Date: Mon, 07 Feb 2000 08:47:34 -0600
Subject: trans-Neptunian planets and the Uranians

[from the Solar Fire documentation:]
The planet Vulcan, the Transneptunian planets and TransPluto are not officially discovered planets, but are important in esoteric and Uranian astrology. They should be treated as experimental.

They should be treated for what they are:

1- they are completely idealized points moving in perfect circles around the sun without any physical acceleration except the Sun's, i.e.
2- they are subject only to the influence of the Sun and are not affected by the gravitational interactions of other large bodies.

Therefore, this is what a scientist would say about the Uranian planets:

"They are mathematically derived points based on assumed circular orbits extrapolated from the time when Witte and Siegrun made their empirical observations. At present, more than 230 objects have been found at the distances where they are supposed to be, but almost all of them have orbital characteristics similar to Cupido only. The small number that share the same mean solar distance as the other 7 Uranians all have highly eccentric orbits that are the polar opposite of what has been assumed. However, most astrologers ignore the existence of these 230 bodies and cling to the idealized and physically impossible but empirically effective extrapolations of Witte's and Siegrun's observations".

At present there are about 230 trans-Neptunians identified, and their orbits are readily available and updated at the Minor Planet Center on a daily basis. A few months ago Albert Timashev made available an update to his freeware "Phaethon" 1.0 Demo that allowed to have the zodiacal positions of all the tnp's available at that time (a dozen more have been found in the last months and many orbits have been updated ever since), and with my freeware "Riyal" you can get the positions of the 4 that can be considered most important. The orbits of some of them are very well known and there's no reason not to start searching for their meaning.

Many of them are similar to the Uranian "Cupido": same mean solar distance and very circular orbits, but those with distances similar to the other Uranians show very eccentric orbits, unlike the Uranian hypotheticals which are perfect circles. Here is the mean solar distance of the 8 Uranian planets:

CUPID     40.998
HADES     50.667
ZEUS      59.214
KRONOS    64.816
APOLLO    70.361
ADMETUS   73.736
VULCANUS  77.445
POSEIDON  83.493

Siegrun and Witte derived their positions from empirical observations over a short time-span. Since they move so slowly, it is probable that a circle could account for their empirically-derived positions. But this would mean that the Uranians were "true" objects only at that time, and are "fake" planets now or in the past centuries --as far as astronomy is concerned.

That is the only thing acceptable physically speaking, since they are moving in flat and perfectly circular orbits completely "immune" to planetary perturbations. If their positions represented something real, it could have been possible only then, not now.

I must add that since they move so slowly, there is a chance that the difference between a perfect circle and the true eccentric motion is not too large over the 80 years or so that separate us from the time of Siegrun and Witte.

Let's make an experiment:

1996TL66 has about the same mean solar distance as Poseidon (85 AU). At 1-1-1900, its position was 11,27 Capricorn. Calculated the Uranian way (no eccentricity, no perturbations, no inclination) its position at that same date would be 12,00 Aquarius. 

The mean solar distance of Cupido and Hades more or less mark the limits of the cubewanos. Let's take as example 1996TO66, the largest of them all so far, at a distance of 43 AU and with almost zero eccentricity, like the Uranians. Its position 1-1-1900 was 8,21 Scorpio. Calculated the Uranian way it would be 15,52 Pisces.


[following section on how their orbits are derived in Spanish]

Date: Sat, 28 Oct 2000 11:19:47 -0600
Reply-To: astro_club@egroups.com
Subject: Re: [astro_club] TNP x Revilla

Las actualizaciones de los "transneptunianos" que realizo periódicamente en Riyal no tienen nada que ver con los planetas hipotéticos de la astrología Uraniana. Cuando me refiero a "tnp", se trata de la banda de Kuiper, compuesta por plutinos, cubewanos y "objetos del disco esparcido". Estos son objetos reales.

Los planetas hipotéticos Uranianos no se actualizan nunca, puesto que son órbitas cuasi-simbólicas físicamente imposibles. Constituyen círculos perfectos, sin inclinación orbital (co-planares), sin eccentricidad, afectadas exclusivamente por la fuerza gravitacional del Sol (no se toman en cuenta perturbaciones planetarias), sin aceleración, etc. (una corrección posterior realizada por James Neely hace 2 décadas añade una pequeñaa inclinación y eccentricidad a los primeros 4 de ellos, pero ésto no cambia en nada su naturaleza).

