Vedic Yugas… Five Years Long

This continues my presentation of Vedanga Jyotish – the oldest complete treatise on Indian calendrical astronomy.

Yugas

A yuga contains 5 years, 1830 days, and 62 synodic (lunar) months. Knowing this, we can calculate many other ways of measuring the yuga.

• The star named Dhaniṣṭhā will rise 1835 times. [i.e. A yuga has 1835 sidereal days. A sidereal day is the duration between the rising of a star, in this case Dhaniṣṭhā. Every year there is one extra sidereal day than a normal day (measured as the duration between the rising of the Sun), and there are five years in a yuga.]
• There will be 67 lunar cycles. [62 synodic months in 5 years, plus one extra cycle for each year]
• The moon will rise 1768 times. [sidereal days minus one day per each lunar cycle]
• The Moon will cross the equator 134 times [the number of constellations traversed by the Sun in 5 years, minus one]

The yuga has 60+1 months of sunrises, 60+2 synodic months, and 60+7 lunar cycles. There are 30 sunrises in such a month. The solar month however has 30.5 days.

In a yuga, the Moon enters each constellation 67 times. The Sun stays in each constellation for 13 5/9 days.

Since Dhaniṣṭhā will rise 1,835 times, and since there are 27 constellations like Dhaniṣṭhā, there are 49,545 lagna [ascendants] in a yuga (1,835 x 27 = 49,545).

Since there are six ṛtu in a year, if we apply this to the Moon’s “year” (a lunar cycle) we find that there are 402 lunar ṛtu (“seasons”) in a yuga (67 x 6 = 402).

Beginning of the Yuga

The five-year yuga begins when the Sun and Moon come together in Dhaniṣṭhā. It will be the lunar month of Maghā, the solar month of Tapas. The Moon’s waxing will begin, and both the Sun and Moon will begin moving northward in reference to the equator. The Yuga ends with the waning moon of the month of Pauṣa.

When the Sun and Moon are at the beginning of Dhaniṣṭhā’s area, they begin moving northward. When they are in the middle of Āśleṣā they begin moving southward. In the Sun’s case this always happens in the months of Māgha and Śrāvaṇa, respectively.

Solstices during the Yuga

Tithi [lunar-phase-day] and nakṣatra of the beginning [winter solstice] and midpoints [summer solstice] of each year of the yuga:

• First Year:           1^st waxing / Dhaniṣṭhā [“Winter”]             7^th waxing / Citrā [“Summer”]
• Second Year:     13^th waxing / Ārdrā                                          4^th waning / Pūrva Bhādrapadā
• Third Year:          10^th waning / Anurādhā                                                 1^st waxing / Āśleṣā
• Fourth Year:       7^th waxing / Aśvinī                                            13^th waxing / Pūrva Aṣāḍhā
• Fifth  Year:          4^th waning / Uttara Phālgunī                        10^th waning / Rohiṇī

Comment: this translation should be fact checked. The details may be in wrong arrangement.

Equinoxes during the Yuga

The equinoxes of the Yuga occur:

• First Year:           3^rd waxing (“Vernal”)      9^th waxing (“Autumnal”)
• Second Year:     Full Moon                            6^th waning
• Third Year:          12^th waning                         3^rd waxing
• Fourth Year:       9^th waxing                            Full Moon
• Fifth Year:           6^th waning                           12^th waning

The formulae for obtaining this information:

Double the ordinal of the equinox; subtract one; then multiply by six. This number is the number of waxing and waning periods of the Moon which have passed between the beginning of the yuga and the equinox in question. [odd numbers are waxing periods, even numbers are waning periods.]

If you half this number you will know on which tithi [lunar-phase day] the equinox will occur.

Maintaining Synchronicity Between the Calendar and Reality

Every two synodic months and two synodic days, a new season begins. However, the eighth season begins on the 15^th synodic day [not the 16^th].

Comment: The addition of two and sometimes one synodic day is a method for synchronizing approximated and rounded cylindrical measurements.

