Good evening,

Thanks to Dr Graham for clarifying the misunderstanding about Hipparchos' zodiacs. Apparently there are at least two quoted as such, perhaps more.

My references have been exclusively to the one cited by Prof. Dr. Auguste Bouche-Leclercq. Fixing its arc of precession at 0 ecliptical degrees at about 140 BCE gives us an equal-signs 'sidereal' zodiac including each of the twelve alpha stars of the ecliptical constellations in the equal signs bearing the same names. The corridor is only about 40' of ecliptical arc wide. Al-Risha must be in the sign of Pisces, Regulus in the sign of Leo.

Best regards,

lihin

Quote:
"Also, I'm not sure what you mean by "reached" and then "backwards""
- You are not familiar with calculating the apparent position of stars. The reason is (mostly) the annual aberration as explained.

Yes, I'm sorry, I had deleted that bit but you got to it first! I got muddled as to which was going backwards, the VP or the "fixed" factors.

You don't have to use a fixed star or radio source to define a sidereal fiducial, all you need is a point in time (an "epoch") and a sidereal reference frame. The sidereal reference frame has already been established with great precision by modern astronomy, so there is no room for imprecision as long as one uses that reference frame.

I realise this is how it's conventionally been done, but I didn't know there was general agreement on a "sidereal reference frame". I first got interested in using the galactic nodes (galactic equator/ecliptic colures) as the reference frame, rather than an epoch, on reading Hamlet's Mill by Santillana and Von Dechend, which deals with the cultural and cosmological importance of the milky way... and by observing the latter! I was comforted in this line when I read Addey (Harmonics in Astrology), who although favouring a tropical zodiac, writes "we are looking for a point or points in the circle of the ecliptic which have a substantial identity capable of producing effects. Fixed stars could possibly answer the requirement but we would have many points, all producing effects. It is much more likely that such effects are generated from the point where two great circles intersect or from some kindred factor identifiable to astronomy. For such points there are several contenders. First we have the points of intersection of the ecliptic and celestial equator. This must be the most likely choice. A second such pair of points would be the intersection of the ecliptic with the plane of the galaxy (now said to be situated at about 29? Gemini-Sagittarius."
What bothers me about the current method of determining sidereal positions in terms of drift away from an "epoch" when "the two zodiacs coincide" is that it makes it look like the sidereal one is the moving one. I read a few years ago about some Indian astronomers (not astrologers) who were seeking to introduce a new sidereal convention for measuring along the ecliptic with one or other of the galactic nodes as the zero point - can't find it now unfortunately. In any case, proper motion, at least, should be neglibible as compared to the proper motion of a given fixed star - if only because we are inside the galaxy, which is itself an aggregate.

Using a mean position only (no nutation and no aberration), I get 3-4 May 1998. Nutation at the time was -8 arcseconds, which added to aberration will produce the results I gave. NOTE: a calculation with the nutation added but with no aberration gives 25-26 June 1998... this covers Meeus. Does anyone know the source for the "Usno date" later that year?

Smelyakov apparently "refined" Meuss's "May" to 7th May, very close to your values. Your June dates also suit me just fine!

So geometric/true positions makes no sense for objects outside the solar system.

This doesn't seem to be what is implied by things I've found on the net (mostly various Wiki articles) : "The apparent position of a star or other very distant object is the direction in which it is seen by an observer on the moving Earth. The true position (or geometric position) is the direction of the straight line between the observer and star at the instant of observation. [...] Bradley (who discovered aberration in C18th) was able to formulate a set of rules that would allow the calculation of the effect [of aberration] on any given star at a specified date."
So they seem to think calculated true positions make sense, and they are used as well as observed apparent positions to catalogue stars. But perhaps Meuss, USNO, Smelyakov were using mean positions. Fair enough.
As for the USNO source, there are references to it all over the net, mostly buried deep in stuff about the Mayan long count, which I'll spare you. I definitely found astronomy sites about it 10 years or so ago, and I think there was something on the site of the USNO itself, but can't find it now. They seem to do lots of work on radio sources, and to be the foremost authority for precise timing of solstices and equinoxes. I noted for certain that they said ithe date was 27/10/98. I was told by a physics forum that their value would be the most reliable. But now most of the details out there concern Meuss and Smelyakov.

I checked what my astronomy software Sky6 could do - with maximum zoom, the intersection galactic equator/ecliptic reaches 18h RA between mid and late May, crosses retrograde mid October and "hovers" over it till late December, then leaves it direct from about 24 December. With this software, it does indeed look as though the peak of the station is late October, but this sort of precision may be impossible with home software.
However with Redshift software, the alignment is exact only on 31 October 1998. It does not move back and forth, so it must use mean values, and may be less precise.

Graham
(Still no comments, anyone, on using a symmetrical tropical zodiac starting with 0 Taurus, solstices at 0 Leo and Aquarius etc???)

