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Our Solar System, Real and Imaginary

Here is a table of a few of the bodies in the Solar System that orbit the Sun, including all the known planets, as well as some others:

Name       Sidereal Year         Distance from Sun    Bode's Law
           (days)                (astronomical units)

Mercury             87.9691           0.387            0.4           4       4 +      0
                                                                   ...
                                                       0.41875       4 3/16  4 +        3/16
                                                       0.4375        4 3/8   4 +        3/8
                                                       0.475         4 3/4   4 +        3/4
                                                       0.55          5 1/2   4 +      1 1/2
Venus              224.70069          0.723            0.7           7       4 +      3
Earth              365.256363         1.000            1.0          10       4 +      6
Mars               686.980            1.524            1.6          16       4 +     12
Ceres                                 2.767            2.8          28       4 +     24
Pallas                                2.774
Juno                                  2.669
Vesta                                 2.362
Jupiter          4,332.589            5.204            5.2          52       4 +     48
Saturn          10,759.22             9.582           10.0         100       4 +     96
Uranus          30,707.4896          19.201           19.6         196       4 +    192
Neptune         60,223.3528          30.047           38.8         388       4 +    384
Pluto           90,465               39.482
Eris           203,600               67.67            77.2         772       4 +    768
2010 JJ124                           82.872
2005 RH52                           157              154         1,540       4 +  1,536
2010 NV1                            294              307.6       3,076       4 +  3,072
Sedna        4,163,850              518.57           614.8       6,148       4 +  6,144
2012 DR30                          1104            1,229.2      12,292       4 + 12,288

Included in that list are the first four asteroids to be discovered. Once, they, too, were referred to as planets, but they were dethroned when it became apparent that there were a large number of other bodies in the Asteroid Belt.

It is, of course, the same cause - the discovery that there are a host of bodies similar to Pluto in the Kuiper Belt - that has led to the fate of Pluto.

The Bode-Titius Law was an empirical rule that seemed to correspond well with the distances of the classical planets from Mercury to Saturn from the Sun. The discoveries of Ceres, Uranus, and Neptune all confirmed the validity of this general rule.

This table is not intended to seriously suggest even that Eris should be considered to be Planet X, let alone that 2005 RH52 is Planet Y, 2010 NV1 is Planet Z, Sedna is Planet AA, and 2012 DR30 is planet BB. Some of those bodies were chosen for inclusion because their distances fit with the slots in Bode's Law, while others just as massive and important at in-between distances were ignored. Instead, it is to show that while the main Asteroid Belt just occupies one of the slots in Bode's Law, the bodies being discovered in the Kuiper Belt range over a span of distances including several of the slots in which planets were anticipated.

Note, too, that while an intra-Mercurial planet, Vulcan, was once hypothesized, Bode's Law doesn't imply the presence of such a planet; but it could be interpreted as implying an infinite series of intra-Venusian planets, of which the slot in which Mercury is considered to lie would constitute the limiting bound.

The following image

illustrates symbols used by astronomers and astrologers.

Here is the key to the symbols on the diagram:

