Tuesday, November 19, 2024

Siddhant Period

5 Siddhantas

Astronomical knowledge was very well developed during the Vedic and Vedang periods and was further developed and updated in subsequent periods.

सिद्धान्तis one of the sub-branches of  Ganit Skandha. 
For various branches of Astronomy see 

 Knowledge of the position of the Sun, Moon, and other planets was required for calendrical, religious, and daily rituals. 

The history of astronomical works can be assessed from the oldest known group of  5 ancient सिद्धान्त known as पंचसिद्धांतिका  written by Varahmihira (500 CE)

These 5  सिद्धान्त are 

पितमहः,वसिष्ठ,रोमक,पौलिश ,सौर

Varahmihira in his पंचसिद्धांतिका  says that the सिद्धान्त written by Paulisa is fairly accurate, but not as accurate as Saura/Surya Siddhant. The accuracy of others is doubtful.

These Siddhantas outline methods for calculating the mean positions of the Sun and Moon, as well as the orbital periods of other planets. They provide a comprehensive explanation and calculations regarding mean motion मध्यमाधिकारः /adhikara on mean places and the average number of revolutions of the planets. Additionally, the texts discuss the length of the year, the concept of yugas, and methods for intercalation and synchronization.

For example 
One of the couplets describes a method of calculating the length of the day. It says 

द्विघ्नं शशिरस्(61)भक्तं द्वादश हिं दिवसमनम्

" Multiplying  (the number of days elapsed after WS or the days to go before the end of Ayana, beginning with SS ) by 2 and dividing by 61. Add 12 (Muhuratas) to the quotient, and the result will be the length of the day"

Surya Siddhanta of the पंचसिद्धांतिका group had assumed the commencement of Yuga at midnight and that it postulates the Yuga system. ( It is assumed that all planets including the Sun and The Moon were together on this day)@@@. Dixit has confirmed this aspect, by comparing the data of Surya Siddhanta to the actual longitudes, so calculated as per Surya Siddhanta as of 1887.
 
Al Biruni commented that पौलिश siddhant was compiled by Paulus—ul—Ynani, or Paulus the Greek. Professor Webber refuted his claim, stating that Paulus's work was related to astrology and not astronomy.

Al Biruni states that Surya Siddhant was compiled by Lata. Prof Weber connects it with Ptolmey's works. However, Surya Siddhanta of the पंचसिद्धांतिका group  was not complied by Lata . Dixit proves both the contentions incorrect. 

पितमहः and वसिष्ठ सिद्धान्त appear to be old, as they are similar in concept to Vedang Jyotish. The other siddhantas appear to be around the pre-Saka period, i.e.,200-50 BCE. Dixit proves Dr Thibaut's argument that their antiquity around 400 CE was wrong.

पितमहः,वसिष्ठ,पौलिश ,सौर,रोमक are as per their chronological order of antiquity.
The Five Modern सिद्धान्त

The elements described by पंचसिद्धांतिका group differ from those in the more modern Sidhantas. They primarily differ in the length of the year and the planets' mean motion, position, number of revolutions etc. The data is updated and more accurate, and hence the epitaph modern.
 
The five modern सिद्धान्त  are वसिष्ठ,रोमक,सौर सोम, ब्रह्म सिद्धान्त . It is not clear if two सोम siddhantas existed.

All five siddhantas declare themselves to be divine and are actually so regarded.Other siddhantas ,such as  पंचसिद्धांतिका ,विष्णुधर्मोत्तरः,ब्रह्मसिद्धान्तः are also regarded divine.

Surya Siddhanta is more popular than other siddhantas. It is believed that it was compiled during the second or third century CE.

Surya Siddhant was first translated into English by Dr Ebenzer Burgess in 1860. Prof Whitney further added extensive notes to it. Prof Whitney believed that Hindus borrowed it from the Greeks. However, Burgess clarifies at the end of his book that it was The Greeks who borrowed it from the Hindus

The contents of all the Siddhantas provide explicit astronomical details, making it challenging to summarize the information succinctly. Anyone interested in a detailed study is encouraged to explore the references listed below.

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@@@With the advancement of technology, changing times, and evolving concepts, a new thought process has emerged. The latest astronomy software can now simulate past events and accurately show the positions of the nakshatras and planets.

These new revelations may directly conflict with the findings of ancient scholars, as well as with established beliefs and rituals. More research and studies are needed to uncover the truth.

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References
1. SB Dixit " Bhartiya Jyoti's Shastra" Part 2
2. William Brennand " Hindu Astronomy"
3. Coolebroke Essays.
4. Dr Thibaut's Essays on Surya Siddhanta 
5. Dr Ebenzer Burgees's Translation of Surya Siddhant
6. Dr Nilesh Oak talks


Wednesday, October 9, 2024

The Tropical Year Calendar


The Tropical Year Calendar

Julian/Gregorian 

 The tropical year is the time, taken by the Sun, to pass from the vernal equinox to the vernal equinox. It equals 365 days, 5 hours, 48 minutes, and 46 seconds, or 365.2422 days. The tropical year is used, to keep track of seasons, planting, and harvesting. There is a need to create a calendar, with a whole number of days per year to accurately follow the tropical year without losing synchronization with the seasons over a period of time.

We begin with a calendar of 365 days per year. Our calendar year is shorter than the tropical year by 0.2422 days. So to correct (approximately), we add 1 day every four years (leap year). Thus, three calendar years are 365 days long; the fourth calendar year is 366 days long. The average length of the calendar year in days now becomes (3 x 365 + 366)/4 = 365.25 days.

