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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
2021 PH27             114.589            0.4617049        0.475         4 3/4   4 +        3/4
'Aylo'chaxnim         151.191            0.5554167        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
Icarus                409                1.078
Mars                  686.980            1.524            1.6          16       4 +     12
Vesta               1,325.75             2.362
Iris                1,346.493            2.386
Metis               1,346.705            2.386
Hebe                1,379.702            2.425
Juno                1,592.4664           2.669
Ceres               1,680                2.767            2.8          28       4 +     24
Pallas              1,684.9              2.774
Hygiea              2,034.762            3.142
Jupiter             4,332.589            5.204            5.2          52       4 +     48
Hidalgo             5,024                5.741
Saturn             10,759.22             9.582           10.0         100       4 +     96
Chiron             18,523               13.70
Chariklo           22,987               15.822
Uranus             30,707.4896          19.201           19.6         196       4 +    192
Neptune            60,223.3528          30.047           38.8         388       4 +    384
2003 YL179         88,283.4             38.8020066
Orcus              89,557               39.174
Pluto              90,465               39.482
2002 MS4           98,429               41.739
2015 DR248         99,782               42.1020169
Salacia           100,073               42.184
Varuna            101,980               42.718
Haumea            103,410               43.116
Quaoar            105,495               43.694
Albion            106,334               43.925
1999 JA132        108,717               44.5794211
Arrokoth          108,726               44.581
Makemake          111,845               45.430
2020 FQ38         124,153               48.7048733
2013 TE172        124,178               48.7115095
1999 KR16         124,475               48.7890637
2014 UQ229        131,477               50.6021460
1995 TL8          139,251               52.578
2011 GM89         139,713               52.6938510
2013 TJ229        158,415               57.2970248
2014 JM80         180,021               62.3949752
2010 JE215        180,066               62.4054573
Gonggong          202,484               67.485
Eris              203,600               67.67            77.2         772       4 +    768
2013 SN102        208,864               68.8933913
2016 MM56         220,877               71.5103818
2001 XB255        237,327               75.0181604
2002 AR91         238,205               75.2030381
2014 DQ143        247,534               77.1539067
2020 BC95         254,949               78.6871239
2014 OY393        271,750               82.8107197 
2010 JJ124        285,305               82.872
1996 TL66         278,211               83.403
2015 TV361        314,383               90.4845922
2008 ST291        372,469              101.3121724
2022 QV62         439,902              113.1979773
2014 JW80         589,363              137.5698911
2016 GA277        698,108              154.0104042
2005 RH52         702,689              157              154         1,540       4 +  1,536
2012 VP113      1,633,792              271.5
2010 NV1        1,696,005              294              307.6       3,076       4 +  3,072
2022 QE78       1,951,619              305.6315358
2021 PN72       1,993,938              310.0339167
Sedna           4,163,850              518.57           614.8       6,148       4 +  6,144
Leleakuhonua   18,222,065             1085
2012 DR30      23,451,607             1104            1,229.2      12,292       4 + 12,288

Included in that list are the first four asteroids to be discovered, Ceres, Pallas, Juno, and Vesta, along with a few others. Once, those four were also 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, although some of the most well-known bodies at other distances are now mentioned. Other relatively unimportant bodies have also been added because their orbital periods are close to those of a hypothetical planet proposed by astrologers. 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.

Incidentally, the orbital periods for Iris and Metis given above are from the proper elements for those bodies, not from osculating elements, so, although strong perturbations from Jupiter would no doubt lead to secular changes in them, one could concieve of them as "chronocrators", an astrological term sometimes applied to Jupiter and Saturn, given the long period of about 20 years between their conjunctions. Since Jupiter and Saturn, with orbital periods of about 12 and 30 years respectively, are not in an exact 5:2 resonance, the positions of their conjunctions slowly change.

The time between heliocentric conjunctions of Iris and Metis would work out to 8,553,438 days, on the order of twice the orbital period of Sedna.