Aries          0°     Conjunction       80°     Binonile         Sun                   5 Astraea       1221 Amor        Chiron    Dark Moon Lilith  Tishtar
Taurus       180°     Opposition       160°     Quadnonile       Moon                  6 Hebe          2063 Bacchus     Chariklo  Transpluto        Az
Gemini       120°     Trine             22 1/2° Quartosquare     Mercury               7 Iris           763 Cupido      Nessus                      Priap
Cancer        90°     Square            67 1/2° 3x Quartosquare  Venus                 8 Flora         1864 Daedalus    Pholus    Demeter           Haurang
Leo           60°     Sextile          112 1/2° 5x Quartosquare  Mars                  9 Metis         1108 Demeter     Thereus   Hermes            Vanand
Virgo         45°     Semisquare       157 1/2° 7x Quartosquare  Jupiter              10 Hygiea         433 Eros        Pylenor   Persephone        Vakshya
Libra         30°     Semisextile                                Saturn               11 Parthenope      75 Euridike    Hylonome                    Utopia
Scorpio      135°     Sesquiquadrate                             Uranus               12 Victoria      2212 Hephaistos  Okyrhoe   Cupido            Rasi
Sagittarius  150°     Quincunx                                   Neptune              13 Egeria         103 Hera        Elatus    Hades             Proserpine
Capricorn             Parallel                                   Pluto                14 Irene          944 Hidalgo     Asbolus   Zeus              Isis
Aquarius              Contraparallel                                                  15 Eunomia        430 Hybris      Echeclus  Kronos            Anubis
Pisces        72°     Quintile                                   Ceres                16 Psyche        1566 Icarus      Pelion    Apollon           Osiris
             144°     Biquintile                                 Juno                 17 Thetis          42 Isis        Bienor    Admetos
              36°     Semiquintile                               Pallas               18 Melpomene     1181 Lilith      Crantor   Vulcanus
             108°     Sesquiquintile                             Vesta                19 Fortuna         93 Minerva     Cyllarus  Poseidon
              40°     Nonile                                                          26 Proserpina     350 Ornamenta   Amycus
              51 3/7° Septile                                    Ascending Node       28 Bellona       3200 Phaethon
             102 6/7° Biseptile                                  Descending Node      29 Amphitrite      80 Sappho
             154 2/7° Triseptile                                 Black Moon Lilith    35 Leukothea     1170 Siva
                                                                 Part of Fortune      37 Fides         2102 Tantalus
                                                                                                       1685 Toro

The first column contains the signs of the Zodiac. These have only one conventional form, except in the case of the sign Capricorn.

Then there are two columns joined in one group that contain the various astrological aspects. The symbols for the quintile and related aspects come from a very old book on arithmetic; the rest are in current use by astrologers. The number of degrees in each aspect is given. Two planets are in parallel when they occupy the same degree of declination; they are in contra-parallel when one occupies the same degree of north declination as the other occupies of south declination.


Incidentally, quintiles as an astrological aspect were invented by Johannes Kepler. While skeptical about astrology as conventionally practiced, he did believe that the planets could have an influence on us; thus, he considered the planets and their aspects to be reasonable, but signs, decans and terms to be too arbitrary to be given credence. Thus it could be said that he anticipated Michel Gauquelin.

In general, astrology does contain enough arbitrary elements that it does stretch credibility that the system could have arisen from actual successful observations through folk empiricism.

The remaining alternative that would allow for the system of astrology to be valid - as opposed to being originally a knowingly fraudulent concoction - would be that it arrived by some sort of revelation. And, indeed, in antiquity it was believed either that one King Nechepso had a vision in which astrology was revealed to him, or that the Patriarch Abraham (!) was given its secret, either by God or by the Watchers, apparently a borderline group associated with the fallen angels.

While neither the Tetrabiblos of Ptolemy nor the Carmen Astrologicum of Dorotheus the Egyptian cites earlier authors, they are both cited and quoted in three other early works on astrology: the Mathesos of Firmicius Maternus, the Anthologies of Vettius Valens, and the Apotelismatica of Hephaiston of Thebes.


Then we have a column divided into three parts vertically.

First, there are the planets, including Pluto. Uranus, Neptune, and Pluto all have alternate symbols; the last ones for Uranus and Neptune, though, are only in use by some astrologers in the Netherlands. The second one for Neptune, intended to commemorate LeVerrier, its discoverer, is rarely used at present.

In this part, separated by a dividing line, we also have on the right the symbols used for these planets by the astrologers of the Werkgemeenschap van Astrologen (WvA), also known as the "Ram School"; the symbol for Venus is unchanged, and those for the Moon and Neptune are recognizable, but the rest are significantly altered. (They use the conventional symbols for the Ascending Node and the Part of Fortune also.)

