Chapter 14, Text 7:
bhacakra-nābhau viṣuvad dvitiyam samasūtragam
ayana dvitayan caiva catasraḥ prathitāstutāḥ
The two solstices and two equinoxes are the thread upon which the core of the zodiac exists.
tad atareṣu saṅkrānti dvitayam dvitayam punaḥ
Two borders are between each point.
bhānor marakara saṅkrānteḥ ṣaṇmāsā uttarāyaṇam
karkādestu tathavasyāt ṣaṇmāsā dakṣināyaṇam
It takes the Sun six months to reach the northern solstice after entering Capricorn; and six months to reach the southern solstice after entering Cancer.
meṣādyo dvādaśaite māsāstair eva vatsaraḥ
The twelve divisions beginning from Aries are certainly the months which constitute a year.
Division 5, Chapter 21, Text 3:
sa eṣa udagayana-dakṣiṇāyana-vaiṣuvata-saṁjñābhir māndya-śaighrya-samānābhir gatibhir
The sun moves at varying speed between the northern solstice, southern solstice, and equinotical points.
ārohaṇāvarohaṇa-samāna-sthāneṣu yathā-savanam abhipadyamāno
Its rise towards the northern solstice, its fall towards the southern solstice, and its crossing the middle point can be known by observing time.
makarādiṣu rāśiṣv aho-rātrāṇi dīrgha-hrasva-samānāni vidhatte.
The days and nights grow longer and shorter, revealing which of the signs – Capricorn, etc. – the Sun is in.
yadā meṣa-tulayor vartate tadāho-rātrāṇi samānāni bhavanti
When the Sun is in Aries and Libra, the days and nights are equal.
yadā vṛṣabhādiṣu pañcasu ca rāśiṣu carati
tadāhāny eva vardhante
hrasati ca māsi māsy ekaikā ghaṭikā rātriṣu.
When the Sun is in the five signs starting from Taurus, the days grow longer and nights which grow shorter, month by month.
yadā vṛścikādiṣu pañcasu vartate
tadāho-rātrāṇi viparyayāṇi bhavanti.
When the Sun is in the five signs starting from Scorpio, the days and nights change in the opposite way.
I’ve done a number of videos on this subject, here is a complete playlist. Transcripts and more information below.
What are the twelve signs? They are a way to measure space.
Space is like as a sphere all around us. The Sun and planets move through a narrow band anchored around the middle of that sphere. The twelve signs divide this narrow band into twelve discrete sections.
The easiest way to explain is to use an analog clock. The clock’s round face represents space, the circular band through which the Sun and planets move. The hour hand represents the Sun. The minute hand represents the Moon.
Let’s take a clock before it has any hands or markings on its face. Put the hour hand in place and watch it move around the clock’s entire circle. This movement represents the Sun moving through the circle of space (a "year").
Now put on the minute hand. It's movement represents the Moon moving through the entire circle of space (a "month").
Now let’s set both hands to the 12 o’clock position, get out a pen, and let the clock start running. The minute and hour hands both move, but the hour hand moves much slower. Whenever the minute hand comes back to the 12 o’clock position, mark the clock face right where the hour hand is pointing. You’ll wind up with twelve marks.
What you’ve just done is exactly analogous to creating the twelve divisions of the zodiac. Each mark on the clock is the border of a new sign. There are twelve of them because the Moon makes twelve cycles through space in the time it takes the sun to make one. So, each sign contains the amount of space travelled by the Sun during the time it takes the Moon to make one complete circuit.
Take a protractor and measure the distance between each of the twelve marks on your clock. Each one is the same: 30 degrees. That’s why each sign consists of 30° of the complete circle of space.
Sidereal and tropical zodiac systems both follow this definition. The only difference is where they start“marking the clock.”
Tropical signs starts from where path of Sun and planets intersects the celestial equator. This point is called “equinox.”
Sidereal signs start reference to a specific star. There are several different opinions about which star should be used, and how. The most popular is the Lahiri Zodiac, which says the signs begin at a point 180 degrees opposite the star named Spica.
Sidereal signs start from a stellar reference point, but they are not literally the stars themselves, which form thirteen divisions of the circle of space, each one a different size (some twice the size of others). Obviously these constellations are not identical to the sidereal signs, which like the tropical signs, are twelve in number and each one equal in size.