A Non-Empirical Planetary Spacing Rule

The Bode-Titius Law was based on the observed distances of the planets from the Sun only, as a rule those distances seemed to fit without a reason being offered.

There was one other, earlier, famous attempt to offer calculated distances from the Sun for the five planets known to the ancients. Here, as illustrated by the image at right, I am referring to Kepler's Mysterium Cosmographicum.

According to Humboldt's Cosmos, quoting from a paper by Isaac Newton, the distances from the Sun in Astronomical Units that Kepler had calculated were:

Planet        Kepler's Estimate     Actual Distance

Mercury        0.38806               0.3870986
Venus          0.72400               0.7233316
Earth          1.0                   1.0
Nars           1.52350               1.5236882
Jupiter        5.19650               5.2028335
Saturn         9.51000               9.5387621

The rationale behind Kepler's scheme was that the ratio between the aphelion of one planet and the perihelion of the next would correspond to the ratio between the distances of the centers of the faces and the vertices of one of the Platonic solids.

Planet       Periheliion          Aphelion
   Solid         Face/Vertices       Perihelion/
                 Ratio               Aphelion Ratio

Mercury      0.31                 0.47
   Octahedron       1.73205            1.53
Venus        0.72                 0.73              
   Icosahedron      1.25841            1.34
Earth        0.98                 1.02
   Dodecahedron     1.25841            1.35
Mars         1.38                 1.67
   Tetrahedron      3                  2.96
Jupiter      4.95                 5.45
   Cube             1.73205            1.65            
Saturn       9.01                10.07

The Growth of the Known Solar System

In ancient times, astrology dealt with seven bodies; the two Luminaries, the Sun and the Moon, and the five Planets, Mercury, Venus, Mars, Jupiter and Saturn.

By the time of Ptolemy, it was recognized that the Earth was a sphere rather than a small flat disk, but the planets and luminaries were still thought of as revolving around the Earth at the center.

The first step in expanding our conception of the Solar System was, of course, taken by Nicolaus Copernicus, who proposed that the Earth went around the Sun instead. Galileo saw the moons of Jupiter in his telescope, which made the Copernican theory more plausible, and in his writings set forth a persuasive defense of that theory. Kepler then took astronomy further away from Ptolemy, by replacing epicycles with elliptical orbits following the law that equal areas were swept out in equal times.

Finally, Isaac Newton established that an inverse square law for the gravitational force, followed by the ordinary physical laws of mechanics, would lead to the planetary motions described by Kepler. By giving a physical basis to Solar System phenomena, he ended the era when the heliocentric theory was something that could be credibly debated.

Newton's explanation of the Solar System in physical terms opened up a large vista of new possibilities. Pierre-Simon de Laplace, in his Traité de Mécanique Céleste provided the mathematical tools with which to study how the planets departed from strictly following Kepler's Laws because their masses, while much smaller than that of the Sun, were still not utterly negligible, and so the orbits of planets were also slightly affected by the gravitational attraction of other planets, leading to perturbations.

In 1781, shortly before the publication of Laplace's book began, Sir William Herschel observed Uranus, eventually coming to the conclusion that it was not merely a comet, but was actually a new planet. In 1801, Giuseppi Piazzi discovered Ceres; afterwards, other asteroids were discovered in rapid succession. At first, these bodies were taken to be new planets, but as the number of known asteroids grew, it was eventually decided to place these smaller bodies in a different category. Of course, this anticipates the fate that befell Pluto after the discovery of Eris.

Studies of the motion of the new planet Uranus led to the conclusion that its motion could not be exactly accounted for due to perturbations from the existing planets, primarily Jupiter and Saturn. Both the French astronomer Urbain Le Verrier and the English astronomer John Couch Adams made calculations which led to an accurate prediction of the position of Neptune; but as it was Le Verrier who was able to secure telescopic observations to confirm his prediction, he, and the observer Johann Gottfried Galle, are credited with the discovery of Neptune.

