SIDEREAL RIGHT ASCENSIONS

by Juan Antonio Revilla

#1

Sidereal astrologers work by necessity with sidereal coordinates... or so one would think. In practice, the truth is that while sidereal longitudes are used, when it comes to the right ascensions and declinations (e.g. in the calculation of parans), and the latitudes, almost always tropical positions are used exclusively. This seems to be a contradiction, and it brings to the surface some practical problems regarding sidereal astrological techniques that I would like to discuss in some detail.

Definition of the ayanamsa

The ayanamsa can be defined as the amount of precession (in longitude) accumulated from one date (the epoch) to another. Since precession is a function of time, the ayanamsa definition requires an epoch or starting point in time. This "zero point" is traditionally described as the time when the spring equinox coincided with the pre-defined origin of coordinates or fiducial, which may be a fixed star, the time of a peculiar astronomical alignment, or an empirically or statistically derived more or less "fixed" point in space, a point that is not subject to precession.

The fixed point belongs to the sidereal or quasi-inertial reference frame, against which moves or rotates with varying velocity the tropical reference frame, subject to precession.

We can also define an ayanamsa as simply an angle or an arc of the circumference between the tropical zero point and an arbitrary sidereal zero point of longitude established by convention. This arc of celestial longitude, as in the traditional definition, is dynamic, and changes as the moving tropical zero point is dragged by the Earth's precessional motion away from the sidereal zero point.

The difference between the two definitions lies in the absence in the second definition of a historical coincidence in the past between the tropical and the sidereal zero points, or in other words, the absence of the concept of an "original", historical sidereal zodiac, defined by its zero point coinciding with the spring equinox of a certain moment in the historical past.

The sidereal zero point can be defined anyway one wishes. The only requisite is that its starting point in time be clearly defined. There is no need whatsoever of a historical tradition about the beginning of the sidereal zodiac coinciding with the spring equinox of some historical era. Its zero point does not have to be defined in terms of a historical spring equinox. The only thing needed is that it is fixed to a pre-defined zero point in time.

In astrological, mathematical terms, whether the sidereal zero point corresponds to some historical Spring Equinox is irrelevant.

The first definition is behind the several "sidereal" astrologies based on an assumed historical sidereal zodiac the zero point of which is "truer" than all the others. The second definition is behind the usual practice of erecting precession-corrected solar returns.

#2

Let me make some general statements to describe what --normally-- sidereal astrologers do astronomically speaking:

1-) represent the zodiacal positions of planets using a fiducial (the particular sidereal zodiac) which is approximately free of precession in longitude. In practical terms, the tropical positions are used as a source, and a simplified formula of precession in longitude is applied to them that ignores the effects on the longitude of the motion of the moving ecliptic over the fixed ecliptic.

2-) ignore the precessional displacements in latitude, right ascension, and declination. In practical terms, use the sidereal zodiacal longitudes obtained from the approximate method above, but keep working with the tropical latitude. If needed, strictly tropical --not sidereal-- right ascensions and declinations are often used.

3-) use tropical, not sidereal, time-units with sidereal positions, and viceversa, use sidereal time units but tropical positions. In practical terms, when the "bija" corrections in progressions are ignored, sidereal astrologers use tropical time units with sidereal positions, or, as in the parans of the PSSR, use sidereal time units with tropical positions.

Very often astrologers believe that they are working in a sidereal reference frame simply because positions are being represented in the (or a) sidereal zodiac, whereas the zodiac in which one chooses to represent the positions is irrelevant.

When a spatial relationship (the representation of position in the tropical or in a sidereal zodiac) is considered in isolation of the corresponding time relationship (using tropical or sidereal time units), we see the practice among some siderealists of calculating secondary and tertiary progressions without the "bija" correction, which is equivalent to working with tropical measurements while representing the results in the sidereal zodiac.

This is not a sidereal but a tropical calculation, and in order to be consistent one would need also to calculate the time of transits tropically.

Because in the calculation of transits no time-transformations are necessary, i.e., the relationship between time units is 1:1, only the spatial relationships are considered. However, one becomes aware of the time dimension in transits when comparing the difference in time between a tropical and a sidereal transit. This difference is a good illustration of how space and time are always together and inseparable.

Another illustration of an inconsistent practice is when tropical astrologers use precession-corrected solar returns (the concept of "return" is a seemingly time-based concept), but keep calculating transits in a tropical-only reference frame (transits having the semblance of merely spatial relationships).