People on either side of the issue tense up over this question, because the perception is that if one defines the zodiac incorrectly then ones astrology, and all of its history and heroes, must be completely bogus. This is a misconception. Using the wrong zodiac does not invalidate an entire astrological system. Many factors are unaffected by how we define the zodiac signs. For example:
It’s also very important to note that the further back we go in history towards the early AD centuries, the smaller the difference between tropical and sidereal starting points becomes. Astrologers 1700 years ago, for example, faced no difference at all between the sidereal and tropical definitions.
One definition of the zodiac might be “correct” and the other “incorrect,” but this does not mean that using the wrong one renders your astrological system useless, or discounts its rich history. If we define the zodiac correctly, however, our astrological systems will become clearer and simpler to use. This will only become truer as we move into the future and the discrepancy between the sidereal and tropical starting points continues to increase.
Modern India is a bastion of the sidereal zodiac. Thus it comes as a great shock that India’s own classical literature defines the zodiac tropically! Probably no one is more shocked by this than Indians themselves, who faithfully assumed they had been “following the ancients” by using a sidereal zodiac. Let’s look at a sample of what Indian classical texts actually say.
The most authoritative, fundamental Indian text on astronomical astrology is Sūrya Siddhānta, a title which declares the book to be “Perfect Conclusions of the Sun.” Several early places of the book seem to disfavor sidereal and favor the tropical definition of the signs:
A solar month begins when the Sun enters a new zodiac sign. There are twelve months in a year.
60 seconds (vikāla) make a minute. 60 minutes (kāla) make a degree. 30 degrees (bhaga) make a sign. 12 signs (rāśi) complete the circle (bhagaṇa).
In one age (yuga) the circle of stars lags behind 600 revolutions towards the east. Use a formula [math omitted for brevity] to find the current location (ayana) of the equinox relative to the stars.
The above references could support the tropical zodiac, but texts 7-10 of the Fourteenth Chapter explicitly and unequivocally put it in black and white:
It is well-known that the circle of signs is split by two diameters. One is the line from equinox to equinox. The other is the line from solstice to solstice. Between each solstice and equinox are two other markers. Each solstice /equinox and the two following markers represent the three strides of Vishnu.
The Sun has entered Capricorn when it begins moving north for six months. It has entered Cancer when it begins moving south for six months. Seasons last for two signs each, beginning from Capricorn with the frozen season. The twelve signs named Aries, etc. are the months which altogether comprise the year.
Here, Sūrya Siddhānta plainly says that solstices and equinoxes define the 12 signs of the zodiac. Capricorn is defined by the Sun beginning to move north at the winter solstice, and that Cancer is defined by the Sun beginning to move south at the summer solstice.
Śrīmad Bhāgavatam is held by most Indians to be penultimate Pūraṇa representing the full maturity of Indian thought. Its fifth division concerns astronomy. Texts 2-6 of the 21st chapter of that division define the twelve zodiac signs, unambiguously, as tropical:
Outer space is measured by relation of heaven and earth. The Sun is the king of all the planets, in the center of everything, keeping everything together. It moves to the north, crosses the equator, and moves to the south. When it goes north of the equator days get longer. When it crosses the equator days and nights are equal. When it goes south of the equator days get shorter. On this basis the Sun moves through the twelve divisions called Capricorn and so forth.
The Sun is at Aries and Libra when the days and nights are equal. Passing through Taurus, etc. the days become longer and then decrease until again equal with the night. Passing through Scorpio, etc. the night becomes longer and then decrease to again become equal with the days.
Thus it is impossible to deny that Śrīmad Bhāgavatam presents a tropical definition of the 12 zodiac signs.
The stars of sidereal space are a valid and important astrological entity. India (and almost all cultures) has a valid system of dividing sidereal space with the Moon as the focal point, not the Sun as in tropical space. This system has 27 divisions, not 12, because there are that many sunrises during the time it takes the Moon to complete a full circuit of the heavens.
The idea of 12 sidereal signs comes from wrongly assuming that the correlation between the stars and signs is permanent. In fact, there is no permanent correlation between the two, the signs eternally and very gradually drift backwards through the stars - a phenomena commonly known as "precession of the equinox."