The intent of these changed symbols is to more clearly illustrate relationships between the meanings of the planets that, in some cases, have been said to be expressed in their traditional symbols. Thus, Venus is a cross below a circle; the symbol for Mars is in fact a cross above a circle in the Ram notation, but the conventional one has been said to express this as well.

Thus, the symbols of the planets in their system - including three hypothetical planets whose symbols will be noted in below when we reach the appropriate part of the diagram - have these components:

Sun              Circle,   Crescent
Moon             Crescent
Mercury          Crescent, Circle
Venus            Circle,   Cross
Mars             Cross,    Circle
Jupiter          Crescent, Cross
Saturn           Cross,    Crescent
Uranus           Cross,    Crescent, Circle
Neptune          Crescent, Cross,    Circle
Pluto            Cross,    Circle,   Crescent
Demeter          Circle,   Cross,    Crescent
Hermes           Crescent, Circle,   Cross
Persephone       Circle,   Crescent, Cross

Second, there are the four original asteroids. For Vesta, first the original form of its best-established symbol is shown. A number of simplified forms of this symbol were also used. Next is the original symbol devised by the mathematician Karl Friedrich Gauss for that body. Finally, the symbol, loosely based on part of the first symbol, currently popular with present-day astrologers is shown.

Third, there are symbols for more abstract points in the sky. The Moon's ascending and descending nodes are followed by the "Black Moon Lilith", which has the same position in the sky as the Moon's apogee, but it is instead the alternate focus (alternate to the barycentre of the Earth-Moon system) of the Moon's orbit. Also shown is the symbol for the Part of Fortune. First is the symbol traditionally used. Since that symbol can also serve as a symbol for the Earth, more recently a modified symbol has come to be used by some modern astrologers in which the crossbars are diagonal.


The Part of Fortune is calculated by the formula:

Ascendant + Moon - Sun

in a day birth, or

Ascendant + Sun - Moon

in a night birth. Some authorities do not include the reversal for a nocturnal birth in its definition. Numerous other Arabic Parts exist.

At one time, in addition to Arabic Parts, antiscia and dodecatemoria were also used in astrology. Today, the Arabic Parts are sometimes used, and midpoints are also used by some astrologers.

The antiscia are determined by this formula:

Antiscion = 180° - Planet

that is, the positions of planets are reflected along the axis from the cusps of Cancer and Capricorn to obtain their antiscia.

This is how antiscia are described both in the Mathesos of Firmicius Maternus, and how they are used today by Uranian astrologers. Other sources give other definitions: one, that the current convention is to reflect planets along the axis from the Midheaven to the Immum Coeli, another that planets were called antiscia in the Tetrabiblos when they were in contra-parallel aspect.

The dodecatemorion of a planet can be a body on a chart calculated by adding twelve times the angular position of the planet within its sign to the cusp of that sign. Dodecatemoria can also be considered to be areas on a chart, like decans or terms, each one 2.5 degrees in length, having the character of the twelve signs in order, starting in each sign with that sign itself, thus matching, for a planet located within it, the sign in which the dodecatemorion of the planet by the first definition would land.

On this subject, it might be noted that the individual degrees are assigned rulers through monomoira as follows: the first degree of each sign has the same ruler as the sign itself (among the seven classical planets), and then the planets are assigned as rulers to the successive degrees of that sign in the same order

Mars
Sun
Venus
Mercury
Moon
Saturn
Jupiter

as the ruling planets of the decans were classically assigned (as opposed to the modern method, where the first decan has the same ruler as the sign, the next as the sign four signs ahead, in the same triplicity, and the third decan as the sign in the same triplicty four signs behind).