 

If the end of the waxing or waning period [the syzygy of Earth, Moon and Sun] occurs before mid-day, you can omit that day from the calendar. If not, subtract 30 kāṣṭhā  from the kāṣṭhā of the syzygy  for each waxing or waning period elapsed [since the Yuga began].

Comment: I am not clear on the exact meaning of the second half of this statement.

An Interpolated Verse

Comment: I will mention a verse without a number and found in only one of the two versions of the book, clearly added to the text at a later date:

 

Note the zodiac sign that Jupiter is in when the Yuga begins. Count it from Pisces. Divide that by five. Take the remainder. That is the number of the year in the five-year cycle.

 

- Vic DiCara

www.vicdicara.com

Vedāṁga Jyotiṣa – Part 1

I will organize this presentation in leiu of the work of Professor T.S. Kuppanna Sastry and Dr. K.V Sarma. It combines the two versions of Vedāṁga Jyotiṣa found in Ṛg and Yajur Veda.

Introduction

I purify myself by bowing my head to the Creator, whom I envision as being the power within the five-year cycles [“yuga”], and the body on which days, months, seasons, and half-years are limbs.

I also bow my head to the Goddess of Intellect, Sarasvati – so that I may write on the science of time, as explained by Sage Lagadha.  This science is meritorious and dear to the learned, because by it one can understand the perfect times to make auspicious endeavors.

The Vedas exist so that we can successfully obtain the results of our efforts and sacrifices, but doing so is very dependent on timing. Therefore one who understands the science of time, Jyotiṣa, also understands the science of successful efforts.  So they say that this science of Jyotiṣa is the foremost appendix to Vedic knowledge – much like the feathers of a peacock, or the treasures of a dragon.

Anyone who understands the Vedas and also understands the movements of the Sun and Moon will become prosperous in this world and afterwards will go to where the Sun and Moon move about in the heavens.

Measuring Time

The time it takes to pronounce a long vowel is an akṣara. Five of them is a kāṣṭhā. Four groups of thirty-one kāṣṭhā are a kalā. 10.05 kalā is a nāḍikā. Two nāḍikā are a muhūrta. Thirty muhūrta are a day, which is equivalent to 603 kalā.

A year is 366 days. It has two ayana, six ṛtu, and twelve months.

A yuga is five years.

Also: a nāḍikā is three sixteenths of an āḍhaka, during which time a clepsydra will drain 50 pala of water. Four āḍhaka are a droṇa. And a Ṛtu equals 4.5 constellations.

Comment:

Assuming for now that a day is “24 hours” the approximate modern values of these time units are as follows.

Droṇa:                 512 minutes (>8.5 hours)

Āḍhaka:             128 minutes

Muhurta:           48 minutes

Nadika:               24 minutes

Kalā:                     2.4(-) minutes

Kāṣṭhā group: 4.5(-) second

Kāṣṭhā:                1(+) second

Akṣara:                ¼ of a second

Now, for the longer periods of time, approximately:

Yuga:                    5 years

Year:                     366 days

Ayana:                 183 days

Ṛtu:                       61 days

Month:                30(+) days

The text gives three ways to check the measurements in the real world. We can do it starting from the Akṣara, assigning it the amount of time it takes to pronounce two short-vowel syllables or one long-vowel syllable in normal speech. Or we can start from the āḍhaka, assigning it the amount of time it takes to drain a clepsydra (basically a pot with a pinhole in it) holding a fixed amount of water. Or we start from the ṛtu, assigning it the amount of time it takes the Sun to move 60 degrees of arc in reference to a zodiac star.

Since we have mentioned the zodiac stars, lets now pull together the definitive verses concerning the zodiac constellations.