In turn, the motion of Neptune was studied in hopes that it might lead to the discovery of further planets beyond it. For a time, it seemed that there were unaccounted-for perturbations of both Uranus and Neptune which did point to the existence of an additional planet, dubbed "Planet X". The astronomer William Henry Pickering was one of the leaders in carrying out these calculations.

This led to the astronomer Percival Lowell organizing a telescopic search for a planet that might correspond to the predictions being made, which culminated in the discovery of Pluto by Clyde Tombaugh in 1930. However, there were doubts about whether or not Pluto was actually massive enough to account for the perturbations which started the search that led to its discovery. After Pluto's moon, Charon, was discovered in 1978, it was proven that Pluto had nowhere near enough mass to significantly affect the orbits of Uranus and Neptune.

The astronomer Robert Harrington continued the effort to find Planet X by calculation, which had been left off after the discovery of Pluto, after this; but in 1992, E. Myles Standish adjusted the mass of Neptune based on data from the 1989 Voyager 2 flyby; that reduction in the mass of Neptune eliminated the need for an additional planet to explain unknown perturbations.

This raises two questions. One is that, since it becomes practical to determine a planet's mass if it has known satellites, and Triton, one of Neptune's two largest satellites, was discovered shortly after the discovery of Neptune (the other, Nereid, was only discovered in 1949, after the discovery of Pluto), it would seem that there would only be room for very slight adjustments to the mass of Neptune subsequently.

The other is that if a small adjustment of Neptune's mass is enough to account for the residuals of Uranus and Neptune that suggested the existence of the Planet X that Pluto was thought to be, why had that possibility never occured to anyone at the time calculations were undertaken to find the orbit of Planet X, instead of only after the data from Voyager was available? However, I have learned that W. H. Pickering did note that his Planet T might have an orbital period very close to that of Neptune, and to an extent, this seems to me like coming close to the truth.

Other interesting bodies were discovered simply by being seen for the first time where nothing had been before, and then followed on subsequent nights to determine their motion, without any advance predictions.

In 1977, Chiron, the first of the Centaurs, was discovered by Charles Kowal, with an orbit between those of Saturn and Uranus. The second discovery of a Centaur was that of Pholus in 1992, and the largest known Centaur, Chariklo, also with an orbit between those same two planets, was not discovered until 1997.

In 1992, the first Kuiper Belt Object other than Pluto to be discovered was known at the time as 1992 QB1; it is now the minor planet 15760 Albion. Six months later, David Jewitt and Jane Luu discovered a second one in addition, 1993 FW, now with the number 181708; it has been nicknamed Karla, after the Soviet nemesis of George Smiley in the novels of John le Carré, but it does not yet have an official name.

The year 2005 was marked by the discovery of Eris by Mike Brown, a body more massive, but slightly smaller in size, than Pluto. Although it orbits the Sun at a distance more than three times that at which Pluto orbits the Sun, because a number of other smaller Kuiper Belt Objects were already known at the time, it was feared that the situation following the discovery of the first asteroids would repeat itself, and the number of Kuiper Belt Objects discovered that would be added to the list of the planets of the Solar System would be excessive; therefore, the International Astronomical Union, in 2006, adopted a formal definition for planets of the Solar System; as this meant that Pluto would no longer be considered a planet (without qualification: the asteroids are also all termed "minor planets", and Pluto, Eris, Ceres, and a few other bodies are termed "dwarf planets") it was felt as an uncomfortable change by many. While this was understandable, I cannot see that there was any reasonable alternative to the decision that was made.

Incidentally, the suggestion has been made that the term "planet" should also apply to the natural satellites of the planets, and it has been noted that, at one time, this was how the term was used in books on astronomy. From the perspective of geology, this would make sense; they are also other worlds, and they were formed from dust and gas in the Solar System in the same manner as the planets. So far, though, such a change has been too radical to be seriously considered.