As there have been many sets of meanings for the individual degrees of the Zodiac, none having universal assent, that there is one thing about the individual degrees with a solid traditional origin should be of interest. Also, this suggests taking the monomoirion of a planet in the same fashion as one would take its dodecamorion, except multiplying the distance of a planet from the cusp of its sign by thirty instead of twelve, and then taking that distance from that cusp. However, that would make more sense if the sequence of sign rulers rather than the sequence of decan rulers was used, but that would cause the Sun and Moon to occur less often as rulers. Of course, with Uranus, Neptune, and Pluto replacing one occurence of Saturn, Jupiter, and Mars, all that is needed are two other bodies to replace one occurence of Venus and Mercury to eliminate the issue of bias.


The next column contains the elaborate and pictorial symbols that appeared, primarily in the pages of the Astronomische Nachrichten, which were selected for many early asteroids at the time of their discovery. Also shown for Hebe and Hygeia are the considerably stylized symbols in use by present-day astrologers, and for Psyche the completely new glyph based on the Greek letter psi.

After that, another column contains a few of the symbols assigned by present-day astrologers to a number of other asteroids.

Next, we have the symbols for the Centaurs, a group of objects whose largest member is Chariklo, but whose best-known member is Chiron, the first one to be discovered. There are alternate symbols for these bodies, but some of them require permission to use, which seems the surest way of ensuring that such a version of the symbol for a body will not become the symbol for that body, appearing in standard astrological typefaces. While, for that reason, I have omitted most of the alternate symbols for the Centaurs, I have included an alternate symbol for Chiron which I remember seeing in one astrological magazine at the beginning of an article about it shortly after its discovery.

Finally, we have another two conjoined columns. These deal with hypothetical bodies, mostly planets, but a few moons as well.

I start with the Dark Moon Lilith. This is the third Lilith in this diagram, after the Moon's apogee and the asteroid 1181 Lilith. It was a second moon of the Earth thought to have been discovered by Georg Waltemath in the late 19th Century. Two symbols are given; Sepharial originally used the capital Greek letter Theta, the type for that character being available; more recently, a symbol like the mathematical symbol for the empty set was used in an attempt to give it a more distinctive symbol.

Next are the three hypothetical planets used by the Werkgemeenschap van Astrologen (WvA), also known as the "Ram School". (Note that there is also the asteroid 1108 Demeter, the symbol of which we saw earlier. Incidentally, asteroid 360 is named Carlova. There is also an asteroid 399 Persephone, which does not have a symbol shown here.) Note also that the symbol used for Persephone is the same as that shown as an alternate symbol for Uranus used by some astrologers in the Netherlands: the alternate symbol for Neptune indicated as used by astrologers in the Netherlands was used for Neptune in the document which was my source for those two alternate symbols. Of course, rather more startling is that the glyph for Hermes is identical with that for the planet Mercury. Of course, Hermes is the Greek word for Mercury. This, however, as we have seen, does not cause confusion because of the fact that these astrologers use a different symbol for Mercury as well as for several other planets.

Following them are the Uranian planets, as used by the Hamburg school. (Note that there is also the asteroid 763 Cupido, whose symbol we saw earlier.) And in the second column of this group are the planets (and two moons, Tishtar and Az) used by the Avestan school of astrologers in Russia. (Note that there is also the asteroid 42 Isis, the symbol of which we saw earlier.)

Incidentally, Tishtar is the Farsi word for Sirius, and Vanand is Farsi for Vega, but, of course, no confusion will be occasioned to astrologers outside Iran.


Demeter, Hades, and Poseidon, however, at one time really were present in our Solar System, although not as planets or asteroids.