This calendar system was actually instituted for use in the Roman Empire by Julius Caesar around 46 BC. But since the Julian calendar was 0.0078 days (11 minutes and 14 seconds) longer than the tropical year, errors in timekeeping gradually accumulated. Between 46 BC and 1582 AD, this accumulated error amounted to a total of: 0.0078 x (1582 + 46) = 12.7 days. In 1582, Pope Gregory XIII reformed the calendar by specifying that all years divisible by 4 are to be leap years except for century years, which must be divisible by 400 to be leap years. Now, in 1200 years:

  1. A total of 300 years (including all century years {since any century year = N x 100, where N = an integer}) are divisible by 4 and are therefore candidate leap years.
  2. A total of 900 years are not divisible by 4 and are therefore regular years.
  3. Twelve-century years are possible leap years.
  4. But only 3 century years (out of the 12) are divisible by 400 (i.e., {400, 800, 1200}, {1600, 2000, 2400}, etc.), so only 3 century years are actually leap years.

Since 12 - 3 = 9, Gregory's rule eliminates 9 leap years out of 1,200. Thus: 300 - 9 = 291 years are actual leap years, and 900 + 9 = 909 years are regular years. The average length of the year becomes (291 x 366 + 909 x 365)/1,200 = 365.2425 days, with an error of 365.2425 - 365.2422 = 0.0003 days per year, or one day every 3,333.3 years.

The Gregorian calendar came into use in Roman Catholic countries in October 1582 when the seasons were brought back into step by eliminating 10 days from the calendar then in use. Thursday, October 4, was followed by Friday, October 15 (which caused some apprehension and anxiety amongst the people, especially those with birthdays on the eliminated dates!).

 Britain and its colonies did not introduce the Gregorian calendar until September 1752 by which time an additional one-day correction was required (actually, {1752 - 1582} x 0.0078 = 1.33 day). Some British documents from the period before the British reform actually contain two dates, an old and a new.

Hijri 

The Hijri calendars are purely Lunar and hence the year is also lunar and not tropical, measuring 354 days and 355 days during the leap year. An extra day is added to the last month 11 times in a block of 30 years. Usually 2nd,5th, 7th, 10th, 13th,15th,18th,21st, 24th, 29th year in the cycle of 30 years. In the course of 33 years, the beginning of the Hijri year runs through the whole course of seasons. The months and seasons are not in sync. 

This practice of adjustment varies in different countries and sometimes at different periods in the same country.

This Hijri calendar is not tropical.

Akbar tried to adjust the Hijri calendar with the seasons and termed it "The  Fasli year" (To synchronise the month with harvest/फसल time)used only for commercial purposes. 

 This facilitated in collection of harvest tax. (Harvest time and Hijri month varied every year ). The commencement of this year was in July. It was more or less a mix of the " Vilayati Year (used in some parts of Bengal), Amli Era of Odisha and Bengali San" with Hijri month names.

 In most parts of India, it was a Solar year, however different customs of different parts of India caused a divergence of reckoning. It was later discontinued.

   The original Hijri calendar was followed for all other aspects.

Hindu

In contrast just see our Hindu calendars, where the months are Lunar and the year is Solar. In fact, the Hindu calendar is lunisolar. The 5-yearयुग and intercalation system of adjustment is followed to keep in step with seasons and the actual position along the ecliptic.

One month, known as अधिक मास is added every 30 months, therefore in a युग of 5 years 59 days get added, thus the synchronisation with the seasons is nearly real-time. (My blogs on the Vedic period give out details)

 This was available in the Vedic period, earlier than 1500 BCE, even before the Europeans could think of it!

Thursday, September 5, 2024

Vedang Period -3

 Astronomical Mentions in Other अङ्गः of Vedas

कल्पः(Manual of Rituals)

कल्पः has various सूत्र (सूत्र is a large collection of such aphorisms in the form of a manual, it is a distinct type of literary composition, based on short aphoristic statements, generally using various technical terms.सूत्र forms a school of Vedic study).

 Types of कल्पःसूत्र are

1. श्रौतासूत्र has यज्ञ Rituals

2. गृह्यासूत्र- has Domestic Ceremonies

3. धर्म सूत्र-has -Religious and Social Laws

4. शुल्बसूत्र-has Geometry and Mensuration 

सूत्र with some important astronomical mentions are

अश्वलायन श्रौतासूत्र

Names of months based on nakshatra and seasons are found in this text.  The reference to seasons indicates that spring was considered the year's first season.

Tithi is not mentioned specifically ,however use of words चतुर्दशी, अष्टमी indicate Tithis. Like in this verse 

मार्गशीर्ष्यं प्रत्यवरोहणं चतुर्दस्यम् गृह्यासूत्र 2-3-1, mentions Month and Tithi

ध्रुवमरुन्धतिं सप्तर्षिनिति दृष्ट्वा वचम्विसर्जेता |   गृह्यासूत्र 1-7-22

This gives out the names of the Pole star (Dhruva), The Great Bear (Saptrishi) and Arundhati (Alcor)

Definite instructions are given for doing certain rites on auspicious Nakshatras,for example,fields should be ploughed on उत्तरा भद्रपद, फल्गुनि, रोहिणी नक्षत्र.

Without any weather forecast, but with a sound knowledge of the onset of seasons, it is a communication to the general public to commence sowing and other agriculture activities.

नक्षत्र names are mentioned to carry out यज्ञ Rituals, thread ceremonies, etc. However, the auspicity/ gender of the नक्षत्र is not mentioned.