I suggest that these inconsistencies happen mainly for 2 reasons.

First is the habit of astrologers of conceiving things spatially --in this case, as a simple displacement of position in longitude (the Ayanamsa) representing the traditional, simplified application of precession-- instead of dynamically, i.e., as a change in the space *and* time system of reference required by a rigorous application of the dynamics of precession. This idea of time is the essence of precession, and not the seemingly spatial-only relationships or "displacements" with which one associates shifting from a sidereal to a tropical (or viceversa) reference frame.

There is tendency to pay attention only to the spatial relationships or measurements, forgetting that space and time are always related and inseparable. The proof of this is than in sidereal practice, it is often assumed that the only thing needed is a "horizontal" displacement of longitude with respect to the tropical position (the spatial emphasis), leaving aside the displacements in a-) latitude, b-) right ascension, and c-) declination.

Second, the word "sidereal" is not understood in its astronomical sense, i.e., as a reference frame "fixed" in time and space, but in its astrological sense,  i.e., representing zodiacal longitudes in a traditional, historical,  "sidereal zodiac" based solely (and artificially) on an approximate formula of precession in longitude.

These inconsistencies would disappear completely if:

- the word "sidereal" were associated with the reference frame and not with a particular traditional sidereal zodiac

- sidereal time units were used with sidereal positions, tropical time units with tropical positions

- rigorous precessional corrections to all coordinates were used instead of the artificially simplified ones

- the sidereal zero point were understood in space as well as in time.

#3

Before continuing, it may be useful to offer an astronomical definition of the word "sidereal". The conventional definition is "measured with reference to (or in the background of) the stars". My Anchor Dictionary of Astronomy edited by Valerie Illingworth (New York, 1980) provides this definition on page 406:

"sidereal. Related to or measured or determined with reference to the stars".

This definition is tautological, because it does not explain what "with reference to the stars" means. A better definition is given further below (emphasis mine):

"sidereal month. The time taken by the moon to complete one revolution around the Earth, measured with respect to a background star or stellar group CONSIDERED FIXED IN POSITION".

"sidereal year. The time taken by the Earth to complete one revolution around the Sun with reference to a background star or stellar group, which is REGARDED AS FIXED IN POSITION".

In other words, "sidereal" means a fixed stellar reference frame. A reference frame fixed in space and devoid of motion or rotation is called "inertial". Because stars have proper motion, in practice, astronomers use a "quasi-inertial" frame based on a "fundamental catalog" (such as the FK5), consisting of reference stars with very well-known proper motions, and in the last years, for more accuracy a standard set of very distant radio sources with negligible proper motion instead of fundamental stars has been used.

Astronomers invariably use the stellar or sidereal reference frame to calculate ephemerides of solar system objects. This is necessary in order to model as accurately as possible their motion (hence the term "dynamical reference frame"). Extreme efforts are taken in order to arrive at the ideal inertial space, presently defined arbitrarily around the mean equinox and ecliptic of January 1, 2000 (J2000).

Once planetary positions have been calculated for J2000, precession, nutation, aberration, etc. are applied in order to establish the "of date" apparent geocentric coordinates which are found in astrological ephemerides. But the reduction from J2000 to apparent position is made rigorously, applying precession also to the latitudes and accounting for the effect of the latitude on the precession in longitude, a factor that is ignored by sidereal astrologers, who use the tropical positions as source to convert back to their "quasi-sidereal" reference frame and results in inaccurate, approximate positions.

The use of J2000 to represent positions is equivalent to using the mean equinox and ecliptic of J2000 instead of A.D. 221 (in the case of the Fagan/Bradley zodiac) or the time of birth as zero point. The difference is that it is done rigorously. If one were to take rigorously A.D. 221 as the zero point of coordinates, the long time-span  from then to the present would result in displaced coordinates when compared with the standard astrological procedure. In my next post I will illustrate these differences with an example.

#4

Normally, sidereal astrologers do not apply precession to the coordinates of a radix. What they do is REPRESENT THE LONGITUDES IN THE SIDEREAL ZODIAC, i.e., add the ayanamsa to the longitudes only, keeping the representation of latitude, declination, and right ascension strictly tropical.

In order to apply rigorous precession to the longitudes, latitudes, right ascensions, and declinations, we need to know the epoch or zero point of the coordinates. Having the position of the ayanamsa in the tropical zodiac --the usual procedure-- is not enough. We need to know when in time the ayanamsa was exactly zero.