Helpful little 3D animated model showing how different coordiante systms work (ecliptic, equatorial, galactic) and which helps visualise the how they fit together:
http://upload.wikimedia.org/wikipedia/c ... c_anim.gif

Graham F wrote:I realise this is how it's conventionally been done, but I didn't know there was general agreement on a "sidereal reference frame".

Not among astrologers, for them the conventional and imprecise way is by means of the ayanamsa, but I was referring to the "celestial reference frame" used by modern astronomers and represented by the concept of a "fundamental epoch" such as J2000, which is strictly sidereal, it is accepted by all and is as precise and accurate as modern technology allows. I don't know why astrologers keep ignoring it.

Thanks for the quote from Addey.

The apparent position of a star or other very distant object is the direction in which it is seen by an observer on the moving Earth. The true position (or geometric position) is the direction of the straight line between the observer and star at the instant of observation.

I had to correct my reply here because I realized that I was confusing the geometric position with the correction for light-time, which is meaningless in the case of stars and is therefore ignored. With this cleared up I can understand the meaning of "geometric" star positions as (essentially) the apparent position minus aberration.

I must thank Graham for helping me think this over clarify the point.

As for the USNO source... I think there was something on the site of the USNO itself, but can't find it now... I noted for certain that they said the date was 27/10/98. I was told by a physics forum that their value would be the most reliable.

There are many references to this date and USNO, but it is mere hearsay. One source wrote "someone told me", but no reference to the actual USNO authority who "said it".

The exact date is of no practical interest, except for someone like me who enjoys delving into the mathematical astronomy behind it.

J.

Good morning,

Dr Graham has enquired about answers to his initial question.

From the perspective of a tropical zodiac, the question appears irrelevant. Were Klaudios Ptolomaios alive today, he would presumably dispense altogether with naming the tropical signs by astronomical constellations, as is often practised today with dials in ex. gr. the Aalen and Hamburg schools of astrology. The detachment of astrology from mythologies effected by the adoption of a tropical zodiac was intended.

The tropical zodiac of the northern hemisphere is rigorously geocentric. Geocentrically, the fixed stars proceed, move forward with reference to the ecliptic, resulting in periodic changes in for example rising, culminating and setting fixed stars viewed from a specific location, as was recently discussed in a thread in the mundane section of this forum.

Astrologers who apply a tropical zodiac feel perhaps less inner desire than others to pin themselves to some point of reference amongst the fixed stars, be it the Milky Way, the Galactic Centre or what have you. Everything moves, floats, dances. Change is the constant. Primordial Chaos is changeless, notions of Cosmos change. Ordo ab Chao, Chao ab Ordo.

An example: probably most astrologers working with a tropical zodiac would have no fundamental issue using the Earth-Moon barycentre as point of reference instead of the centre of the Earth. However, in practice such an innovation would be of little consequence, as only the position of the Moon differs by a maximum of few seconds of ecliptical arc.

Best regards,

lihin

Lihin wrote:

[Klaudios Ptolomaios] would presumably dispense altogether with naming the tropical signs by astronomical constellations,

Yes, I presumed it was clear from my posts that it's not the names of the signs/zoidia that interest me, but their rulerships. If the 30? from the VP were ruled by Venus, the next 30 by Mercury, the 30 leading up to the S solstice by Moon, the 30 from the solstice by Sun, etc (so that the WS would fall between the two Saturn "signs"), then of course it would make no difference whether you called the 1st one Aries, Taurus, Pisces or simply Number 1. Or you could call it by the name of a constellation near which it appeared to fall, it really doesn't matter.
As I asked in my first post, if the zodiac is considered to be arbitrary in terms of the constellations, why not go for symmetry (of rulerships, as well as of rising signs)? Antiscial "equivalent" signs would then have the same rulers, and contra-antiscial "complementary" ones would have complementary rulers (Mars/Venus, Mercury/Jupiter, Sun-Moon/Saturn).
Could this simply be a mistake by Ptolemy, which was then perpetuated? Would it not perhaps be internal evidence suggesting an older origin of the 12-fold zodiac, to a time when the equinoxes fell in early Taurus and Scorpio, the solstices in early Aquarius and Leo? Regulus, Antares, Fomalhaut and Aldebaran would then justifiably and logically be the four "Royal stars".

Graham

Good afternoon,

This time i think i have understood, at least in part, Dr Graham's train of thought.

In my humble understanding it was not the intent of Klaudios Ptolomaios to peg the zodiac, systems of rulerships, etc. to a particular period of prior history, ex. gr. when the vernal point of the northern hemisphere was at or near the beginning of the constellation of Taurus. On the contrary, the intent was to detach astronomy-astrology from any such peg, thus rendering it more universal.

Within the 'tropical astrological mind-set', the symmetries amongst signs, rulerships etc. are determined by the order and the rising times of the signs. As has recently been discussed in another thread, i concur with Ms Margherita and other members of the 'Italian school' that there are in fact two tropical zodiacs, one for the northern, the other for the southern hemisphere, offset by 180 ecliptical degrees or six signs.