At the other end of the Solar System, the advance of the perihelion of Mercury was greater, by 42 arc-seconds per century (being 574 arc-seconds per century instead of 532 arc-seconds per century, which was expected), than could be explained by the perturbations from the gravity of the other planets. This led to a planet orbiting closer to the Sun than Mercury, called Vulcan, being postulated. Eventually, however, it was learned that not only was there no such planet, but that instead the additional advance of the perihelion of Mercury could be accounted for by a completely un-anticipated cause: the changes to the law of gravity which resulted from Albert Einstein's General Theory of Relativity; this factor implied that the perihelion of Mercury would advance by an extra 43 arc-seconds per century. (The one extra arc-second per century is believed to be little enough that the uncertainties in our knowledge of the motions of Mercury and the masses of other planets is enough to account for it.)

The search for other bodies in our Solar System still continues.

Of course, as astronomers turn their telescopes to the area near the ecliptic for other reasons, such as the study of distant galaxies located there, they will at times encounter new asteroids, as these bodies are very numerous; indeed, for this reason, they were nicknamed the "vermin of the skies".

In 1980, a paper by Walter and Luis Alvarez proposed that the extinction of the dinosaurs 65 million years ago was due to the impact of an asteroid on the Earth, because of a layer of rock at the boundary between the Cretaceous and Tertiary epochs with an elevated level of Iridium. Later, in 1984, David M. Raup and Jack Seposki presented statistics about past mass extinctions which appeared to indicate that some of those extinctions were occurring with a distinct periodicity of 26 million years, including that of the dinosaurs 65 million years ago. This was shortly followed by a paper by Richard Muller, Piet Hut, and Marc Davis, which postulated that our Sun could have a red dwarf star as a companion with an orbit of 26 million years that is responsible for disturbing the Oort Cloud so as to send asteroids our way. This is the body that has been dubbed "Nemesis".

The discovery of the distant KBO 90377 Sedna in 2003 by Mike Brown, Chad Trujillo, and David Rabinowitz, because of its highly eccentric orbit, led to speculation about how a close encounter with another body might have disturbed it from what would have originally been a distant nearly circular orbit. After a second similar asteroid, 2012 VP113, was discovered in 2012, investigation of this possibility began in earnest.

One proposal was advanced in 2012 by Rodney Gomes, and another in 2014 by Chad Trujillo and Scott S. Sheppard. The most well-known suggestion, however, is that advanced in 2016 by Konstantin Batygin and Mike Brown, about a body generally referred to as "Planet Nine".