Sobre cómo es que pueden calcularse órbitas hipotéticas, pues en realidad no es tan difícil, especialmente ahora en la época de las computadoras. Existen programas freeware en la Web que calculan una órbita a partir de 3 o más observaciones, de manera que lo único que se necesita para calcular una órbita es una tabla de observaciones, sean reales o hipotéticas.

La ley de Titius-Bode no tiene nada que ver con esto. Una orbita consiste de 6 elementos:

1- el semieje mayor (distancia solar media)
2- la eccentricidad
3- la longitud del perihelio
4- la inclinación
5- la longitud del nodo ascendente
6- su longitud media o anomalía media.

Como las órbitas de los planetas Uranianos son circulares (eccentricidad=0) no hay perihelio, y como son co-planares (inclinación=0), no hay nodo ascendente. Por lo tanto el problema es muy sencillo, pues los elementos se reducen a sólo 2: distancia solar media y su posición en un momento dado.

La distancia solar media se deriva mediante una fórmula aplicada a su movimiento aparente en el cielo, que corresponde a la tercera ley de Kepler. Por ejemplo: el planeta hipotetico "Nibiru" completa una órbita en 3600 anos (="P"); ésto significa que, por fuerza, de acuerdo con la tercera ley de Kepler (a^3 = P^2), su distancia media ("a") del sol es 234.892 AU.

El movimiento medio y su posición en un momento dado son cantidades empíricas. Simplemente se hace una lista de los lugares donde uno cree que el planeta imaginario "debería" estar en diferentes momentos del tiempo. En el caso de los Uranianos, puesto que se mueven muy lento (==> muy lejos del sol), no hay gran diferencia entre el cálculo geocentrico y el heliocentrico, por lo tanto dicha lista y la fórmula anterior es todo lo que se necesita.

Las cantidades propiamente dichas se pueden encontrar en el código fuente de Astrolog y de las Swiss Ephemeris.


[added June 2001]

To: Centaurs@yahoogroups.com
Date: Sun, 17 Jun 2001 16:18:03 -0600
Subject: Re: [Centaurs] Re: Russian Hypotheticals


With the sole exception of Cupido and perhaps Hades, the Uranians are far beyond the Kuiper belt, which is considered the outer limit of the solar system to this day. Those Uranians move in the region of the scattered disk objects, which are objects of very high eccentricity. A nearly-circular orbit in this very remote region is not likely to be found with present-day instrumentation because it would not be possible to observe such an object, in addition to being very improbable in view of the structure of the Kuiper belt as it is known today.

Furthermore, it is obvious that the more asteroids you put into the equation, the more likely you will find one that resembles in its motion the orbit at least of Cupido. There will be not one Cupido but many "Cupidos", because that's what the laws of chance dictate.


The very small eccentricity sometimes used ***for the first four only*** doesn't modify the position of the object but for a few arcminutes, and doesn't change the virtual circularity of the orbit, so, in practical terms, they are all circular. If they were not, allowing for eccentricity would significantly change the position, which is not the case.

They are circles or practically perfect circles. If they are not, then the positions calculated for them at the present time --with an insignificant eccentricity or with 0 eccentricity-- are all wrong.




To: Centaurs@yahoogroups.com
Date: Sun, 17 Jun 2001 21:37:09 -0600
Subject: Re: [Centaurs] Re: Russian Hypot


... confirming the Uranian planets' efficacy does not have anything to do with the fact that they are in many ways astronomical and physical absurdities. It has to do with the nature of Astrology, with the fact that --in my opinion, of course-- things in Astrology work very well even though they do not or cannot physically exist.

The more transneptunian bodies are found, the more it becomes questionable --astronomically and physically speaking-- to speak of them as physically feasible while ignoring or refusing to investigate those that are REALLY there. This has nothing to do with whether they work or not. Astrologically, I think they make a lot of sense, and are one very good example of how and why Astrology works, and of how and why Astrology is not a mapping of the heavens but a mapping of the human imagination.




To: Centaurs@yahoogroups.com
Date: Wed, 20 Jun 2001 13:41:30 -0600
Subject: Re: [Centaurs] Imaginary and hypothetical planets 


The inventors themselves are muddling things up because they assume a physical existence and then carry out absurd calculations, such as perfect circles and perfectly coplanar orbits which are not subject to planetary perturbations, as in the case of the Uranian planets. This is the equivalent of something that cannot exist physically.