Using the Bureau des Longitudes precession formulas, the resulting epoch (the root of the polynomial used to calculate the Fagan/Bradley Ayanamsa) is September 11, A.D. 221, julian day 1802031.7973. This date is dependent on the numerical quantities of precession in the ecliptic and may vary if one uses other quantities. The BdL formulas, for example, may have an error of in 1.8" or 1.9" in A.D. 221, so this date may be off by about 2 weeks.

data used for the example: J.F. Kenedy dies, November 22 1963  UT 18h30m00s.

Let's see the positions with the usual procedure:

            longitude  latitude  rightasc.   decl.
Moon      = 17Cp00'36"  -2,33'   20h57m46s   19s51
Sun       =  5Sc30'10"   0,00'   15h50m10s   20s06
Mercury   = 15Sc30'59"  -1,36'   16h31m20s   23s30
Venus     = 27Sc13'01"  -0,55'   17h22m30s   24s05
Mars      = 26Sc17'32"  -0,49'   17h18m30s   23s55
Jupiter   = 15Pi34'59"  -1,30'    0h38m26s    2n30
Saturn    = 23Cp05'00"  -1,12'   21h20m35s   16s48
Uranus    = 15Le34'57"   0,46'   10h46m36s    8n36
Neptune   = 21Li41'31"   1,43'   14h55m52s   14s58
Pluto     = 19Le50'09"  13,40'   11h23m20s   18n50

The rigorous application of precession gives:

Moon      = 16Cp59'43"  -2,22'   19h15m09s   24s56
Sun       =  5Sc29'41"   0,12'   14h12m53s   13s17
Mercury   = 15Sc30'37"  -1,23'   14h50m16s   17s58
Venus     = 27Sc12'34"  -0,42'   15h38m50s   20s24
Mars      = 26Sc17'05"  -0,35'   15h35m06s   20s05
Jupiter   = 15Pi34'09"  -1,33'   23h09m23s    7s10
Saturn    = 23Cp04'18"  -1,03'   19h40m32s   22s43
Uranus    = 15Le34'18"   0,41'    9h13m11s   16n58
Neptune   = 21Li40'44"   1,53'   13h22m53s    6s47
Pluto     = 19Le46'26"  13,36'    9h48m19s   27n52

The first tabulation is a simple representation of longitudes after a change of the zero point in the circumference. Although this is what is usually called "sidereal", astronomically speaking it makes little sense.

The second tabulation shows the positions in a truly sidereal reference frame, defined by the ecliptic and equinox of the zero point in time of the Fagan/Bradley ayanamsa. Note that, when the latitude is high as in the case of Pluto, the difference in the longitude is more significant.

differences in longitude and latitude:

Moon    =   -0'53"         + 11'
Sun     =   -0'29"         + 12'
Mercury =   -0'22"         + 13'
Venus   =   -0'27"         + 13'
Mars    =   -0'27"         + 14'
Jupiter =   -0'50"         -  3'
Saturn  =   -0'42"         +  9'
Uranus  =   -0'39"         -  5'
Neptune =   -0'47"         + 10'
Pluto   =   -3'43"         -  4'

Even though the time spanned from A.D. 221 to 1963 is considerable, the differences in longitude are small, except in the case of Pluto, although a difference of 4 arcminutes can still be considered small. The differences in latitude are larger, but perhaps not very significant because the latitude is little used anyway. The only common use of latitude that I can think of is for converting to right ascension and declination.

That the differences are small is encouraging. It means that one could use a more rigorous precession method without having to deal with very different results that would make them impractical.

The right ascensions and declinations are another matter, because in sidereal practice they are strictly tropical, they are never precessed, for reasons unknown to me:

differences in right ascension between tropical and A.D. 221:

Moon    =    -0h42m37s
Sun     =    -0h37m17s
Mercury =    -0h41m04s
Venus   =    -0h43m40s
Mars    =    -0h43m24s
Jupiter =    -1h29m03s
Saturn  =    -0h40m03s
Uranus  =    -1h33m35s
Neptune =    -1h32m59s
Pluto   =    -1h35m01s

differences in declination (in degrees and arcminutes):

Moon    =    +5,05'
Sun     =    -6,49'
Mercury =    -5,32'
Venus   =    -3,41'
Mars    =    -3,50'
Jupiter =    -9,40'
Saturn  =    -5,55'
Uranus  =    +8,22'
Neptune =    +8,11'
Pluto   =    +9,02'

The differences in right ascension and declination, logically, are very large, the coordinates totally different. Using them would require a lot of experimentation in a previously unexplored field (as far as I know), and personally, or intuitively, I am not tuned to this way of handling the right ascensions.