Astrological (and a Few Astronomical) Symbols

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         Ascending Node               5 Astraea       1221 Amor           1685 Toro            2060 Chiron    Dark Moon Lilith  Tishtar        Sigma  
Taurus       180°     Opposition       160°     Quadnonile            Moon        Descending Node              6 Hebe          2063 Bacchus        3216 Harrington     10199 Chariklo  Transpluto        Az             Pan    
Gemini       120°     Trine             22 1/2° Quartosquare          Mercury     Black Moon Lilith            7 Iris           763 Cupido         1996 Adams           7066 Nessus                      Priap          Isis   
Cancer        90°     Square            67 1/2° 3x Quartosquare       Venus       True Black Moon Lilith       8 Flora         1864 Daedalus       1997 Leverrier       5145 Pholus    Demeter           Haurang        Morya  
Leo           60°     Sextile          112 1/2° 5x Quartosquare       Mars        White Moon Selena            9 Metis         1108 Demeter         784 Pickeringa     32532 Thereus   Hermes            Vanand         Hermes 
Virgo         45°     Semisquare       157 1/2° 7x Quartosquare       Jupiter     True White Moon Arta        10 Hygiea         433 Eros           1886 Lowell               Pylenor   Persephone        Vakshya        Osiris 
Libra         30°     Semisextile                                     Saturn      Part of Fortune             11 Parthenope      75 Euridike     136108 Haumea         10370 Hylonome                    Utopia         Midas
Scorpio      135°     Sesquiquadrate                                  Uranus                                  12 Victoria      2212 Hephaistos   136472 Makemake       52872 Okyrhoe   Cupido            Rasi           Lion
Sagittarius  150°     Quincunx                                        Neptune                                 13 Egeria         103 Hera         225088 Gonggong       31824 Elatus    Hades             Proserpine
Capricorn             Parallel                                        Pluto                                   14 Irene          944 Hidalgo       90377 Sedna           8405 Asbolus   Zeus              Isis           Vulcan
Aquarius              Contraparallel                                                                          15 Eunomia        430 Hybris                             60558 Echeclus  Kronos            Anubis         Loki
Pisces        72°     Quintile                                      1 Ceres                                   16 Psyche        1566 Icarus                             49036 Pelion    Apollon           Osiris
             144°     Biquintile                                    2 Pallas                                  17 Thetis          42 Isis                               54598 Bienor    Admetos
Ophiuchius    36°     Semiquintile                                  3 Juno                                    18 Melpomene     1181 Lilith                             83982 Crantor   Vulcanus                         Nibiru
             108°     Sesquiquintile                                4 Vesta                                   19 Fortuna         93 Minerva                            52975 Cyllarus  Poseidon                         Nemesis
              40°     Nonile                                                                                  26 Proserpina     350 Ornamenta                          55576 Amycus
              51 3/7° Septile                                                                                 28 Bellona       3200 Phaethon                                           Jason
             102 6/7° Biseptile                                                                               29 Amphitrite      80 Sappho                                             Dido
             154 2/7° Triseptile                                                                              35 Leukothea     1170 Siva                                               Hercules
                                                                                                              37 Fides         2102 Tantalus                                           Wemyss-Pluto

The first column contains the signs of the Zodiac. These have only one conventional form, except in the case of the sign Capricorn. Below the conventional signs of the Zodiac is a symbol used to represent the constellation Ophiuchius, sometimes considered to be a thirteenth sign of the Zodiac.

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.

One can go further in a criticism of astrology. The planets Uranus, Neptune, and Pluto are given interpretations by most astrologers which correspond to the names that they were given by astronomers. This also applies to the asteroids Ceres, Pallas, Juno, and Vesta, the Centaur Chiron, and many other Solar System bodies by the astrologers who use them.

A possible reason for that is obvious. Astrologers are all in agreement that the next planet after Saturn is commonly known as Uranus. If this were taken as irrelevant for determining its interpretation, but it was used, then even mainstream astrology would be divided into many different schools, creating a situation considerably different from the current one where, although there certainly are divisions, tropical versus sidereal, heliocentric versus geocentric, the Hamburg school and the Ram school, in general there is still one large consistent mainstream, with numerous minor side branches.

But that reason is obviously irrelevant to the influences, if any, that the planets actually exert. And so we have a situation where it must be the case that the planets exert such strong and compelling influences that they force astronomers to give them their correct names that genuinely reflect their influence... and yet, somehow, the prognostications of the future coming from astrologers have not been obviously so uncannily accurate that the validity of astrology is no longer even subject to question... as would be expected if the influences of the planets were so powerful and compelling.

Interestingly enough, most of the claims that I've heard that some astrologer or another is making predictions with uncanny accuracy have been in reference to astrologers not making use of any bodies other than those known to the ancients, but as there is good reason not to give credence even to those claims, no conclusion can really be drawn in relation to this question.

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, and I have shoved them over to the right in their spaces in the chart to indicate they're in a special category. The second one for Neptune, intended to commemorate LeVerrier, its discoverer, is rarely used at present.

The hypothetical planets Isis and Osiris proposed by George Sutcliffe, which will be discussed some more below, don't seem to have symbols that I have been able to find online. However, I vaguely remember seeing symbols assigned to them in one very old astrology magazine I had seen. The first two alternate symbols for Pluto, as opposed to the symbol combining the letters P and L, which is the standard official symbol also used by astronomers, on the other hand are very common in astrological publications. The first one is a modification of the symbol of Venus, and the second a modification of the symbol for Mars; my vague memory of what I had seen used as symbols for Isis and Osiris makes me wonder if those two symbols, being easily available, weren't the ones used for those two planets respectively, Isis being female and Osiris being male, using the modified Venus symbol for the first, and the modified Mars symbol for the second would at least seem to make a sort of sense.