Zodiac Constellations

The zodiac constellations with their deities are:

1. Kṛttikā                           Agni (God of fire)
2. Rohiṇī                            Prajāpati (the Creator, Brahmā)
3. Mṛgaśīrṣā                     Soma (God of the immortal elixir)
4. Ārdrā                             Rudra (God of destruction)
5. Punarvasu                   Aditi (Goddess of space)
6. Puṣya                             Bṛhaspati (God of prayer)
7. Āśleṣā                            Naga (Dragons)
8. Maghā                           Pitṛ (Ancestral spirits)
9. Pūrva Phālgunī           Bhaga (God of love)
10. Uttara Phālgunī         Aryamā (God of vows)
11. Hasta                             Savitā (God of awakening)
12. Citrā                               Tvaṣṭā (God of design)
13. Svāti                               Vāyu (God of breath/air)
14. Viśākhā                         Indrāgñi (God of sacrificial fire)
15. Anurādhā                     Mitra (God of devotion/ friendship)
16. Jyeṣṭhā                         Indra (Chief of the gods)
17. Mūla                              Nirṛti (Goddess of destruction)
18. Pūrva Aṣāḍhā             Apa (Goddess of water)
19. Uttara Aṣāḍhā            Viśvadeva (All divinities)
20. Śravaṇa                         Viṣṇu (God of existence)
21. Dhaniṣṭhā                    Vasu (Gods of elements)
22. Śatabhiṣaj                    Varuṇa (God of night/ the underworld)
23. Pūrva Bhādrapadā    Ajaikapāt (Fire dragon)
24. Uttara Bhādrapadā Ahirbudhnya (Water dragon)
25. Revatī                            Pūṣan (God of protection)
26. Aśvinī                             Aśvini (Twin children of the Sun)
27. Bharaṇī                         Yama (God of death)

Those who understand the science of sacrifice recall that the names of these gods should be used in place of our own name, according to the constellation under which we are born, whenever we make serious sacrifices and efforts.

Ārdrā, Citrā, Viśākhā, Śravaṇa and Aśvinī have “fierce” qualities. Maghā, Svāti, Jyeṣṭhā, Mūla and Bharaṇī  have “harsh” qualities.

Importance of Cross Multiplication

The following very common elementary equation will often be used in our calculations: a/b = c/x. Which is solved as: x = bc/a.

To be continued… stay tuned…

- Vic DiCara

www.vicdicara.com

Reconciliation of the Tropical and Sidereal Zodiacs – Complete & Edited

Dear Readers,

I would like to thank you for the attention you pay to the articles I post. Recently I posted an important string of five articles on the topic of sidereal and tropical zodiacs. Now I would like to present you with a complete version, in one place, and with more editing and (I hope) clarity. The paper is available as a PDF so you can print it or put it on your e-Reader, or distribute it to your friends or colleagues. Please click the link to read and download the paper.

RECONCILIATION OF THE TROPICAL AND SIDEREAL ZODIACS

Please feel free and encouraged to redistribute this paper without need for any further permission.

Thank you,

Vic DiCara

Reconciliation of the Tropical and Sidereal Zodiacs. Part V: Conclusion.

This is a continuation from previous posts.

The True Sidereal Zodiac

One thing is very certain, there is a sidereal zodiac in Indian astrology, and I bet in all astrological systems from the ancient great cultures. Yet this sidereal zodiac is not twelve but twenty-eightfold!

The Sun and Moon, kings of the heavens, travel through space. During one complete journey of the Sun, the Moon makes twelve revolutions (each year there are twelve full-moons, “months”). Therefore, the Moon divides the Sun’s path into twelve sections. Conversely, while the Moon makes one complete journey through the heavens, the Sun makes twenty eight (in each moon cycle there are twenty eight sunrises, “days”). Therefore, the Sun divides the Moon’s path into twenty eight units.

Thus we have interwoven manners of dividing the zodiac. One has twelve and pertains to the path of the Sun. The other has twenty-eight and pertains to the path of the Moon. One of them is tropical by nature, the other sidereal!

I’ve already explored the logic, evidence and common sense decisively concluding that the Sun’s twelvefold zodiac is tropical. Now let’s explore the sense, logic and evidence in concluding that the Moon’s twenty-eightfold zodiac is sidereal.