However, using precession-corrected right ascensions and declinations from the time of the radix will result in very small differences from the strictly tropical coordinates, with the advantage that they would be sidereal, instead of working sidereally sometimes, tropically others, or using both sidereal and tropical within the same calculation (as in the PSSR).

#5

The practice of ignoring precession when dealing with the latitude, the right ascension, and the declination of the planets evidences that sidereal astrologers are using a definition of precession which is a simplification of the astronomical complexities of precession in the real world. This is not necessarily wrong as long as it is understood that it does not correspond to the physical reality of precession.

In other words: sidereal astrologers often work with strictly tropical --not sidereal-- coordinates. When tropical right ascensions and declinations not corrected for precession are used, or when tropical time units are the basis for the calculation of progressions (without the "bija corrections") they are working in a tropical reference frame.

This happens because for most astrologers (tropical and sidereal alike) the word "sidereal" means simply representing the zodiacal longitudes in some historical or traditional zodiac (a merely spatial conception), failing to see the time dimension, the fact that "sidereal" is not "in such and such a zodiac" not subject to precessional displacement in longitude, but a mathematically defined space and time reference frame.

NOTE: other examples of the paradigmatic emphasis on spatial relationships in astrological thinking at the expense of more dynamical perspectives are discussed in my essay "On the Seed Metaphor": http://www.expreso.co.cr/centaurs/essays/seed.html

The astronomical incongruence of the way astrologers deal with precession was discussed by Dieter Koch in the documentation to the Swiss Ephemeris. He wrote  [see the section "In search of correct algorithms"]:

"... the whole ayanamsa is subtracted from a planetary position which is referred to the ecliptic of the epoch t... Because the ecliptic is not fixed, it cannot be correct just to subtract an ayanamsa from the tropical position in order to get a sidereal position... This does not make sense... The traditional method of computing sidereal positions is geometrically not sound and can never achieve the same degree of accuracy as tropical astrology is used to."

Dieter provides an example of what happens when the usual procedure of adding the ayanamsa to a tropical position in order to (allegedly) obtain its sidereal position is used over a long time span:

"As an effect of this procedure, objects that do not move sidereally, e.g. the Galactic Center, seem to move. If we compute its precise tropical position for several dates and then subtract the Fagan/Bradley ayanamsa for the same dates in order to get its sidereal position, these positions will all be slightly different:

 Date             Longitude         Latitude
 01.01.-5000  2 sag 07'57.7237   -4°41'34.7123 (without aberration)
 01.01.-4000  2 sag 07'32.9817   -4°49' 4.8880
 01.01.-3000  2 sag 07'14.2044   -4°56'47.7013
 01.01.-2000  2 sag 07' 0.4590   -5° 4'39.5863
 01.01.-1000  2 sag 06'50.7229   -5°12'36.9917
 01.01.0      2 sag 06'44.2492   -5°20'36.4081
 01.01.1000   2 sag 06'40.7813   -5°28'34.3906
 01.01.2000   2 sag 06'40.5661   -5°36'27.5619
 01.01.3000   2 sag 06'44.1743   -5°44'12.6886
 01.01.4000   2 sag 06'52.1927   -5°51'46.6231
 01.01.5000   2 sag 07' 4.8942   -5°59' 6.3665

 "The effect can be much greater for bodies with greater ecliptical latitude. "Exactly the same kind of thing happens to sidereal planetary positions, if one calculates them in the traditional way. It is only because planets move that we are not aware of it.

You can see here the precession in latitude, or more exactly, the accumulated displacement between the ecliptic of the epoch (here 1950) and the ecliptic of date, normally ignored in sidereal practice. You can also see how the longitude is rotating or librating around its 1950 value.

This example of a point which is known to be fixed or unmoving in quasi-inertial space like the Galactic Center, shows to what extent the usual sidereal practice is based not on a concept of "sidereal" as a reference frame, but of "sidereal" as exclusively a representation of zodiacal positions based on a conventional or traditional fiducial point not subject to precession in longitude.