The final alternate symbol for Pluto is said to be often used in European astrological publications.

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.

In the next column 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. As with the Moon's Nodes, there is both a true and an osculating version of this point; and so the osculating version is used by some astrologers, particularly in Russia, as the True Black Moon, and as well complementary points are known as the White Moon Selene and the True White Moon Arta, shown subsequently.

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


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, two columns joined in one group contain a few of the symbols assigned by present-day astrologers to a number of other asteroids.

However, I have just learned, from the documentation for the Swiss Ephemeris software, that the body named "Harrington" for which I gave a symbol may not have been the asteroid 3216 Harrington, but instead one of that astronomer's estimates for the possible position of a Planet X beyond Neptune.

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.

Hypothetical Planets (and Moons)

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 (Walter Gorn Old) 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.

Waltemath gave precise orbital elements for this moon:

Mean longitude, noon Berlin time, January 1, 1898: 214.73°

Mean synodic period: 117.00593 days

Siderial month: 119.227434 days

Draconitic month: 118.003952 days

Anomalistic month: 120.5915 days

Mean daily motion: 3.0194393012°

Perigee April 8, 1898, noon Greenwich time

Descending node: February 8, 1898, 06.72 PM Greenwich time, at 315° 13' longitude.

Inclination: 2.5 degrees

Eccentricity: 0.1587

The Berlin meridian was apparently located at about 13° 23' 41.9" East longitude, so noon on that meridian would be 34.8 seconds after 12:53 PM Greenwich time. I will admit I'm suspicious of perigee happening at noon exactly, and it's odd to use decimal hours for a time that is still by the 12 hour clock rather than the 24 hour clock.

Immediately below that symbol is the symbol for Transpluto, one possible symbol for an anticipated planet further out.

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.

The orbital periods of these hypothetical planets are claimed to be:

Persephone       600 years
Hermes           720 years
Demeter          900 years

which are suspiciously round numbers.

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.)

The orbital periods of these hypothetical planets are claimed to be:

Cupido      262.5  y
Hades       360.66 y
Zeus        455.64 y
Kronos      521.8  y
Apollon     576    y
Admetos     617.14 y
Vulcanus    663    y
Poseidon    720    y

Below them are the four hypothetical planets proposed by Maurice Wemyss (a pen name for one Duncan MacNaughton, who passed away on October 1, 1973, at the age of 81) in the first volume of his five-volume work The Wheel of Life; or Scientific Astrology. He gave the name Pluto to one of those hypothetical planets, his work having been written (and published) long before its discovery. Following Charles Jayne, I've called this body "Wemyss-Pluto" in the key to the diagram to reduce confusion.

In the third volume, he gives more information about these four bodies, including a short ephemeris of the presumed heliocentric positions of all of them except for Dido, the position of which he notes as uncertain.

Jason is said to have an orbital period of about 45 years, with an orbit between that of Saturn and Uranus.

Dido is said to have an orbital period of about 360 years, similar to that claimed for Sutcliffe's Isis.

Hercules is said to have an orbital period of about 654 years.

And Wemyss-Pluto is said to have an orbital period of about 1,366 years, much longer than the 248 year orbital period of Lowell-Pluto.