There is a valid need to correlate the signs and stars because their relationship is important for defining very long periods of time (“ages”) and for knowing how and when to keep solar and lunar calendar systems synchronized.
Babylonians measured the correlation of their autumnal equinox with the heliacal rising of stars they called The Scales. Greeks measured the discrepancy of tropical Aries against a stellar counterpart bearing the same name. Ancient and Classical Indians measured the heliacal position of the equinox in reference to their fixed stars. For example, the Ṛg Veda notes Kṛttikā as the “first” star and the beginning of the celestial circle, because in Ṛg Vedic times, four to five thousand years ago, Kṛttikā heliacally rose with the Vernal Equinox. Later Indian works from nearly two thousand years ago note Aśvinī as the first star, because at that time Aśvinī was the star heliacally rising with the equinox.
Projecting the 12 zodiac divisions into space, based on the then-current position of the vernal equinox, was useful for mathematics and essential for long-term timekeeping, but opened a door for people to think of the signs as stellar entities. It is an easy mistake to make considering that for centuries there was almost no significant difference between the signs and their homonymic sidereal namesakes.
Now let’s examine how fundamental western texts define the zodiac.
Mul.Apin is one of the oldest existing documents of astronomical astrology. It reveals that the ancient Babylonians used a lunisolar calendar of twelve 30-day months per year. They anchored these twelve divisions to the equinoxes and solstices, and created stars to serve as reference points for the occurrence of solstices and equinoxes.
Mul.Apin 1.3.1-12 says:
On the 15th of Tashritu the Scales, the Mad Dog, EN.TE.NA.BAR.HUM and the Dog become visible; 3 minas is a daytime watch, 3 minas is a nighttime watch. 
This says that when the days and nights are of equal length (an equinox) the ecliptic star called “The Scales” (Modern-day Libra) rises heliacally (just before the Sun). This occurs on the 15th day of their month named Tashritu (an Autumn month). Similarly, Mul.Apin also says that when the nights are shortest (summer solstice) the ecliptic stars of modern Cancer rise. And when the nights are longest (winter solstice) the ecliptic stars of modern Capricorn rise.
What we see in Mul.Apin is that the solstices and equinoxes are fundamental to the Babylonian’s twelvefold division of space, and that reference stars are used to measure the discrepancy between tropical and sidereal time. The Babylonian’s would insert leap months to re-sync the stars with the equinoxes periodically. This explains why they gave stars the same names as the twelve signs.
One cannot convincingly argue that the Babylonian’s had a sidereal twelvefold zodiac, because the Mul.Apin explicitly describes eighteen sidereal divisions of the ecliptic.
Ptolemy’s Tetrabiblos is thought of as the “bible” of Western Astrology. 1.10 of that text defines the zodiac with a tropical starting point:
The zodiac is a circle, so there is no clear “beginning” to it. But the sign that begins with the Vernal Equinox, Aries, acts as the beginning.
The next section, 1.11, makes it perfectly clear that the signs are defined in relation to the solstices and equinoxes.
There are two signs at solstices: Cancer is the 30° interval beginning at the Summer Solstice. Capricorn is the same from the Winter Solstice. There are two signs at equinoxes: Aries begins from the Vernal Equinox and Libra from the Autumnal Equinox.
Siderealists suggest that Ptolemy “changed” the Greek system to a tropical one, but I don’t consider this a valid opinion. Ptolemy’s forerunner, Hipparchus, discovered the precession of the equinoxes. Greek authors prior to Hipparchus therefore could not differentiate tropical from sidereal. The first significant post-Hipparchus author, Ptolemy, explicitly states that the “beginning” of beginningless space is judged from the equinoxes and solstices and must follow them, not the stars that temporarily and approximately represent them.
First I explained that the twelve signs are not stars; but are mathematical divisions of space derived from the interplay between the Sun and Moon. So there is no compelling reason to assert that the beginning of the twelve signs should be anchored to a star. It is easier to see the rationale of using the equinox to mark the beginning of the divisions – for this binds the twelve lunisolar polyrhythms firmly to the center of the Earth’s local space.
Siderealists, and Indians in particular, will have a difficult time digesting or accepting this point, because it throws the expertise and validity of their rich astrological history into doubt. “So many great astrologers have been successfully doing it this way in India for so many centuries, how can you say they are wrong?!”