The existence and correspondences between bright fixed stars, especially those near 'centre stage', the ecliptic, and terrestrial events are not at all negated by many if not most astrologers applying tropical zodiacs but rather explicitly included in interpretations. They are grouped into constellations for identification and classification purposes but interpreted primarily based on elemental qualities analogous to planets and / or combinations of planetary elemental qualities. For this reason, astrologers applying tropical zodiacs do not feel they are missing something perhaps more directly addressed by zodiacs more closely approximating the unequal astronomical constellations.

Best regards,

lihin

Lihin wrote:

there are in fact two tropical zodiacs, one for the northern, the other for the southern hemisphere, offset by 180 ecliptical degrees or six signs.

I agree, but that has no bearing on my question. Whatever sequence of tropical rulerships is chosen, I agree with Margherita that it should be reversed in the southern hemisphere. It is the Summer solstice that should always be associated with the lights, the winter one with Saturn, in my view. But that's not the question here, or only incidentally.

it was not the intent of Klaudios Ptolomaios to peg the zodiac, systems of rulerships, etc. to a particular period of prior history,

But that's exactly what a tropical zodiac does - it pegs the zodiac to a particular epoch. And Ptolemy did precisely that - he just pegged it to his own time, despite the assymetry of the rulerships, which would have been symmetrical had he pegged it to the earlier epoch and called the VP 0? Taurus, or called it anything and given the first 30? to Venus, etc.
This is not my original idea, I have taken it from Cyril Fagan and Garth Allen who claimed that the zodiac dated back, in Egypt, to the epoch of Taurus. Whether or not that is historically true, I am bringing up this question of assymetry of rulerships because for me it's the principal sticking point with the tropical zodiac starting with Aries.
Best regards
Graham

hi graham,

this might not be all that related to the topic at hand either but upstream you mentioned the chinese year/zodiac starting with 15 aquarius.. it is my understanding the new year is based off the lunar calendar - new moon in aquarius is the start of their year. maybe i have that wrong and you can enlighten me on how 15 aquarius is the start point? thanks..

James
I don't know. I was just responding to a point raised by Mark, which is interesting but as Mark said, rather off topic. He gave a link to a thread on the forum dealing with this, I looked at it but didn't really see the connection, except that possibly it might hark back in some way to a time when in fact the winter solstice was at 15? Aquarius sidereal. The contributor did not consider there was any connection to the Chinese lunar calendar.
Best
Graham

Good morning,

Dr Graham wrote:

But that's exactly what a tropical zodiac does - it pegs the zodiac to a particular epoch.

Klaudios Ptolomaios' intent was the opposite, as he was aware of geocentric procession of the 'sphere of fixed stars'. Around his time equal signs most closely corresponded to the astronomical constellations of the same names. When reading Tetrabiblos, Book I, Section 11, one may notice for example Ptolemy's definition of 'bi-corporeal', removing it from any reference to the shapes of constellations.

Mr Cyril Fagan's, whose writings i have read with interest and profit, and similar historic analyses were not necessarily mistaken concerning ancient zodiacs pegged to some fixed stars. Nutation and proper motion of fixed stars were apparently not known to the ancients. Perhaps the 'fathers of Western sidereal astrology' previously practised some kinds of modern astrology that did not systematically include interpretations of configurations with bright fixed stars. In my humble opinion, however, some of the time measurement issues of predictive techniques brought up by Mr Cyril Fagan and his followers merit attention.

Today, as the fixed stars have advanced by about one full sign compared to Hipparkhos' time, one might assign appropriate, synthetic new names to the tropical signs based on their tropical attributes by twos, threes, fours and sixes. Of course some well-meaning lovers of mythologies and traditions might be horrified.

Best regards,

lihin

Thank you
I'm not interested in the names of the signs, and I'm now sorry I mentioned the "4 Royal Stars": this was simply to suggest that there may be a history of the 12-fold zodiac before the "Age of Aries".
I would simply like to know why tropical astrologers seem content with a permanently assymetrical system of rulerships (with respect to equinox/solstice axes), while at the same time emphasising the importance of the symmetrical or complementary arrangements of the tropical rising times, day/night lengths (notably in respect of antiscia/contrantiscia). The latter symmetry seems to cry out for a corresponding symmetry of rulerships. Surely some tropical astrologers must have thought about this at some point (if only to reject it for whatever reason - which could simply be that it doesn't seem to work so well, it's not what Ptolemy or Lilly did, etc, but at least you've thought about it). No?
This thread is not about the sidereal zodiac per se (except in as much as it must have been sidereal before it got pegged to 0? Aries), or about the fixed stars, I'm sorry if I got sidetracked and gave that impression.
Graham
(BTW, it's precession, not procession)