Taittiriya Sruti gives out the list of नक्षत्र with their controlling Deities' gender and number, which is still followed as of date for all rituals.

परास्कारःगृह्यासूत्र

This सूत्र is of a later date than अश्वलायन सूत्र and appears to be an updated/revised सूत्र. This सूत्र gives out the list of नक्षत्र auspicious for marriage. These are उत्तरा हस्ता चित्रा उत्तराषाढ श्रावण धनिष्ठा उत्तराभद्रपद रेवती अश्विनी.

However, these do not match with the current prevalent list of marriageable नक्षत्र. The नक्षत्र for marriage and that for agriculture are not the same. The reason seems to be obvious.

This सूत्र describes the results of a childbirth on मूल/मूळ नक्षत्र and inauspicious nature of अश्लेषः नक्षत्र. Is the inauspicious nature of the नक्षत्र is declared because of the timing of the childbirth conflicting with other works? A more rationale thought is required on this.

Interestingly there is a difference of views among the various सूत्र on the effects of नक्षत्र for different purposes.

The names of 12 Rashis, days of the week,वार yog and Karana are not found in this sutra

Other सूत्र

The other सूत्र contains almost all the aspects mentioned above. All the सूत्र define the spring season as composed as चैत्र ,वैशाख OR मधु ,माधव months.

बौधायन शुल्बसूत्र

This सूत्र appears to be of a later epoch and has the mention of 12 Rashi as seen from the verse 

मासद्रये यवाप्येकराशिं संक्रमेतादित्यस्तत्राद्यो मलिम्लुच शुदधोन्यः |     मैत्रेय सूत्र

"When the Sun is found to cross only one Rashi in two months the former is called मलिम्लुच ( intercalary month) and the latter a proper month" 

This सूत्र also gives out the working of the dimensions of the यज्ञ कुण्ड and यज्ञभूमिकाः, depending upon the type of ritual being performed,with respect to Nakshatra

दीर्घचतुरस्रस्याक्ष्णया रज्जुः पार्श्वमानी तिर्यग् मानी यत् पृथग् भूते कुरूतस्तदुभयं करोति

"The diagonal of a oblong(rectangle) produces the combined area of the two separate sides."

This verse also mentions the method to find the square root of 2.

समस्य द्विकरणी । प्रमाणम्तृतीयेन वर्धयेत्

तच चतुर्थेनात्मचतुस्त्रिंशोनेन सविशेषः -   बौधायन शुल्बसूत्र 2:12

"The diagonal of a square. The measure will be increased by a third and by a fourth decreased by the 34th. That is it's diagonal approximately"


Were these verses a precursor to the Pythagoras theorem? 

This सूत्र gives out many such formulas for the construction of temples / ritual places. (Squaring a circle and Circling a square) Some of them are concerned with the position of the nakshatras.

Dr Subhask Kak explains in detail, the astronomical code used for designing the यज्ञ कुण्ड and यज्ञभूमिकाः, in his book mentioned below.

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References
1. SB Dixit " Bhartiya Jyotish Shastra" Part 1
2. William Brennand " Hindu Astronomy"
3. Ancient Indian Astronomy by RN Iyengar.
4. Ancient Astronomy" and"Vedang Jyotish of Lagadha" by Prof TS Kuppanna Shastry
5. Indian Astronomy by BV Subbarayappa and KV Sarma
6. Astronomy in India: A Historical Perspective by Thannu Padmanabhan
7. https://vedicheritage.gov.in
8. The Astronomical Code of Rgved by Subhash Kak
9. Ancient Hindu Science  by Alok Kumar
10. Vedic Irina and the Rann of Kutch by Iyengar, Radhakrishna, Mishra


Tuesday, July 16, 2024

Vedang Period 2

Atharva Vedang Jyotish 

Continuing with the Vedang period of the history of astronomy, Atharva Vedang Jyotish (AVJ) relatively, is of a later period than RVJ and YVJ. It is a text, as told to Kashyap by Pitamah. The time units followed then were as 

12 निमिष= 1 लव

30लव = 1 कला

30 कला = 1 त्रुति

30 त्रुति= 1 मुहूर्त

30 मुहूर्त= 1 अहोरात्र / whole day

The document also gives the list of 15 मुहूर्त, whose measure is compared with the length of a gnomon/stick, which is 12 anguls long. These names must be of the मुहूर्त by day, as my blog Vedang Period 1 refers (since the shadow is measured). The list shows a maximum shadow of 96 anguls cast by"Rudra"  मुहूर्त and 0 anguls by 'Abhijit'  मुहूर्त. It is not exactly 0, but the shadow does not alter in length or direction, hence 0. 

Shadow is not  0 at noon, but it must be shorter than 3 anguls. The lengths of shadows are not the same throughout the year. 

With this method, one can find the approximate, location where VJ was compiled A different method to find the location of the composition of VJ is calculated by SB Dixit.

Karanas and Auspicious Times 

This section gives out the instructions and duties to be observed for a particular मुहूर्त. Like friendly acts to be done on a 'मित्र मुहूर्त' and horror acts on 'रुद्र मुहूर्त'. The chapter also mentions, which acts to be done on a particular Tithi to get auspicious/ unauspicious results. The list of Thiti's includes 'Nanda and 'Bhadra' as in this verse

चतुभिं : कारयेत्कमं सिदधिह तोधिं चक्षणः !

