chart some locations are given to the degree, others to the degree and minute. In the text here I round all angles to the degree. In the belly of the chart are various alignments among the planets and points. For the most part these can be ignored but I set the programs for the major alignments, or aspects, as handy ways to appreciate the cyclorama of planets around the sky. The lines join the associated planets with symbols on them for the aspect. That's really all there is to it! What at first looks like a mysterious cosmic diagram left behind by flying-saucer creatures, is nothing more than a stylized chart of the zodiac for a given moment. If you understand the initial description in this section, you're home free for the following details.
Initial parameters ---------------- At the top left are the place, date, hour for this chart. They are like the setting for a planetarium program. The location in ZET is selected from a humongous list of towns around the world. I stumbled on a wicked glitch. I looked up 'Brooklyn'. There it was among the towns in New York! I selected it and proceded to explore the program. Uh-oh. The horizon was too far north; the timezone offset was too far west. The 'Brooklyn' in the list is NOT the fourth largest city in the United States! It's a hamlet on Lake Ontario in upstate New York! I changed to 'Manhattan', the correct Manhattan in New York City. Under these are other settings:
----------------------------------------------------------------- Tropical - this chart uses the traditional sequence of signs, starting with Aries at the vernal equinox. This is far and away the preferred method. The alternative is 'Sidereal' which uses the current alignment of signs with the zodiac constellations. This method will cause gross confusion for both astrologers and astronomers. Stick with the classical signs! Ecliptic - the rim is the very ecliptic. The alternative is 'equator' but this can cause distortion in the angular relations between planets and be a hindrance in spotting them in the sky. Stay with the ecliptic. Topocentric - the positions are computed for the observer's location on Earth. The alternative is 'geocentric', which is quite adequate for all the planets except the Moon. Meridian - The houses are those of the 'meridian' scheme, where the cusps are placed at 2-hour intervals of hour angle eastward from the upper meridian. There are some 20 other methods of delineating the house cusps, but only one other has any sense for astronomy. That is the 'horizontal' system where the cusps are at 30-deg intervals of azimuth eastward from the upper meridian. ----------------------------------------------------------------
I use these settings as defaults but can change them at will for special purposes. Like astronomy programs, astrology programs can save a set of default parameters that load at each run. In astrology, however, each case may have its own location (birthplace) so the settings are altered far more frequently than in astronomy. The wheel is a snapshot, like a planisphere set to a given moment. ZET, and many other astrology programs, have animation that rotates the sky. The wheel turns around the Earth hub and the planets are carried round with it. If you run the animation for many days, the planet enter and leave alignments, the aspects. Lines delineating the aspects turn on and off. It can look like a kaleidoscope on the computer screen!
The zodiac -------- I find it easiest to picture the chart as a special planisphere view based on the ecliptic rather than the equator. The observer is in the middle, looking south. Medium coeli is near the top of the chart, in the 'front' of the sky while looking south. Imum coeli is behind and below you. Some astrologers call these points zenith and nadir. The real zenith and nadir are not shown at all in the wheel chart because, except in the tropic latitudes, the ecliptic never reaches them. The zodiac above the horizon extends from the descendent in the western sky, up thru the medium coeli, down to the ascendent in the eastern sky. The rest of the ecliptic, ascendent thru imum coeli to descendent, is below the horizon and not visible at the instant. Probably the biggest obstacle to a clear reading of the chart for astronomy is the dispersion of the zodiac signs and constellations. Astrology of today is founded on the works of Ptolemaeus, some 2,000 years ago. The names of the signs at that time did line up more or less with the constellations. By now they are one step west, relative to the stars, due to precession. The slippage is about 28 degrees, not quite a full sign. Hence, it is really not feasible to rename the signs to better match the stars. It may have been wise in early times to letter the signs, like alpha thru mu. This would have avoided the contention about precession among astronomers and astrologers. Never the less, by mentally indexing the signs you can visualize where among the stars the planets sit. This tactic can be only approximate because the constellations are of various lengths along the ecliptic while the signs are zones of 30 degrees each.