This is the traditional "sidereal astrology paradigm": represent the zodiacal positions of planets using a fiducial which is free of precession in longitude, but ignoring how precessional motion is in the real world. Ignore the precessional displacements in latitude, right ascension, and declination. But even the "sidereal" longitudes have been calculated with a simplification of precessional motion in longitude, so they are really "quasi-sidereal". The latitudes, the right ascensions, the declinations, and often, the time units used by sidereal astrologers, are often strictly tropical.

So, clearly, everything depends on how one defines the word "sidereal". It is one thing to be a "sidereal astrologer" (including of course the Indian version), and a different thing to work astrologically in a sidereal reference frame. The two things are assumed to come together in theory. They are separate in practice. If understood in the astronomical sense, "Sidereal" astrology is not wholly sidereal, or it is "sidereal" only in a limited, inaccurate and simplified way.

Since precessing the right ascensions and declinations would result in very large differences with what has already been done, one would think that it is in the use of PRECESSION-CORRECTED POSITIONS --where the corrections are small-- where a real and practical, truly accurate sidereal or "fixed", quasi-inertial reference frame can come into place in Astrology.

#6

In principle, "precession-corrected" (tropical) positions and "truly sidereal" positions are exactly the same, the difference being only the point in time that is chosen as fiducial:

1-) precession-corrected positions (usually) use the radix as fiducial

2-) sidereal positions use September 11, A.D. 221 as fiducial

NOTE: This date refers to the Fagan/Bradley sidereal zodiac, which I use as example in this exposition.

In other words: a "sidereal astrologer" uses the tropical zodiac of the year 221 as fiducial, a "tropicalist" who works with precession-corrected positions uses the time of the radix as fiducial. Both are "precession-corrected" tropical positions, the only difference is the amount of time or of accumulated precession which results from the fiducial or starting point chosen. Both are sub-sets of a purely sidereal (or quasi-sidereal) reference frame.

Astrological measurements can be either tropical or sidereal, independent of  whether one uses a tropical (or sidereal) zodiac or not. That this is often not recognized is another example of how much astrologers are controlled by a purely spatial abstraction at the expense of the more realistic, dynamical model that includes both space and time.

Confusion is created by the habit of associating the word "sidereal" with a specific sidereal zodiac of some astrological tradition or school. "Sidereal" is a system of reference to measure movement, and is independent of any of the traditional zodiacs used by astrologers, sidereal or tropical. The question of sidereal or tropical is not simply a question of what traditional zodiac one uses, but a question of how one wants to measure time.

If one subtracts the precession accumulated from the time of the radix to the tropical positions of a specific date, one is effectively using a sidereal zodiac with its zero point defined as the position of the equinox at the date of the radix. The tropical position of 0 Aries when a person is born is considered fixed in a quasi-inertial or "fixed" reference frame, and precession is counted from that day on. A precession-corrected tropical solar return is a strictly sidereal construct based on a sidereal reference frame the starting point of which is the radix.

Another way of saying it is that a "tropical" precession-corrected return represents positions in a sidereal zodiac the starting point of which is the vernal point of the radix, while a purely "sidereal" return represents positions in a sidereal zodiac the starting point of which is the vernal point of September 11, A.D. 221 (in the case of the Fagan/Bradley zodiac).

"Sidereal" is by convention a "fixed" reference frame, against which the precessional motion is observed and measured. The astrological concept of "a radix" is almost the same thing: something "fixed" in time against which one charts everything that happens in time. From this perspective, precession-corrected (=sidereal) solar returns and transits appear to be the most logical way to proceed, since the birth chart is conventionally considered "fixed" in time and space.

This is the principle behind the use of a sidereal reference frame. What zodiac (tropical or sidereal) one chooses to represent the positions is irrelevant form a mathematical or calculation standpoint, unless one gives special weight to purely astrological considerations, such as where the zodiacal signs should begin or end, a consideration that for many astrologers (including myself) is of little interest.

A "fixed" sidereal reference frame is no different than what is assumed about the moment of birth or the birth chart, the concept of "radix", the radix moment having a different weight than all the others and used as the common reference frame for all. The radix space and time coordinates are the basic reference frame in Astrology.

Is astrological analysis (or, for that matter, the analysis of a human life) a question of anything against anything or is it by necessity structured around certain "privileged" or meaningful events?