The moons of Jupiter have had a convoluted history insofar as their names are concerned:

                        Marsden      Nesterovich    Karpenko

   I 1610 Io
  II 1610 Europa
 III 1610 Ganymede
  IV 1610 Callisto
   V 1892 Amalthea
  VI 1904 Himalia       Hestia        Atlas         Adrastea
 VII 1905 Elara         Hera          Hercules      Ida
VIII 1908 Pasiphaë      Poseidon      Persephone    Helen
  IX 1914 Sinope        Hades         Cerberus      Leda
   X 1938 Lysithea      Demeter       Promethius    Latona
  XI 1938 Carme         Pan           Dedalus       Danae
 XII 1951 Ananke        Adrastea      Hephaestus    Semele
XIII 1974 Leda

The four Galilean satellites of Jupiter were given their present names by Simon Marius soon after Galileo discovered them; like Galileo, he was one of the first people to turn the telescope to the heavens. However, while modern historians of astronomy accept that he had independently discovered these moons just one day after Galileo, in his own time, since he did not present evidence for this claim, which he only advanced four years later, he faced skepticism, and that may have contributed to astronomers not using his names for these bodies until the 20th Century.

Those four names were the only officially recognized names for any of the moons of Jupiter until 1975. But prior to 1975, unofficial names were given to many of those moons. In the case of Amalthea, the unofficial name was ultimately accepted as the official name; it was first bestowed on this moon by the popular French astronomer Camille Flammarion shortly after its discovery in 1892.

The unofficial names for Jupiter VI through Jupiter XII that saw occasional use between 1955 and the adoption of the official names for these moons were suggested originally by Dr. Brian G. Marsden (in a paper that occupied pages 308 through 310 of volume 65 of the Journal of the British Astronomical Association); two other series of names for those moons were also suggested by two Soviet astronomers.


Several other hypothetical planets have been used by some astrologers from time to time. Two early ones, Isis and Osiris, not the same as those used by the Avestan school, were originally proposed by George Sutcliffe, and they recieved considerably more attention from mainstream astrologers than most other hypothetical planets since, but I have not been able to locate their symbols. A short booklet by the astrologer Charles Jayne, "The Unknown Planets", listed many hypothetical planets used by other astrologers.

In October 1900, George Sutcliffe gave a lecture in Bombay titled "Two Undiscovered Planets", but this was about two intra-Mercurial planets, which he called Vulcan and Adonis. Vulcan, of course, had been the standard name for an intra-Mercurial planet; Jacques Babinet used it in 1846, and then Urban Le Verrier hypothesized a planet by that name as an explanation for the perihelion advance of Mercury later found to be due to General Relativity. An apparent observation of Vulcan was made by Edmond Lescarbault in 1859; while it is now realized to have been erroneous, naturally the tentative ephemerides calculated based on it by Le Verrier are still used by some astrologers.

I've been trying to find more information about the hypothetical planets Isis and Osiris; it was through an Internet search that I found that it was George Sutcliffe who was responsible for these planets being considered by some astrologers.

Alan Leo, in his book A Thousand and One Notable Nativities gives the position of Isis at the start of 1800 as 13 degrees Sagittarius, and that of Osiris for the same time as 23 degrees Leo, and the annual motion of Isis as one degree, and that of Osiris as 21 minutes and 49 seconds. In a footnote, Leo notes that those annual motions are in sidereal terms, and must be corrected by subtracting one degree every 72 years to obtain positions in the tropical zodiac. That, of course, is equivalent to subtracting 50 seconds of arc per year, thus changing the motions to 59 minutes and 10 seconds for Isis, and 20 minutes and 59 seconds for Osiris.

Another source, though, gives the annual motion of Isis as one degree and 50 seconds, and that of Osiris as 22 minutes and 32 seconds, adding 50 seconds in the first case and 43 seconds in the second to those base figures instead of subtracting. And, as the Age of Aquarius succeeded the age of Pisces, the first point of Aries in the tropical zodiac moves backwards through the sidereal zodiac of stars, so indeed the conversion from sidereal coordinates to tropical coordinates is done by adding 50 seconds of arc per year instead of subtracting.

As well, Nicholas De Vore's Encyclopedia of Astrology gives a short table of the positions of Isis and Osiris for a few dates. In that table, Isis and Osiris are not shown as moving at a uniform rate, but their positions are closer to those with a positive correction for precession than to either Leo's or the raw figures.

Copyright (c) 2012, 2015 John J. G. Savard


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