The houses -------- Unlike the universal acceptance of the signs there is massive dispute about the houses. The idea is to build a set of 12 divisions of the zodiac based on the observer's location to complement those based on the celestial sphere. No general consensus was so far reached, despite centuries of debate, on the proper construction of the house divisions. The runaway most prevalent scheme is the Placidus system, because thruout most of the 20th century there were cheap, widely-available, tables for only this system. Tabulations for other schemes were too costly and hard to find.. For astronomy I find, of the 20 and more house methods out there, only two of use. Astrology computer programs, recognizing the lack of agreement on a house method, let you select the method you want. I set ZET for the meridian houses, spaced at 2-hour intervals of hour angle from the upper meridian. Where these hour circles cut the ecliptic are the cusps of the houses. The other useful scheme is the horizontal house, set up as 30- degree intervals of azimuth from the upper meridian. The house cusps are where the azimuth circles cut the ecliptic. The houses circles stay still on the horizon while the signs, planets, points roll behind them in diurnal motion. The cusps slide north and south along the circles, according as the declination of the ecliptic at each intersection. The medium coeli, by definition in the meridian system, is the cusp of the 10th house. Imum coeli is the cusp of house #4. Houses are numbered eastward from #10 at medium coeli, thru 12, then 1, and continuing back to 10. House #1 is in the eastern sky while #7 is in the western sky. In many charts, the labels for the 4th and 10th house is omitted because they are the imum and medium coeli. The meridian houses show what point of the ecliptic is on the meridian at 2-hour increments thruout the day. For example, in the chart the medium coeli, 10th house, is the 4th degree of Cancer (Cancer 4) Two hours ago, at 22:00 on December 23rd. it was the 6th degree of Gemini (Gemini 6). This point now at 0h is at the cusp of the 9th house. The cusp of the 11th house will be on the meridian in two hours, at 02:00 on the 24th, and is the 2nd degree of Leo (Leo 2). To help you over the hurdle of sign versus constellation, the medium coeli at chart time is in the beginning, front, cusp, of constellation Gemini. In two hours it'll be the front of Cancer. Two hours ago it was the front of Taurus.
Ascending node ------------ Astrology tracks many fake planets, most of which are of no value for astronomy. A couple are, believe it or not, of good value. At the cusp of Pisces you see a squiggly symbol which you may recognize from orbital mechanics. It's the ascending node symbol. In particular, it's the ascending node of the Moon's orbit. The descending node is usually not marked but it is opposite, 6 signs away. When marked, it uses the up-side-down squiggly symbol. When the Moon, the white crescent symbol near medium coeli, is near either node, she is close to the ecliptic, with latitude near 0 degree. When she is 90 deg east of the ascending node, she is near her maximum north latitude of +5.5 degrees. 90 deg west of the ascending node puts the Moon near her maximum south latitude, -5.5 deg. Thus, the ascending node helps assess the Moon's latitude for possible star and planet occultations and for eclipses of Sun or Moon.
Lilith ---- Lilith is a strange point for having either of two meanings. Lilith for astronomy should be set to be the apogee of the Moon's orbit, like for this article. The other sense is the second, empty, focus of the Moon's orbit. Astrology programs allow the selection. In the middle of Scorpius (which astrologers call Scorpio) you see a black crescent with a plus sign under it. This is the astrological symbol for Lilith for both meanings. The opposite point, usually not marked, is the perigee of the Moon's orbit. When the Moon is near Lilith, she moves at her minimum angular speed thru the stars, about 11-1/2 degree/day. Her angular speed increases with elongation from Lilith until the maximum, about 14-1/2 degree/day, at the perigee, 6 signs away. Lilith helps visualize the speed of the Moon for indexing her position during the night. The planets, in contrast, move so slowly that you may leave them fixed during the night where they are at chart time.
The Planets --------- Astrologers include all nine (yes, nine) planets and a bunch of asteroids in their basic chart construction. Astrology programs let you turn off the unwanted ones, like I did here to leave only the classical planets from Mercury thru Saturn. Asteroids on the chart will be in very misleading places. They wander so far from the ecliptic that they can not be properly plotted to match their places in the sky. I just don't use them at all. The classical planet symbols are those used widely by astronomers until the mid 20th century. Even today, they are handy for note taking or other quick writing. Scanning from west to east, we see no planets in [the signs of] Aries, Taurus, Gemini, up to medium coeli. Thus, the entire western sky is bare of planets. Crossing into Cancer we got two planets, Moon and Mars. Moon is in Cancer 4 and Mars is in Cancer 3. Medium coeli is Cancer 4, so the Moon and Mars are also on the meridian. This you already figured out because Mars is at opposition, being then on the meridian at local midnight, which is chart time. That the Moon is also near the meridian and near Mars is pura mente an accident. Note that the Moon is also opposite the Sun, so she is in her full phase. Yes, on the night before opposition, Mars is overshined by the full Moon! Continuing east, we find Saturn in Virgo 9. Venus is in Scorpius 22, near conjunction with Lilith. This aspect has no significance at all in astronomy. We come round to imum coeli to find Sun, Mercury, and Jupiter clustered near the cusp of Capricornus (the astrologer's Capricorn). Sun is in Capricornus 2; Mercury, Capricornus 6; Jupiter, Capricornus 1. All three are in mutual conjunction a are in mutual opposition to Moon and Mars! Moving onward thru Aquarius and Pisces we find no more planets. This completes the circuit of the zodiac for 24 December 2007 at 0h in New York. We got three planets up in the night sky (Moon, Mars, Saturn) and four down (Venus, Sun, Mercury, Jupiter).