 तिथिनक्षत्रकरणमृहतंतरीति नित्यशः 

This verse gives out only 4 अङ्गः (parts), they areतिथि ,नक्षत्र ,करण ,मुहूर्त not 5, which we are familiar with  a पञ्चाङ्ग . (वार्/day is not mentioned)

Following verses 90 and 91 give out the auspicious/inauspicious nature of the planets depending upon the strength of the Moon, ie, with the number of kalas or the phases of the Moon. 

तिथिरेकगुणा प्रोक्ता नक्षत्रं च चतुर्मुणं ।॥ वारचाष्टगुणः प्रोक्तः करणं षोडश्लान्वितं ।। € ० ॥ दात्रिंशद्ुणो योगस्तारा षष्ठिसमभ्विता ॥ चंद्रः श्तगणः प्रोक्तस्तस्माच्चंद्रबला बलं ।। ९१ 

 समीक्ष्य चंद्रस्य बलाबलानि ग्रहाः प्रयच्छंति श॒भाश्भानि

The following verse mentions the planets as day lords of the week. Though no specific order of the days have been mentioned . The day/ वार् seems to have been introduced for the first time .

आदिस्यः सोमो भौमश्च तथो बुधवहस्पती ।। भार्गवः शनेश्धरस्चंव एते सप्त दिनाधिपाः ॥६३॥।।

Other verses give out more names of planets applicable to the names of the days. Like सूर्य लोहितांग, सोमसुत, देवगुरु, गुरु ,भृगु, शुक्र ,सूर्यसुत.

This AVJ also gives out for the first time, the prediction part of astrology. Verses from 103 to 109 give out the names of 27 नक्षत्र to be divided into 9 groups with 3 नक्षत्र in each group. These give out the nakshatra at birth, for action and for foundation. 

Verses 25-27 give out the controlling deities of the 27 nakshatras without naming the nakshatras. The list of deities starts with the deity of Kritika Nakshatra. Confirming the Krittikadi system in vogue at that time.
 The 28th Verse says

नक्षत्रदेवता एता एताभियक्ञकमंणि । यजमानस्य शास्त नामि नकषत्रजं स्मृतं ।।

" The holy perceptors/शास्त्रजन: ordain that those performing the rituals should adopt a name based on the nakshatra at birth"

Other astronomical works describe a method by which persons are given names according to the Nakshatra quarter/चरण at birth. This system is still followed, even, today.

ग्रहोल्कालनिनिं्तिः कपेदहिंश्च पीडयत ।। यच्च दुयं भवति तत्‌ तत्परवक्ष्याम्य

his verse ordains "To do or not to do" certain acts on these nakshatras and describes the fears and horrors which befall when certain nakshatras are accompanied by planets/ comets/meteors etc.

The AVJ text describes the nakshatra-based system of astrology, similar to today's practice based on 12 Rashis/Zodiac signs. 

The text suggests its antiquity due to the absence of 12 zodiac signs, challenging the common belief that the system of prediction was borrowed.

Roger Billiard published his book " L'Astronomie indienne investigation des textes Sanskrits et des donnes numeriques" in 1971 and shows how accurate the tables and celestial observations made by Hindu priests during the Vedic and Vedang periods. His estimate of VJ is around the 10th century BCE. Indian scholars have dated the antiquity of the Krittikadi system in the Rgveda to around 2500 BCE using astronomical references.

Ptolemy's Almagest was published in 150 CE 




............to continue with the composition period of RVJ, YVJ and astronomical mentions on other अङ्गः of Vedas.


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References
1. SB Dixit " Bhartiya Jyotish Shastra" Part 1 pages 70-83
2. William Brennand " Hindu Astronomy"
3. Ancient Indian Astronomy by RN Iyengar.
4. Ancient Astronomy" and"Vedang Jyotish of Lagadha" by Prof TS Kuppanna Shastry
5. Indian Astronomy by BV Subbarayappa and KV Sarma
6. Astronomy in India: A Historical Perspective by Thannu Padmanabhan
7. History of Astronomy in India" by SN Sen, KS Shukla



Friday, June 28, 2024

Vedang Period 1

 Vedang Jyotish 

As we know there are six parts/अङ्गः of the Vedas. These are 

शिक्षा(Phonetics)
कल्पः(Manual of Rituals) 
व्याक्रण(Grammar),written by Panini
निरुक्त(Etymology)
ज्योतिषः(Astronomy and Astrology), by Lagdha
छन्दसः(Prosody/Rhythm, Intonation),written by Pingla

Vedang Jyotish is written in an aphoristic form or sutra style - a style noted for the depth of its contents.

The word Astronomy originates from Middle English and Old French astronomie, which in turn was derived from Latin astronomia, through Greek, from astronomos, meaning  ‘star-arranging’.

One of the oldest Hindu texts on astronomy is Jyotish. Often it is confused with astrology, which deals with the prediction part. It was the earliest document on astrometry. but not exactly a Star Catalog. The astrology part was added later as जातक स्कंध.

The वेदांग ज्योतिष was more of a handbook on astronomical information which was used for 
1. Day-to-day life of people
2. Knowledge of seasons for agriculture
3. Religious purposes, fix suitable times for rituals and यज्ञः, times of New and Full Moon for दर्शपूर्णमास and चातुर्मस.
4.  Rules and calculations for year beginnings, Solstices, equinoxes, Solar and Lunar eclipses and adjustment of lunar months to be in sync with Solar cycles.
5. In short it was a precursor to पञ्चाङ्ग and the modern calendar.
 
 The text is found in two recensions - Rigved Jyotish (RJ) and Yajurved JyotisH(YJ). Though the contents of both recensions are the same, they differ in the number of verses. While the Rigvedic version contains only 36 verses, the Yajurvedic version comprises 44 verses. This difference in the number of verses is perhaps due to the addition of explanatory verses by the priests. Atharva Jyotish (AJ) is composed in a later time frame, than RJ and YJ. It is more of an improvement on RJ and YJ.