The symbolical link between the concept of "sidereal" (i.e. fixed in time and space) and the concept of "radix" provides the framework to understand the different possibilities; one can categorize the types of events being compared --i.e., birth against anything else, a human biography, a process, or simple unrelated events.  For example, one can think of:

1-) precession-corrected positions when one date or chart is seen in reference or with respect to the other (the radix)

2-) tropical-only positions when both are seen comparatively in reference to themselves only (in equal or "democratic" terms, giving the same weight to the 2 moments)

3-) a traditional sidereal zodiac when both are seen in reference to something else that includes both. The traditional sidereal zodiac is especially useful when one is comparing 3 or more independent dates or charts.

These may be more philosophical considerations that are not related directly to this discussion, but I can see now why I feel that a better understanding and practical application of precession, as opposed to the trivial, boring discussion of competing zodiacs-- is so immediately vital and appealing or important to me.

#7

The rigorous precession in right ascension and declination can be used to apply a precession-correction whenever the positions are derivative from the radix, i.e., when "precession-corrected tropical" is applicable. Since precession from this perspective accumulates from the time of the radix only, instead of from A.D. 221, the resulting displacement of the right ascensions and declinations is relatively small.

Riyal --for example-- has always performed this precession correction by default, unless the "precession-corrected" global option is de-activated. And because I had assumed that sidereal astrologers always used sidereal coordinates --I was wrong--, when Riyal works in "absolute sidereal mode" (e.g., with positions in the Fagan/Bradley sidereal zodiac), the precession-correction from the time of the radix cannot be deactivated. To de-activate it, one must put the program back in tropical mode.

Later on, I learned --to my surprise-- that normally sidereal astrologers, including Fagan, did not apply precession-correction to the right ascensions and declinations, i.e., did not work sidereally but tropically, or worked sidereally in some cases, tropically in others. Until someone explains to me the logic of this, this makes little sense astronomically and for this reason Riyal in sidereal mode forces the precession correction from the time of the radix (e.g., bija rates of progression, precession-corrected right ascensions and declinations, etc.).

When the same precession correction is applied rigorously to the longitudes and latitudes, the nutation in longitude must be removed. When one considers the ecliptic of t0 (=birth or whatever other time one chooses) as fixed, then by definition it is removed from the Earth and becomes "sidereal", therefore, the transits to this fixed ecliptic are free of the polar wobble that constitutes nutation. (I must thank Dieter Koch, co-author of the Swiss Ephemeris, who in a recent e-mail exchange made this clear to me.)

When one works in a sidereal reference frame, all transiting positions are measured with respect to it and are therefore free of nutation; but there is a difference of opinion with respect to how one takes the original natal positions. If they are considered sidereal positions to start with, the precession should be removed from the natal positions; this is the approach of the Swiss Ephemeris. But it  seems to me that the natal positions are fixed-tropical, not fixed-sidereal. It is their tropical positions, the tropical zodiac at the time of birth, what is being fixed in inertial space or the space of the fixed stars, and therefore nutation should not be removed from the natal positions.

A precession-corrected transit can be defined as the time when a transiting planet crosses exactly the same point *in the natal ecliptic* at which a natal planet was when you were born. The ecliptic at the time of the transit has moved with respect to the ecliptic at the time of birth (at a rate of approximately 47" per century). The ecliptic at the time of birth is considered fixed in the space of the fixed stars, but the natal planets are referred to this ecliptic plane and not the stars, and therefore should include the effects of nutation.

In other words, the original natal positions are not "sidereal" to start with, but tropical. Then, this tropical ecliptic is frozen in inertial space, and the transiting planets are measured with respect to this fixed ecliptic of birth. Transits are measured not with respect to the sky of the fixed stars, but to the ecliptic of birth. Obviously, if we are working sidereally all along from the start, then of course the natal positions should not include the nutation.

If you have been able to follow this discussion since the first post (sidereal right ascensions 1), you will realize that this takes us to the original concept of a starting point in time. In a precession-corrected tropical scheme, the time of birth or of the radix is unquestionably the starting point, but, is there such a starting point *in time* in the sidereal zodiac? Should there be one? There is no question that one should remove the nutation from the Fagan/Bradley (or any other) sidereal zodiac, but should we rigorously correct for precession the positions to A.D. 221?

In normal practice the longitudes are being calculated back to A.D. 221 all the time because one is using an amount of accumulated precession (the ayanamsa) that is valid only for a starting point in A.D. 221. One is normally not aware of this fact because the correction is seen as a simple displacement of position along the circumference of the zodiac (a spatial consideration), without realizing that precession is both in space and time. Precession has no meaning if it is seen only in terms of space.

Juan Antonio Revilla
San José, Costa Rica
May, 2005