Retrograde -------- The retrograde motion of a planet is very important for both astronomy and astrology, yet few astronomy programs tell you directly when a planet is in retrograde. You have to step the planet a day to and fro and see how its longitude changes. Astrology programs make this motion clear in their output. When in retrograde, a planet's longitude decreases with time. On the chart, see the little 'R' next to Mars and Saturn? This indicates that these planets are in retrograde. All the other planets, with no 'R' on them, are in prograde. Mercury is in progade. This means that he is in a superior, not inferior, conjunction. Mercury continues his direct movement to cross from morning to evening apparition. If there was a 'R' against Mercury, the motion would be retrograde and the conjunction would be an inferior one. Mercury would be scooting westward to get from evening to morning sky. Do not confuse retrograde motion with a decrease of elongation from the Sun! Mercury can lag the Sun's pace so the Sun catches up to him and form the conjunction. It's only in the final days before inferior conjunction that Mercury reverses tracks into retrograde. Here's what Mercury does in late 2007-early 2008, taken from an astronomy program: ------------------ date event ----------- --------------------------- 2007 Sep 29 greatest eastern elongation 2007 Oct 12 enter retrograde loop 2007 Oct 23 inferior conjunction 2007 Nov 1 leave retrograde loop 2007 Nov 8 greatest western elongation 2007 Dec 17 superior conjunction 2008 Jan 22 greatest eastern elongation 2008 Jan 28 enter retrograde loop 2008 Feb 6 inferior conjunction 2008 Feb 17 leave retrograde loop ---------------------------------- In the morning sky, the decrease of elongation, as Mercury heads toward superior conjunction, must be direct. It is, in fact, faster than the Sun's pace to catch up to him. A similar train of reasoning applies to Venus. At chart time Venus happens to be prograde as a morning star during western elongation. The Moon's ascending node is always retrograde. This particular chart doesn't flag it. Some other programs plot the chart with the 'R' next to the ascending node so you can't miss it..
Part of Fortune ------------- This is a fake planet of no use for astronomy that I can figure out. I include it here only in answer inquiries from my article 'Astrology for astronomers?'. I turned it off for the chart here. The explanation in astrology tends to read like dreamy feminist tracts from the 1970s. I spare you the particulars and note here only the calculation of Part of Fortune. This is for curiosity, you know? The longitude of the ascendent and of the Moon are added, then that of the Sun is subtracted. From data in the chart, the PoF is at:
longitude of ascendent Libra 03 = 183 longitude of Moon Cancer 04 = 94 ----------------- --------- --- sum --- 277 longitude of Sun Capricornus 02 = 272 ---------------- -------------- --- difference 005 longitude of PoF Aries 05 <-/
If I had PoF turned on, it would be plotted in the beginning of Aries with its symbol, looking like a railroad crossing sign. It is in a square aspect with Moon-Mars and with Sun-Jupiter-Mercury, in conjunction with descendent, and in opposition with ascendent.
Symmetry ------ If you look carefully at the medium coeli, it is not exactly the midpoint between ascendent and descendent. It is close ONLY by chance for the instant hour. In general MC is severely offset from the midpoint because of the ecliptic obliquity. The ecliptic can rise to the left or right of the east point. Think of the displacement of the Sun's rising point with the seasons. He rises to the left of east in summer; right of east in winter. The setting point of the ecliptic, the descendent, is opposite the ascendent, and is displaced to the same amount from the west point. Think of the full Moon settings. In summer she sets left of west. The winter full Moon sets right of west. When the ascendent is to the left of east, there is a larger arc of ecliptic from it to the meridian than from meridian to descendent. Because the wheel chart shows the ecliptic, the MC is right of the midpoint EVEN THO IT IS STILL THE LOCATION OF THE MERIDIAN!, causing what looks like an asymmetry in the sky. When the ascendent is right of east, the lesser arc lies between it and MC; the greater, MC and descendent. MC is then left of the midpoint on the chart. The astrology chart shows clearly the ascendent displacement relative to due east. When the cusp of house #1 is above the ascendent on the chart, above the horizon in the sky, the ascendent is left of due east. When the cusp of house #1 is below the ascendent, below the horizon, the ascendent is right of due east. I must emphasize that this applies to the houses of the meridian system. It is not a general rule for any wheel chart. For the Placidus houses, the cusp of house $1 is fixed at the ascendent. You can still appreciate the shift by the MC. when it is left of the midpoint of the chart, the ascendent is right of east and vice versa.