Rigved and Yajurved Jyotish

This text mentions Panch samvatsar yuga पंच संवत्सर युग (5 year period). Varahamira's Brahat Samhita gives out the names of these 5 years as 
संवत्सर,परिवत्सर, इदावत्सर ,अनुवत्सर, इद्वत्सर.
The astronomical references in these texts describe the sun's movement, the seasons' commencement, and epochs of Solstices and Equinoxes.
Verses 8-16 give out the position of the Sun(with respect to the Sun's and the Moon's nakshatras), at the beginning of each संवत्सर युग.

For example 

स्वराकमेते सोमाकौ यदा साकं सवासवौ ॥ स्यात्तदादियुगं माघस्तपः शुक लोयनंहय दक्‌
भते श्रविष्ठादौ सुर्यचि्रमसावुदक्‌ । सार्पं द्तिणाकंस्तु मःचश्रावणयोः सद 

" When the Sun and the Moon come to Dhanishtha,( β Delphini) together, then the yuga, Magha(month)and Tapas (season), light half of the month and winter Solstice all come together"
" The Sun and the Moon turn towards North in the beginning of Dhanishtha and toward South in the middle of Ashlesha. The Sun always does this in the months of Magha and Shravan"

धमंवृद्धिरपाप्रस्यः षपा-ह्वास उदग्गतौ ॥ दक्षिणेतौ विषयंस्तौ षण्मुहुत्यंयनेन त्‌ ।! ७ ॥।

" During the Sun's northward journey, the day increases, by 1 prastha measure of water, and the night becomes short. During the southward journey, the conditions reverse. The increase of time during one Ayana is equal to 6 Muhuratas" 

(An increase of 1 prastha is equivalent to 4/61 Nadika.)

The texts also mention the rules to calculate the next Parva (event), equinox, eclipse and other calendric data, and in doing so we get a glimpse of the units of time used during that period.

Many time units were defined by the movements of astronomical objects and were further broken down for day-to-day requirements. Different names have been used to denote a time unit. 

We often hear time units such as घटिका,पल,कला,द्रोण्, नाडी /नाडिका,युग.
 What could be the relation between them and how the name of the time unit evolved?

 RJ and YJ mention the time units but do not mention the inter-relationship with them. 
 The unit of time known as पल appears to have been derived from the time which takes for one पल (spoon) full of water to trickle out from a vessel/घटिका. So a larger unit is Ghatika and the smaller unit is Pal. 
RJ and YJ mention the time units for calculation purposes, however, all inter-relationships with various time units are not found.

As verse # 16 of RJ says

कला दश च विंश स्थाद्‌ दविमहतंस्तु नाडिक ॥ हित्रि्ञस्तत्कलानः तु षटरातीश्यधिकं भवेत्‌ । १६॥
यजःपाठ- | कला दक्न सविक्षाः...... ।॥ दयत्रिरत तत...... ॥

" 10(1/20) kalas make 1 nadika, 2 nadikas are equal to 1 Muhurta and 30 Muhurtas or 603 Kalas make one day"

 Bhaskaracharya and others have mentioned that 1 Drona is equivalent to 4 adhakas. The  Verse 17 from VJ should be read as 

नाडके ह मूहूतंस्तु पंचाशत्पलमाहकं ।॥ चतुभिं राक द्रोणः करप वधते त्रिभिः ॥ १७॥।।

" 1 Muhurta=2 nadikas; 50 Palas =1 Adhka;4Adhkas=1 Drona- this being larger than 1 nadika by 3 kudavas"

Verse 24 from YJ clarifies as 

पलानि पंचाहादथां घुतानि तदाढक द्रोणमतः प्रमेयं ।।
 तरिर्भिर्हीनं कडवेस्तु कायं तप्नाडिकायास्तु भवेश्प्रमाणं ।। २४ ॥

"The vessel known as Adhaka holds 50 palas of water. Measure 1 drona of water with. Throw away water equal to 3 kudavas in volume. Then the time needed  for the remaining water (to trickle out) is known as 1 Nadika "

No explanation or reference is found in VJ regarding the units "Prastha and Kuduva" Similarly VJ does not give any relation with Prastha and Nadika 

Astronomers and mathematicians of the later era deduced the inter-relationship with various time units. Bhaskaracharya, explains Lilavati's verse in establishing the relationships with time units.

पलानि पंचाहादथां घु तानि तदाढक द्रोणमतः प्रमेयं ।। 
तरिर्भिर्हीनं कडवेस्तु कायं तप्नाडिकायास्तु भवेश्प्रमाणं ।। २४ ॥    लीलावती .

" 4 Kudavas=1 Prastha
  4 Prastha=1 Adhaka
  4 Adhakas =1 Drona "
As per VJ, 1 Adhaka=50 Palas. 

For those keen to see the derivation, click here for proof to show 1 Prastha=4/61 Nadika and 1 Nadika=109 5/8 pal. 

Though VJ does not give any relation stating that 1 Ghatika =60 Pal. An identical division of time and space was adopted at a later period. 
See the forthcoming blog... 

This measure of, 1 Nadika=109 5/8 pal, has been adopted but appears inconvenient. Later  Commentators and scholars stated that this relation was convenient for calculations! These calculations were required to calculate the exact moments to find out the position of the Moon, the number of days elapsed or to go for the next ayana (Uttarayana/Dakshinayana) and thus the Solar year and the related seasons for calendric purposes for everyday use.