In other words, what people like Siegrun and Witte were doing was:


1- Let us assume that there is a planet here, and ignore the fact that it could very well (at least) be in the opposite point 180 degrees away.

2- Let's assume that the inferred positions have been found in a completely objective way in which the subjective interpretations of the observer have not intervened in the conclusions, i.e., thinking that there is a planet there with such and such characteristics.

3- Let's make a table of these assumed but perfectly objective inferred positions.

4- Let's calculate a fictitious circular and coplanar orbit, such as none exist in the solar system, that satisfies these assumed positions in the period of the samples.

5- Let's make the orbit subject to the gravitational pull of the Sun only, ignoring planetary perturbations and accelerations, in a way that is physically impossible in the solar system.

6- Let's call this a "hypothetical planet" and let's think of it as if really exists physically.

7- Let's systematize the meaning of these points, categorizing them, and include them within a complete and complex method of analysis. Let's publish the results and let many others use the system with these invented points and confirm the system's consistency and accuracy.

PHASE TWO (James Neely)

1- Let's use modern computer facilities to slightly refine the orbits of 4 of the 8 Hamburg School planets, adding some tiny eccentricities and inclinations to the otherwise circular and coplanar orbits that have been used for 60 years, in order to better satisfy the completely objective, error-free, extremely accurate imaginary positions visualized by the imagination and methods of Siegrun and Witte.

2- Let's publish the revised positions, which differ from the old ones by a few arcminutes only.


1- Let's ignore the existence of more than 500 real transneptunian planets that have been found and whose positions have been consistently observed, photographed, and constantly refined with sophisticated physical models, but who nobody knows what they really mean, and instead stick to the old hypothesized but physically impossible Uranian planets whose meaning has been empirically tested, confirmed, and refined over many decades by thousands of practitioners.

2- Let's proclaim that, if none of the Uranians has been found yet, it is because there are many real transneptunians yet to be found some of which will prove to be the 8 Hamburg planets. This is a very safe bet, since when they are about 5000 a few years from now, there will be an average of 1 transneptunian asteroid every 0,04' of the circunferente (about 14 objects per degree of the zodiac), so by necessity one of them will be one of the Uranians.

3- When by chance one of them coincides with the position of Cupido (the only actual possibility because it has an orbit similar to the bulk of the Kuiper belt objects), let's proclaim that its existence has been confirmed, and let's ignore the fact that the large eccentricity of all the other orbits at distances similar to the remaining 7 Uranians will make such a match impossible for them...

... Since one of them has been found, it is only a matter of time until the others are found too!


Rigorously, the only thing you can say is:

1- There is a transneptunian object here, whose zodiacal position at present coincides with the position of one of the hypothetical Uranian planets.

==> this is the easiest requisite. The more tnp's, the more likely you will MANY that satisfy this condition.

2- When examining the orbit it is close to 0 eccentricity and 0 inclination

==> This is the case of many tnp's, specifically those of the Kuiper belt. This means that, judging from what is known today of the physical structure of the Kuiper belt, ONLY CUPIDO and perhaps Hades could be a candidate for this type of match.

3- The positions of the real tnp match that has been found agrees with those at the time of Witte, with the positions that he imagined or assumed "were there"

==> This last step is the most improbable, if not impossible, because Uranians are artificially calculated without planetary perturbations. I have already given concrete calculated examples of this.

Let's do it again for the Cupido case. Sample date 1-1-2000:

position with Neely's refinement = 3, 53' 06" Sagittarius
position with planetary perturbations = 3, 14' 05" Sagittarius
error in the position = 0, 39' 01"

traditional position = 3, 55' 17" Sagitario
position with planetary perturbations = 3, 16' 21" Sagittarius
error in position = 0, 38' 56"

The differences here are relatively small because the eccentricity is very small and the time interval between epoch (1900) and date (2000) is relatively short. We can see also that the difference between the traditional positions and Neely's refinement is small. (The error caused by ignoring planetary perturbations is more significant in practical terms).

These errors are cumulative. If we do the same thing for 1700, we obtain (1-1-1700):

position with Neely's refinement = 8, 49' 45" Libra
position with planetary perturbations = 10, 14' 20" Libra
error in the position = 1, 24' 35"

traditional position = 8, 55' 04" Sagitario
position with planetary perturbations = 10, 21' 38" Sagittarius
error in position = 1, 26' 34"

However, all this is the idealized world of the Uranian planets. The real world is different, because to begin with only Cupido (and perhaps Hades) --with the present-day knowledge about the STRUCTURE of the Kuiper belt-- has any chance of being paired with a real object.