I am sympathetic to this reaction. I went through the same dilemma myself – being of Indian astrological, philosophical and religious background. This is why I felt it important to explain that the zodiac is only one of several fundamental components of astrology, and thus an error in calculating the zodiac does not totally invalidate an astrologer or an astrological system. And I wanted to note that the further back in history we look towards our revered founders, the more insulated they are against the effects of error in this regard, for the discrepancy between the sidereal and tropical measurements grows smaller as we move back towards 300 AD.
But if we indeed value tradition we must never lose sight of its original authorities. Sūrya Siddhānta, Śrīmad Bhāgavatam, Mul.Apin and Tetrabiblos all clearly state that the twelve signs of the zodiac are entirely based on solstices and equinoxes, not stars. If we ignore this, what exactly are we loyal to?
Today the discrepancy between the sidereal and tropical reckoning of the twelve signs is too big to overlook. We cannot postpone taking this issue seriously. Once we admit that stars are not signs, there is no compelling reason to use a star to define the zodiac’s beginning. Beside force of habit, injured pride, the paralysis of shock, or fear of change – is there anything that would stop us all from embracing the unequivocal tropical definitions of the zodiac found in all the ancient and classical literature of the world?
- Vic DiCara
 According to: Hermann Hunger and David Pingree, "MUL.APIN. An Astronomical Compendium in Cuneiform", p. 43
These are the clearest and most complete explanations I have given. I feel that the following parts are the most important. Please be sure to watch them:
What I use is a combination of sidereal and tropical. Sidereal stars / nakshatra, and tropical signs / rashi.
That is very inaccurate. I am merely doing my part and carrying the torch. Many, many important personalities before me have discovered and advocated the same reform I am championing. Similarly there are many others (and their number is growing steadily by the day) who currently share this opinion with me.
In fact, you will be shocked to know that even the very committee who recommended the Lahiri sidereal ayanamsha as the Indian standard in the 1950s expressly stated that it was only a partial reform, and that further reform was required to return the zodiac to proper alignment with tropical seasons. Here are their words, and background, copied from research published by Dieter Koch.
Lahiri was inspired by the astronomy historian S. B. Dikshita, who in the late 19th century wrote an important book on the history of Indian astronomy [History of Indian Astronomy, Part II]. Dikshita came to the conclusion that, given the prominence that Vedic religion gave to the cardinal points of the tropical year, the Indian calendar should be reformed and no longer be based on the sidereal, but on the tropical zodiac. However, if such a reform could not be brought about due to the rigid conservatism of contemporary Vedic culture, one should choose the Ayanāṃśa in such a way that the sidereal zero point was in opposition to Spica, because this would be in accordance with the zodiac of the 16th century astronomer Ganeśa Daivajña.
A similar point of view was maintained by the Calendar Reform Committee, when it recommended the Lahiri Ayanāṃśa: "This recommendation is to be regarded only as a measure of compromise, so that we avoid a violent break with the established custom. But it does not make our present seasons in the various months as they were in the days of Varahamihira or Kalidasa. It is hoped that at not a distant date, further reforms for locating the lunar and solar festivals in the seasons in which they were originally observed will be adopted." (Calendar Reform Committee Report, p. 5)
What doesn't change: All planets are in the same naksatras. Therefore the planetary phases (dasa) are absolutely unchanged. The interplanetary aspects and the aspects of planets upon houses are absolutely unchanged. Transits to planets are also absolutely unchanged. Planetary house positions often remain the same, including navamsha and divisional houses.
What does change: The dignity of the planets always change, which affects their potency (shad-bala). The rising sign, and thus the houses owned by the planets, often change. The planets usually change the signs they occupy.
Yes, I find tropical signs give a simpler, clearer picture more readily, if used properly - for example with whole sign houses and sidereal nakshatras, etc.
Yes. So can you, if you are a good astrologer and do not stick to preconceived notions about your previous observations.
Considering the previous explanation of what changes and what does not change, you can see that the old system had significant accurate details which remain in the new system. Furthermore I wouldn't want you to think that improvement makes the past worse. Improvement makes the present and the future better.