Verses 22 onwards give out the rules, calculations and procedure to calculate the intercalary month in 1 yuga(5 years)and which month to insert when in the solar year to keep the seasons in sync with actuals.

Verse 23 gives out the theory of intercalary month.

तदधं दिनभागानां सदा प्वेणि पवंणि । ऋतुक्ेषं तु तद्वि्ात्‌ संस्थाय सहषवं णम्‌ । २३ ॥
 यजु-पाठ- -यदधंदिनभागानां... । ऋतु... संख्याय... ॥

" Balance of Ritu is obtained by the sum of balances in all parva's; at the end of each parva a balance of half tithi remains"

Why a group of 5 years was considered? As mentioned earlier the months followed were Lunar and the year was Solar. Therefore an adjustment of Lunar months was required to be in sync with the actual Solar year and corresponding seasons. Calculations become easier when calculations are done for a larger period than a smaller period. Hence the scholars deduced that the relation 1 Nadika=109 5/8 pal was convenient!

Verse 31 says 

" A Yuga consists of 61 civil months,62 Lunar Months and 67 Sidereal months" 1 Year =12 Solar months, so 1 Yuga =60 Solar months and 1830 Civil days(तिथि)


A ritual called "सहस्त्र चन्द्र दर्शन " is performed even today to celebrate the longevity of a person at 80 years of age. Why 80? because 1000 lunar months = 80.6 Solar years !

Rule of Three

We all are familiar with the basic arithmetic calculation of 4th unknown term when we have three known terms. (for both direct and inverse proportions). Never wondered that its origin is in the Vedas!

RVJ 24 and YVJ 42, give out the instruction concisely looking like an aphorism.

इति उपयासमुद्देसः भूयो प्य अह्नः प्राकल्पयेत्

ज्ञेयराशी घटाभ्यस्तं विभजित ज्ञानराशिना    

" The known result is to be multiplied by the quantity for which  the result is wanted and divided by the quantity for which the known result is given"




..........to be continued with the composition period of RVJ, YVJ, Atharva VJ and parameters for calendar 

____________________________

References
1. SB Dixit " Bhartiya Jyotish Shastra" Part 1 pages 70-83
2. William Brennand " Hindu Astronomy"
3. Ancient Indian Astronomy by RN Iyengar.
4. Ancient Astronomy" and"Vedang Jyotish of Lagadha" by Prof TS Kuppanna Shastry
5. Indian Astronomy by BV Subbarayappa and KV Sarma
6. Astronomy in India: A Historical Perspective by Thannu Padmanabhan




Sunday, May 12, 2024

Vedic Period 4


                        Astronomy During the Vedic Period-4

                                          Nakshatra नक्षत्र

Nakshatras, as generally understood by all, is a group of stars in the sky used for astrological purposes. Why were they formed or created?  and What is their purpose? and is what we should know. 
The Vedic people first looked at the Sun and Moon to calculate time. The Moon was the basis of the heavenly clock. Therefore it was necessary to know the location/position of the Sun,  Moon and equinocal points in the Sky. These people regularly performed rituals and yagasयज्ञ and to know the appropriate time to perform these rituals, they had to know the exact position/ Location of the celestial object.
Today it is easy to know the position with the help of a celestial coordinate system. In the absence of such a system, a fixed/stationary reference frame was required to ascertain the location/position of a celestial object. 
Nakshatras provided this reference frame, in the sky, to the observers. All our Vedic works, including epics of Mahabharat, and the timing of events are given with reference to Nakshatras. 

The names of months in our Hindu calendar are based on these Nakshatras, this is because the nakshatra in which the full Moon was observed that month was named on that Nakshatra. 

Rashi/ Zodiac signs were adopted into Hindu astronomy around 200 BCE-300CE

The nakshatras are images of earthly objects. Some nakshatras have derived their names from their resemblance to particular figures. There are a few nakshatras who have derived their names differently.

A verse from Taittriya Brahman, 2.7.18.3

प्रवाद्ग्वा अग्रे क्षत्राण्यातेपुः ।॥ तेषामिंद्र: ॥ क्षत्रण्यादत्त ॥ नवा इमानि क्षत्राण्यभ्‌रवान्नितिं ।॥ तन्नक्षत्राणां नक्तत्रत्वं ।।

 derives  the word नक्षत्र as , those which are not,क्षत्र (moveable) are  नक्षत्र. This is as defined in Nirukta, explanation. There is another verse which describes नक्षत्र as the abode of Gods.

Nakshatras, also as stars in general are mentioned in Atharva Samhita 

अप त्ये तावयो यथा नुक्षत्ना यत्यक्तुभिः ॥ सुराय विदवचक्षसे ॥

~The stars and the night escape like thieves on the approach of  the Sun"

 Rk Samhita and Atharva Samhita, mention the word नक्षत्र as stars in general. Post-Vedic works also describe it as stars in general, including those in the Moon's path.