Aspects ----- Elongations in astronomy are almost exclusively banked off of the Sun. To find the elongation between two other planets you must manually subtract their solar elongations. Astrology computes elongations between all pairs of planets! This is z trivial chore for a computer program but those for astronomy don't include this faculty. In astronomy certain elongations are specially noted, like opposition (elongation 180 deg) and conjunction (elongation 0 deg). Others used from time to time are quadrature (90 deg), greatest elongation (27 deg for Mercury, 47 deg for Venus), and stations at the vertices of retrograde loops. Astrology recognizes most of the astronomy special elongations, called aspects, and adds several more.
aspect | elon | equivalent ---------------------+------+------------ conjunct | 0 | conjunction sextile (SEKS-till) | 60 | (not common) square (SKWAIR) | 90 | quadrature trine (TREEN) | 120 | (not common) opposite | 180 | conjunction --------------------+------+-------------
These are the 'major' aspects, promulgated by Ptolemaeus. Over the ages many other elongations were examined but none achieved general favor. Astrology programs offer a wide selection of these plus the ability to enter a custom aspect. I set ZET to show only the major aspects, otherwise the chart would be criss-crossed with aspect lines to the point of illegibility. In astronomy the sense of the elongation is vital, whether it is to the east or west of the home body. Astrologers generally ignore the sense and work only with the absolute value of elongation. You have to manually take the sense from the wheel chart. Aspects are calculated on the fly by ZET and laid out in the chart by lines joining the associated planets. On the line is the symbol for the aspect, a triangle for trine, a square for square (none in this chart), and a 6-point aster for sextile. Conjunction and opposition are usually not labeled, perhaps because they are so obvious. When described in text their symbols are the same as for astronomy.
Lots of aspects ------------- On 24 December 2007 there are lots of aspects! Sun. Mercury, Jupiter are in conjunction. Mars and Moon are in conjunction. The first three are in opposition to the second two. Astrology treats EACH pair as its own aspect, so we have Sun opposite Mars and Sun opposite Moon. Then Mercury opposite Mars and Mercury opposite Mars, and so on. For the conjunction, we got Sun-Mercury, Sun-Jupiter, Mercury-Jupiter. The lines joining each pair overwrite in the center of the wheel, looking like ropes tying Moon-Mars to Sun-Mercury-Jupiter. They in this case obscure the earth at the wheel hub. There is in Scorpius a conjunction of Lilith and Venus, tho not so tight as the other conjunctions. There are trines between Saturn and Sun-Mercury-Jupiter and between ascending node and Moon-Mars. Sextile stands between Moon-Mars and Saturn and between ascending node and Sun-Mercury-Jupiter. Now hold the chart away a bit and relax the eyes. See the huge rectangle in the sky? The corners are Sun-Mercury-Jupiter, Saturn, Moon-Mars, and ascending node. Sides are 120, 60, 120, 60 degrees. The alignments are not precise, but pretty close. One corner is a fake planet, ascending node, invisible. Never the less, this night of the Mars opposition presents very interesting alignments of many planets thruout the zodiac. This configuration is destroyed late on the 24th and is vanished by nightfall because the Moon moves along, out of aspect with the other planets. In the sky, on the night of the 24th, Moon is a dozen degrees east of Mars and almost a day past full..
Kinetics ------ Altho the astrological chart is a snapshot for a single given moment, there is some kinetics we can extract from it. We saw this in the use of meridian houses to tell what's on the meridian at steps of two hours in the day, With these houses we can estimate culmination of the planets. When does Saturn reach the meridian? Saturn sits about 1/5 of the way into house #12. The cusp of house #12 comes to medium coeli (same as culmination) four hours after the instant medium coeli at the cusp of house #10. 1/5 of two hours after that, Saturn comes to the meridian. So, Saturn culminates at
(culm) = (chart hour) + (full houses) + (part of next house) = (00:00) + ((2) * (2h)) + ((1/5) * (2h)) = 00:00 + 4h + 24m = 04:24
This agrees within a couple minutes with astronomy programs. This trick works well for culmination but fails badly for rising and setting. This is a consequence of the ecliptic obliquity. To better appreciate the kinetics of the wheel, you may cut charts at, say, one hour intervals during a night. Or run the program's animation, if available.
Conclusion -------- While astronomers may have little regard for the tenets of astrology, there are features of value. The construction, via an astrology computer program, of the wheel can give an easy-to-read diagram of the zodiac with planets deployed along it for any given moment and location. The information in this chart is valid for astronomy with reasonable interpretation. You may end up using it in parallel with the conventional equatorial chart.