There are about 50 (fifty!) well-known KBO's so far that are in the same distance and velocity range (40-42 AU) of Cupido, but not one of them so far has such a small eccentricity. The smallest eccentricity is 0.0135. This would produce a position of 2,22 Sagittarius in the real world instead of 3,53 Sagittarius as with the Uranian method.


Cupido is right now in 4,32 Sagittarius. If we calculate the positions of ALL 465 slow asteroid orbits, we obtain the following around this position:

2000 KK4    241.6
1998 HM151  241.9
2000 KL4    242.8
1995 GY7    245.9
1995 FB21   246.2
1994 JS     248.4

To be eligible as a match for Cupido, any of these would have to be close to the position of Cupido 1-1-1900:

Cupido = 15,17 Cancer (Neely)
Cupido = 14,42 Cancer (traditional)
KK4    =  4,35 Cancer
HM151  =  5,47 Leo
KL4    = 13,21 Cancer
GY7    = 29,03 Gemini
FB21   =  9,26 Leo
1994 JS=  3,57 Leo

This means that 2000KL4 --for example-- has a good chance of being matched with Cupido... Who is going to investigate? What are the characteristic of 2000KL4? Is it valid to assume that KL4 has the characteristics of the Uranian Cupido without investigating the matter?

The match is not exact, but serves to illustrate (in the case of Cupido only) the following:

-the chance of finding a match or many matches increases rapidly as the number of tnp's goes up.

-does anybody care if there is a match with the real world or not? Is someone investigating this? Why not?

-what is the process of establishing the characteristic of a (presumed) object? Do the asteroids (centaurs, tnp's... ) have their own characteristics or we invent them? Do we interpret reality and a chart the same way that de-Witte did in 1915? Will we arrive at the same meanings?



To: centaurs@yahoogroups.com
Date: Thu, 21 Jun 2001 13:15:19 -0600
Subject: [Centaurs] is 2000KL4 Cupido?

I calculated the positions of the Uranian Cupido (James Neely version and traditional version), and those of 2000KL4, and compared them. The comparison was made with 3680 positions separated by 10 days from 1900 to 2000.

They are never apart more than 3 degrees, and much less than that most of the time.

Is 2000KL4 Cupido? If it is not, it may well be his twin or "double", in terms of its geocentric/heliocentric motion during 1900-2000 at least. In the graph 1900-2000, Cupido and 2000KL4 appear almost indistinguishable.


About the use of hypotheticals

Date: Mon, 15 Sep 2003 17:13:23 -0600
Subject: Re: [Centaurs] Vulcan parameters


Astrology works with abstract coordinate points, almost never with real objects in the sky. This is why hypothetical points with little or no grounding on physical reality (like the Uranian planets, the Dark Moons,  Vulcans, Transplutos, etc.) can work so well.

I consider the use of hypotheticals a subjective choice, much like the choice of house system. I choose to reject them for the same reason I reject working with many other things in Astrology (see my answer to your second point below)

People usually do not know how they are calculated or how they were invented. I think that if they knew, they would understand better why using them is so absurd or why some people reject them.

"Absurd" here does not mean "invalid". I think all these invented points, if you tune to them, can work wonderfully. But knowledge of the subjective, arbitrary, methodologically careless process of inventing them and the "absurd" --though mathematically valid-- way in which they are calculated, could help people make their personal/subjective choice of accepting them or rejecting them.

It is the same with houses. Some systems, such as, Koch and Alchabitius, are based on geometrical absurdities (Koch more than Alchabitius). Yet mathematically, the Koch and the Alchabitius algorithms are quite elegant. People not aware of or unable to understand the underlying absurdity use them effectively and consider them accurate, a judgement which I have no reason to contradict or question.

The accuracy is not related to whether they are mathematically or geometrically sound or not. It is related to the nature of Astrology, to how Astrology works. Astrology does not need its "planets" to "really exist" in order for them to "work" effectively. And in turn, the effectiveness of hypothetical, astronomically absurd points shows that Astrology is something much more complex, or totally different, from the usual ideas people have about it.