अथो नक्षत्राणामेषामुपस्थे सोम आहितः ॥।

~"The Moon is placed among the stars"~

Another metaphoric, description of nakshatra is found in Taittriya Brahman 1.5.2 

 सलिलं वा इवमंतरासीत्‌ । यदतरन्‌ ॥ तत्तारकाणां तारकत्वं । यो वा इहं यजते । अमुं स लोकं नक्षत्र ॥ तन्क्षत्राणां नक्षत्रत्वं ।॥। देवगृहा वं नक्षत्राणि  य एवं वेद ॥ गृह्येवभवति ।\ यानि वा इमानि पृथिष्याहिचत्र्णण ।॥ तानि नक्षत्राणि ।॥ तस्माददलीलनामं शिचित्रे \॥ नावस्येन्नयजेत ॥ यथा पापाहे कुरुते ॥ तादृगेव तत्‌ ॥ |
                                                                    
which says 
"There was water in the centre. The tarakas are said to possess the prosperity of tarakatva(protectiveness) because they floated and saved themselves. He who performs oblation here goes (naksate/नक्षते) to that world. Hence the nakshatra significantly so-called, are the houses of Gods. He who knows this becomes the owner of a house. the nakshatras are the images of earthly objects. Hence a rite and an oblation should not be performed on an ugly nakshatra. It gives the same result as that performed on an inauspicious day"

This derivation traces the word to the root ' naksa'/नक्ष (to go). Virtuous people will go to heaven and become nakshatras. It puts out the idea that the nakshatras are the houses of Gods. (God here means planets, refer to my blog " Vedic Period -3")

Taittriya Samhita 7.5.25 mentions nakshatras as stars in general and in the Moon's path.

यो वा अश्वस्य मेध्यस्य शिरो वेद शीषण्वान्देध्यो भवत्युषा वा अश्वस्य
 मेध्यस्य क्ञिरः सूयंश्चक्षवातः प्राणव्चं रमाः भत्रं दिशः पादा अवां तरदिज्ञाः 
पशंवोऽहोरात्रे निमेषोधंमासाः पर्वाणि मासाः संधानान्युत्वोऽगानि
संवत्सर आत्मा रहमयः केशा न॑शत्राणि रूपं तारका अस्थानि नभो मासानि 

To summarise ~ "Dawn is the head of the horse. Heaven is his eye. The year is his soul. His form are the nakshatras and the stars are his bones”.

There are numerous definitions and derivations of Nakshatra evolved in the later periods. Something like 

 "नचरति, नक्षरति, अथ नक्षत्रति"

~They neither move nor deviate; they do not get destroyed and their greatness never diminishes over time; hence they’re known as nakshatras.~

Names of all nakshatras and their ruling deities are mentioned in various texts. Some describe them, some describe the origin of their manes etc.
Taittriya Samhita 4.4.10 mentions the names of all 27 nakshatras and their deities.

 कृत्तिका नक्षत्रमग्नि्वताग्नर्च स्थ प्रजापतेर्धातुः सोमस्यचं त्वा रुचे त्वा द्युते स्वा भसेत्व्ा ज्योतिषे त्वा रोहिणी नक्षत्रं प्रजार्पतिदेवता मुगशीषं नक्षत्रेसोमो देवता्रानतरडो  देवता । पुनवेसुमक्षत्रम दितिर्देवता तिर्य नक्षत्र बहस्पतिदेवताधेष नकषत्रेसर्पा देवता मघाग्नक्षत्रं पतसे देवता फल्गनीनक्षत्रसयंमा देवता फलग॒नी भैश्रं भगो देवता हस्तो(शक्षतरेसविता देवताचित्रा  नक्षत्रमिंदरो देवता स्वाती चकषत्रं वारं वता विशाखं क्षत्रमिदराण्नी देवतान्‌ राधां नक्षत्र मितो ॥ एकक 1 { | व देवता रोहिणी ्षत्रसिं द्रो देवता {विचृत्ती न्त्रं पितरो देवताषाढानषत्रमापो देवताषा्ा 1 दड्नकषर्ज विश्वेदेवा देवता श्रोणर नक्षत्रं विष्णुर्देवता शविष्ठा नक्षत्रं वसवो देवता शतभिषङनक्षनमिंदरो देवता श्रोष्ठपर्वा नक्षत्रमजएकपाहेवता प्रोष्ठपद न॑क्षत्र्माहर्बुध्नियो देवता रेवती त्त पुषा  | दे वताअश्विनी नश्षत्रसरिवनौ देवतापभरणीनं क्षत्रं यमो देवता पूर्णापश्चाद्यत्ते देवा अदधुः ॥

Atharva Samhita 19.7.1 mentions 

वचिन्राणि साकं दिवि रोचनानि सरीसृपाणि भुवने जवानि ¦ 
अष्टाविज्ञं सुमतिमिच्छमानो अहानि गीर्भिः सपर्यामि नाकम्‌ 

सुहवं मे कत्तिका रोहिणी चास्तु भद्र मृग्शिरः शमाद्रा।
पुनवेसु सूनृता चह पुष्यो भनुराश्लेषः अयनं मघा मे 

The first verse says" I being desirous of welfare, worship the heaven with the speeches, because 28 clusters of stars, like wonderful illuminating lights arranged in the form of nimble serpents, shine in the sky"

This shows that nakshatras are 28 in number. Taittriya Surti has mentioned Abhijit Nakshatra several times, however, the later texts mention only 27 Nakshatras. Why the 28th Nakshatra was dropped? No explanation is found. It appears that it was for ease of calculation?

Most of the verses, during the Vedic period, which describe the nakshatras start from the Nakshatra कृत्तिका(Pleiades). That means the list of nakshatras commenced with कृत्तिका as the first nakshatra during that period.

The Shatapatha Brahmana mentions that the कृत्तिका (Pleiades) "do not swerve from the east". This would have been the case with precision at 2950 BCE and was true also about 2000 BCE and was within 8-13 degrees around 8th to 6th BCE.