The classic textbooks on Indian Astrology (Jyotisha) were written in different time periods. I believe that India has been using sidereal zodiac signs for a very long time – probably about 1800 or so years. Classics written after this time (c. 200 AD) were probably written in reference to the sidereal zodiac. But it is most important to note that about 500 years before and after that key point in history (c. 300 BC – 700 AD) there was practically no difference between tropical and sidereal zodiacs. And even for another 500 years or so on either side (800 BC – 1200 AD) the difference was not very dramatic. Most of the classics were written in this time frame. Therefore even if they were written by authors who had adopted sidereal zodiac signs, the practical difference between tropical and sidereal signs contemporary for those authors was negligible.
The fact that there are no significant “classics” much after this time frame is another evidence that Indian astrology began to lose it’s original potency as the sidereal zodiac became more and more out of phase with the true zodiac signs.
Yes, the methods defined in classics work best with tropical signs. In fact some of the methods defined in the classics cannot work at all without tropical signs. A case in point is the shad-bala system for calculating the potency of a planet. One component of this calculation is declination, which cannot be determined outside of tropical system (“declination” means the distance north or south of the equator).
Frankly, the ascendant is crucial to every technique and the ascendant also cannot be calculated outside of the tropical system.
Most of what we consider classic “astrology” textbooks do not, no. Calculation and interpretation are separate branches of Indian astrology. The Surya Siddhanta is the authoritative text on calculations. It does indicate that tropical planetary coordinates should be used. It instructs us to use ayanamsha is a means of converting sidereal calculations to tropical, and not visa versa as is now the fashion. The Srimad Bhagavatam also contains several chapters on astronomical phenomena and unequivocally defines the zodiac signs as tropical, and the nakshatras as sidereal.
Classic Indian literature sometimes gives example charts, but not the birth data. For example they describe the planetary configurations for Rama and Krishna – but they do not say what birth data creates those charts. This is because the planetary configurations are themselves the most universal and reliable method of determining a point in time – so the ancient scriptures express the time of an important event such as the birth of an incarnation of God, by describing the planetary configurations.
However, since there is no second reference it is not possible to verify if the classics are describing the configurations in a sidereal or tropical reference. It is also particularly confusing because these configurations refer to points in time that are – by our pygmy modern conceptions and methods – extremely distant in the past and therefore very hard to verify by calculations – since over vast periods of time the speeds and motions of planets and the earth are not at all constant.
Why not? It should make perfect sense if you understand what ayanamsha is in the first place. Ayana-amsha is the portion of space (amsha) that separates the sidereal reference from the tropical reference (ayana). It measures the disparity between sidereal and tropical references. So why should it not make sense that there would be a disparity between the sidereal stars (nakshatra) and the tropical measurements of signs (rashi)?
Four or five thousand years ago, when Rg and Yajur Veda were compiled in their currently extant form, the vernal equinox (the "starting line" for tropical reference) occurred when the Sun was near the stars of Krittika! That is why those old Vedas list Krittika, not Ashvini, as the "first" of the 28 nakshatras. Over time, the Sun's location on the vernal equinox drifts backwards against the circle of stars. About two thousand years ago it had drifted into the stars of Ashvini. That is why later compilations and expansions of Vedic literature list Ashvini as the "first" of the nakshatras. The drifting continues, and today the Sun's position on the vernal equinox is in Uttara Bhadrapada's stellar region.
The important point to grasp is that the stars are different from the signs. The signs arise from the interplay of the Sun and the Earth. The stars exist independently from this interplay, on their own in the heavens. Thus the two zodiacs: signs and stars, rashis and nakshatras, are independent of one another and cycle in and out of sync with one another. The amount of distance they have moved out of sync is measured by ayanamsha.
No, they do not. This is a big mistake, and I previously made it myself. There are no planetary rulers of the sidereal nakshatras. The association of planets to nakshatras is only valid in the context of dasa systems for the sake of establishing the chronological order of planetary phases. The planet associated with a nakshatra is different in every different dasa system. So there is no such thing as a planet who "rules" a nakshatra. The nakshatras derive their meanings purely from the nature of the deity who empowers them. Their connection with signs and planets is coincidental. Their connection with a particular deity is essential.
Comments on P.V.N. Rao:
Comments on David Frawley
I comment on all three in one post.
To my knowledge there is only one substantial rebuttal of my paper so far. Here are my responses to that rebuttal [with links to the rebuttal itself, of course].
And sometimes, I just gotta vent!