Summarized in a table, that would be:

Jason            45 y
Dido            360 y
Hercules        654 y
Weymss-Pluto  1,366 y

The information he gives for the positions of these planets is as follows, the heliocentric positions being for the first of January of each year:

Year     Jason         Hercules       Wemyss-Pluto

1800      2.7  CAN     23.0  TAU       0.785 LEO
1810     22.8  VIR     28.5  TAU       3.420 LEO
1820     12.9  SAG      4.0  GEM       6.055 LEO
1830      3.0  PIS      9.5  GEM       8.690 LEO
1840     23.1  TAU     15.0  GEM      11.325 LEO
1850     13.2  LEO     20.5  GEM      13.960 LEO
1860      3.3  SCO     26    GEM      10.595 LEO
 1865    13.35 SAG
1870     23.4  CAP      1.5  CAN      19.230 LEO
 1875     3.45 PIS
1880     13.5  ARI      7    CAN      21.865 LEO
 1885    23.55 TAU
1890      3.6  CAN     12.5  CAN      24.500 LEO
 1895    13.65 LEO
1900     23.7  VIR     18    CAN      27.135 LEO
 1905     3.75 SCO
1910     13.8  SAG     23.5  CAN      29.770 LEO
 1915    23.85 CAP
1920      3.9  PIS                     2.405 VIR
 1925    13.95 ARI
1930     24.0  TAU                     5.040 VIR

And the second column of this group contains 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.

The periods of these bodies are:

 Tishtar        51 d       Retrogade
 Az             69 d

 Utopia        360 d
 Priap           7.89 y    Retrogade
 Rasi            8.1 y     Retrogade
 Haurang        20 y       Retrogade
 Vanand         73 y       Retrogade
 Vakshya       108 y       Retrogade
 Isis          360 y
 Proserpine    665 y
 Anubis        775 y
 Osiris      1,025 y

Incidentally, I have seen the symbol for Proserpine used by astrologers other than those belonging to the Avestan school.

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.

In the third column of this group, I have included the symbols for some older hypothetical planets. Symbols for them were quite difficult to find, but eventually I stumbled across one astrology font, Starfont, which had symbols for them.

Apparently the earliest proposal of hypothetical planets for purposes of astrology was that of bodies called Ov-O and Lacroix, by Charubel (John Thomas) in 1897. Their periods were:

Ov-O      297.657 y
La Croix  340.426 y

The orbital period of Ov-O happens to be quite close to that of Arrokoth, at 297.67 years. Arrokoth is a notable Kuiper Belt Object, as it is visibly the result of two bodies colliding and then sticking together afterwards.

In an item from Modern Astrology for 1905, Charubel is noted as indicating that he does not yet know the period of what would be called Ov-O, and he had thought it to have a longer period than that of La Croix. But he also mentions a number of other bodies, which he refers to as "transcendental Suns" with much longer orbital periods:

Period      Position on          Nature
            September 11, 1826
 2,000 y     TAU 22              BEN  Like Venus and Mercury
 2,100       VIR 11              BEN  Magical (Similar to Ov-O)
 2,200       LEO 22              BEN  Mercurial
 2,540       VIR 12              BEN
 3,600       PIS 14              MAL  Black Magic
 4,100       VIR 13              ?    Magical
 5,700       TAU 16              ?    Magical
 7,000       LEO  7              BEN  Sublime (Greater good, Prophetic insight)
 8,700       CAN 15              BEN  Partially like Uranus
10,200       PIS 18              BEN  Partially like Neptune
unknown      VIR 16              BEN  For worldly good, wealth

the one with a period of 3,600 years being a malefic ruling black magic, the ones with periods of 4,100 and 5,700 years being of an unknown nature, and the rest being benefic.

I have not encountered symbols for these bodies.

Also in 1905, Thomas Lake Harris is on record as proposing three hypothetical planets, Melodia, Polyhymnia, and Vulcan. Accourding to one source, his Vulcan was not the well-known intra-Mercurial planet. As Melodia was given the same 297 year period as Ov-O, and Polyhymnia was described as having an orbit beyond that of Melodia, one might suppose that Melodia and Polyhymnia were simply alternative names for Ov-O and La Croix respectively.