If something exists in Astrology, it is because there is a convention about it. The difference is the level of the convention. For example, the ecliptic, the point where a solar or lunar eclipse occurred, the position of Mars or of 1998BU48 at any point in time, are "hard" conventions that belong to an "objective" reality socially accepted by everybody. Their main characteristic is that they are grounded on something that exists physically, that can be measured, tested, and confirmed by anybody in any part of the world.

This is the only level which I accept in my approach to Astrology. However, it would be extremely foolish to pretend (or actually "dictate") that this is where Astrology ends. Traditionally, Astrology includes a lot of ancient inherited cultural "lore". At "Level 2", you have things like the figure of a Bull in the sky or concepts that equate the tropical sign Aries with Spring, that are an inheritance from Near Eastern and Hellenistic cultures. These are invalidated by the physical (the seasons) and cultural (the astronomical lore) reality of other cultures. Traditional Astrology is highly culturally biased.

Then there are "level 3" conventions, like the 8 Uranian (Hamburg) planets. Their positions 100 years away from the time when the original highly questionable deductions that led to their invention were made, are mathematical "fakes" because no astronomical object moves in the real world without its orbit being physically accelerated by the gravitational pull of other planets in the system. Yet their proposed motion --like that of every other hypothetical point used in Astrology-- is by definition unperturbed.

But this doesn't matter to those who use them because the convention is that their positions are not based on physical observations or measurements. This convention, however, is not shared by everybody in the world, only by those belonging to a community called "the Hamburg School",  "Uranian", or whatever. They have a highly developed and elaborate canon where the 8 hypotheticals are used indistinctively of the "real" physical planets. The Uranian canon is applied successfully by a well-defined, self-consistent astrological community, a sub-culture inside the Western astrological tradition.

Then there are "level 4" conventions, where things like the "dark Moon Lilith", "Vulcan", "Transpluto", "White Moon", like the Uranians based on absurd calculations that violate the laws of physics, are used without following any particular standard. They are like the Uranians, but there is no canon here: their meanings are the result of the work of very few individuals, and are not incorporated into a higher system.

The Sabian Symbols belong to level 2. They are strongly American-biased; there are other sets of symbols, such as the Italian "La Volasfera", which reflect my cultural heritage much better.

Why do I reject levels 2, 3 and 4, and accept only level 1? Why do people accept levels 2, 3 or 4? Where does someone in particular stop and why?



Date: Tue, 16 Sep 2003 07:45:49 -0600
Subject: Re: [Centaurs] Vulcan parameters

... My choice is with regards to physical principles and realities, which, as you say, have the most universal recognition. Hypothetical planets are calculated in violation or disregard of the laws of physics.

In Astrology, we always violate the laws of physics, manipulating units of time by means of metaphor and analogy (transits to a radix, progressions...), but the stuff or material we manipulate are measurements or models of natural realities or principles. Signs, houses, and planets/asteroids, as used in Astrology, are mathematical, simplified  representations of the natural world: the ecliptic (signs), the diurnal motion (houses), the planetary orbits and mass points.

The manipulation is done through highly symbolized cultural codes (aspects, numerology, meanings), but there is always this interaction or reflection of the natural or physical world. However abstract or "away from nature" the astrological mapping may be, it is always the result of a codification of the natural world.

An astrological chart or model is therefore a dialog between Man (codifier) and the World (nature). This gives to the chart a "grounded" quality. When reading a chart, I am using elements of the physical world to represent human "life" or experience, which are totally subjective realities. This is to me the main value of Astrology: through it we can "monitor" our subjectivity, or rather, the interaction between objective and the subjective in our lives.

Some people do not care for or do not need such "grounding". I recently expressed this need when writing about the different ways of calculating the Black Moon:

<<One wonders, with so many options available, if the Black Moon has meaning at all. Astrology is full of cases like this (e.g., house division, asteroids...). There is no easy answer. However, I think this question disappears when astrologers realize that Astrology is what astrologers do: work with more or less fancy and abstract mathematical points in the imagination. Astrology has very little or nothing to do with our relationship with "the sky out there" or with "the cosmos". If you realize this then the efficacy of imaginary points comes to light under a different perspective, one which has to do with cognitive patterns and structures in the human brain and not with astronomical events. It becomes a matter of individual idiosyncrasy the tools you choose to work with, and there is no fear or prejudice against tools that have no solid astronomical basis. Some people simply do not need that basis... however, I do, and I think this basis is important in order to keep Astrology (or astrologers' minds) disciplined and "down to earth", i.e., to keep Astrology healthy.>>