Common Sense

The stars cannot be seen when the Sun is out, but we can almost always see the Moon against a backdrop of stars. Thus it appeals to common sense to the Moon’s movements be measured by its reference to stars.

Logic

While I could thoroughly explain the meanings of the twelve signs by reference to the tropical phenomena they demarcate, the themes of the twenty-eight stars of the Moon’s zodiac cannot be understood with any reference to tropical or even lunar observation. Some correlation to the phases of the Moon to the stages of development over a human lifetime can be utilized for interpretative purposes. But honestly, this only supports some of the meanings within the stars. The root cause of all meaning in the twenty-eight stars has no relationship to the earth (i.e. it is not tropical), and has everything to do with purely heavenly (sidereal) factors. The deities of the heavens reside in or empower each of the twenty-eight stars. The nature of the deity who empowers a star creates the full meaning of that star.

If this leaves some room for doubt, that doubt is removed by the evidence of authority.

Evidence from Authority

We examined Sūrya Siddhānta previously. The second chapter is dedicated to sidereal calculation of the twenty-eight star-sections in the lunar zodiac. The treatise says to convert planetary positions to tropical coordinates, but leaves the twenty-eight stars as they are: as stars, sidereal entities.

We also previously examined the astronomical section of Śrīmad Bhāgavatam. In the 23^rd chapter of the fifth division, two chapters after tropically defining the twelvefold zodiac, the Bhāgavata defines the twenty-eight stars of the lunar zodiac sidereally – in terms of their relationship to the north star, milky way and other purely stellar objects.

Conclusion

Doubtlessly the lunar zodiac is sidereal. That’s why we say it is composed of “stars” (literally, nakṣatra), twenty eight of them. It is now also beyond doubt that the solar zodiac is tropical. That’s why we say it is composed of “signs” (literally, rāśi), twelve of them.

Ancient India, and most likely all ancient great cultures, gave us knowledge that our dank and small modern intuition and cognition still hobbled weakly to grasp the basic definitions of. We waste our effort arguing if tropical or sidereal is the correct definition of the zodiac. If we listen to the ancients carefully, we hear them tell us is that both co-exist in a unified truth.

The two zodiacs, the twenty-eight stars of the sidereal and the twelve divisions of the tropical, are two aspects of one reality – interwoven like yin and yang. The language of astrology cannot fully and clearly sound out by transposing one zodiac definition on another, or by trying to divorce them from their eternal marriage and discount one or the other. We must read both zodiacs simultaneously to hear the full communication from mother nature.

How? When any astrological chart based on an ascendant is cast, we have two strands of interwoven information, calling to mind the two strands of DNA: the tropical positions of planets in the twelve signs and houses, and the twenty-eightfold sidereal positions among the glittering stars of the heavens.

Now it is upon us to explore and uncover the correct methods and sciences for such interpretations. It will not be difficult, because our basic grammar will be far more clearly defined. If your experience is anything like mine, you will find that all of the fundamental techniques preserved in the interpretive texts for regarding signs, houses, lords and combinations, and all the nakshatra based timing techniques will shine forth much more clearly. You will, I think, comprehend the messages they declare to your inner ear with far greater ease and clarity.

May we be so blessed.

Closing Remark

oṁ bhur bhuvaḥ svaḥ

There is bhu: the earth, with its sky of twelve houses.

There is svar: heaven, with its twenty-eight principle sidereal stars.

There is bhuvah: The uniting space linking them, with its twelve tropical divisions – The heavenly Sun, planets and stars shining upon and wandering across the Earth’s equator.

tat savitur vareṇyam, bharga devasya dhīmahī

The brilliant knowledge which will shine forth in the intuitive contemplation of an astrologer is the effulgence of this paradigm uniting heaven and earth: the twenty eight stars hosting the planets, tied to the earth via the twelve divisions.

Hare Krishna

May we blessed with divine knowledge of such incomprehensible subjects. May such knowledge lead us only to divine love, the soul of true peace and joy.

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CONCLUDED

Vic DiCara

www.vicdicara.com

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