However, another source indicates that this is not the case, at least in part, as it supplies information on both La Croix and Polyhymnia:

From the January-February 1927 issue of Revue Française d'Astrologie, we have the following:

Planet          Annual Motion           Position          Date

Ov-O             1° 12' 34"             24° AQU 30'       January 1, 1912
La Croix         1°  3' 27"             12° CAP           September 11, 1826

Polyhymnia          31' 18"             28° LIB 20'       January 1, 1925

This would indicate that Polyhymnia is distinct from La Croix, while the fact that Melodia is not noted is consistent with it being equivalent to Ov-O, although hardly conclusive.

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.

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. Subsequently, I've learned that it was in his book The New Astronomy and Cosmic Physiology that he discussed them, although this book discussed a revised version of his view of those planets, where the period of Isis was reduced to 350 years from 360, which may account for the discrepancies noted below.

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.

What was given in the March, 1906 issue of Modern Astrology was:

        Period           Annual Motion       Position as of Jan 1, 1906
Isis      360 y           1d  0'  0"          0 ARI 46'  0"
Osiris    990.11396 y        21' 49"          3 LIB  1' 49"
F       2,200.33768 y         9' 49"         28 PIS  9' 49"
G       5,658.63158 y         3' 49"         22 VIR  5' 49"

using Charles Jayne's designations F and G for the two planets further out, unnamed in that article. There seem to be some odd coincidences, however, suggestive of either a misprint, or at least that the planets had, for some date, starting positions in whole degrees.

Charles Jayne, in his book "The Unknown Planets", notes that Isis and Osiris, along with two other planets further out, were discussed in the March, 1906 issue of Modern Astrology. This seemed to have contradicted what I read from a source on the web, that these planets were discovered as part of a joint effort between Sutcliffe and Geoffrey Hodson in 1929. However, it turns out that this statement was largely quoted from the same work by Charles Jayne; presumably, what took place in 1929 involved either a refinement or a confirmation of what had been postulated by Sutcliffe as far back as 1906.

Given that Hodson discovered instead two additional planets which he called Morya and Lion, with orbital periods of 625 and 1515 years respectively, as opposed to the 360 and 990 (or 945) year orbital periods of Isis and Osiris, in any case, it appears that two separate efforts were conducted in close cooperation, rather than a joint effort taking place. However, that may have been unavoidable, as seeing a psychic vision is obviously an individual matter.

It turns out that in his book, The Undiscovered Planets, the astrologer Charles Jayne made an unusually prophetic statement:

We postulate a superasteroidal zone out to about twice as far from the Sun as the mean distance of Pluto, which is the innermost planet of the "zone".

The Kuiper Belt is held to extend from 30 AU to 55 AU or thereabouts, which basically corresponds to this description.

However, that astrologers would predict new planets beyond Neptune, and then later beyond Pluto, is not really all that surprising, and so despite the seeming uncanny nature of the coincidence, I cannot be all that impressed, regardless.

This booklet, although it mentions some of the Uranian planets instead, largely concerns Sutcliffe's Isis and Osiris, Hodson's Morya and Lion, and a few other related bodies.

The bodies with which he was primarily concerned with in that work were:

Thus, he had adjusted the periods of Isis and Osiris, and Morya and Lion, based on his own investigations, although in the case of Lion, the change, from 1515 years to 1516 years, is a relatively small one.

It may be noted that Charles A. Jayne was considered one of the foremost experts in rectification, which is the practise of determining an unknown birth time based on events in the life of the native. Hence, this could be considered to make him qualified to determine the periods of hypothetical planets more accurately.

In addition to these bodies, I've also included symbols for the hypothetical planet Vulcan, the one lying within the orbit of Mercury, and for the hypothetical planet Loki which also appeared in Starfont, but about which I have no further information at this time.

Following the symbols for these bodies are two symbols I have found used for the planet Nibiru of Zecharia Sitchin fame, and some symbols for Nemesis, the planet or star hypothesized as being responsible for sending dinosaur-killing asteroids our way.

Copyright (c) 2012, 2015, 2022 John J. G. Savard

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