"Why should the list start with a specific nakshatra?" As previously mentioned in the Vedic Period blogs 1-3, the start of the year was based on either the Vernal Equinox (VE) or Winter Solstice (WS). To determine the exact position of VE or WS, the reference frame of Nakshatras was utilized since it's simple to identify the position of the equinoctial/solstitial colure using the reference frame of Nakshatras.

The Kritikadi system was in force during the Vedic period, meaning the Vernal equinox was in kritika nakshatra and the Winter solstice was in Sharavan/Dhanishta nakshatra. Hence the list started with  कृत्तिका Nakshatra.

 With the help of appropriate software, we can interpolate this conjunction backwards to know the exact date of this period. The diagram below explains this.


As of date, the list of nakshatras starts with अश्विनी and is known as अश्विनादि system. However,अश्विनी Nakshatra is not at the Vernal equinox.
Due to the precession of the equinoxes, we see the conjunction of रेवती/उत्तराभाद्रपद nakshatra with the vernal equinox as of date.
 It takes approximately 900 years for the nakshatra to shift from the equinoctal colure.

                            Origin of the names of a few nakshatras.

The names,पुनर्वसु (Castor and Pollux),चित्रा(Spica), मघा (Regulus)and रेवती(Zeta Piscium) did not indicate nakshatras but were already in use in a different sense. 

पुनर्वसु(a twin star)

अग्नीषोमा पुनवंसु अस्मे धारयतं रथिं ॥     ऋ. सं. १०,१६. १.

 ~is quoted as two Gods, who give shelter to those who offer prayers.~

 A dual form word for a dual star (quite remarkable as to how ancient observers identified correctly), they are seen in Gemini (मिथुन) zodiac sign. Did the sign Gemini get the twin status from this?

Chitra Magha(Regulus), the mighty, is used as chitramagha to denote " one having wonderful wealth. In almost all cultures/folklore this star is denoted as a king and mighty.

रेवती(Zeta Picium) means one possessing wealth and being prosperous.

These names were applied to Nakshatras, due to their munificence, and loveliness.  The people would have experienced, imagined or noticed these characteristics.

Aiteriya Brahaman mentions some legends regarding रोहिणी (Aldebaran),मृग(Lambda Orionis), and मृग व्याध (Sirus). The legends of Rohini, Mrigashirsha, Prajapati and antelope hunting all describe the cluster of stars around the Orion मृगशीर्षconstellation. All cultures have similar stories and legends regarding the Orion.

Taittriya brahman 1.5.2.2 gives out the vision of nakshatriya prajapati as, 

यो वं नक्षत्रियं प्रजापत्तिं वेद ॥ उभयोरनं लोकयोविदु : ॥ हस्त एवास्यं हस्तः ॥
 चित्रा क्षिरः ॥ निष्ट्चा ह्‌ दयं ॥ ऊरू विज्ञाखे ।। प्रतिष्ठान्‌ राधाः ॥ एष वै नक्षत्रियः प्रजापति : ॥
                                                                                                     
~"He who knows nakshatra Prajapati knows him as related to both worlds. Hasta is his hand, Chitra is his head, nistya(Swati) his heart, two Vishakha stars as his thighs, and Anuradha is the place to stand upon. This is nakshatriya Prajapati"~

This description fits the present-day observation, except for the star Swati, which is out of place. This is probably because the Proper motion of this star is faster and hence may have moved out.

Proper motion is the astrometric measure of the observed changes in the apparent places of stars or other celestial objects in the sky, as seen from the centre of mass of the Solar System, compared to the abstract background of the more distant stars.

Origin of the names of अनुराधा (beta Scorpionis) and ज्येष्ठा(Antares, alpha Scorpionis) have been described in Taittriys Brahaman 1.5.2. 

Sayana, in his commentary on this verse, says ' It was a statement by the Gods with reference with the battle with the Demons... "We killed the eldest of them on ज्येष्ठा nakshatra." (Antares is the biggest star in the group, hence the name ज्येष्ठा)

The grammatical number in which the nakshatra names are used helps indicate the number of stars in each group. Mrigashirsha मृगशीर्षः(stars around Orion)and हस्त (group of stars appears as a palm of a hand, hence the name ) are a group of stars, but they are used in singular numbers. 

The singular number nakshatras are 

रोहिणी(Aldebaran),आर्द्रा (Betelgeuse), पुष्य (γ, δ and θ Cancri), चित्रा(Spica),स्वाति(Arcturus),ज्येष्ठा(Antares) ,मूल( ε, ζ, η, θ, ι, κ, λ, μ and ν Scorpionis),श्रावण(α,β and γ Aquilae), शततरका(γAquarii), रेवती(Zeta Picium). Indicating that each of them is a single star.

Nakshatras with dual stars are

पुनर्वसु(Castor and Pollux),पूर्वाफाल्गुनी(Delta and Theta Leonis),उत्तरा फाल्गुनी(Denebola),विशाखा(α, β, γ and ι Librae),अश्विनी (β and γ Arietis)

The balance of nakshatras are plural and have more than two stars.

                                            Saptarishi

The Vedas also refer to certain stars, other than those stars in 27 nakshatras,

अमी य ऋक्षा निहितास उच्चा नक्त" दद्र कुह चिहिवेय्‌: ॥
                                                                                 ऋ.सं. १ २४. १०
~" These Bears which appear to be placed at high elevation at night go somewhere in the day"~ 
( These constellations are popularly known as The Great Bear)

Shatpath Brahaman 2.1.2.4 observes 

सप्तर्षनु ह स्म वे पुरर्षा इत्याचक्षते ॥
~" The Saptarishis were called bears in ancient times"~

And Tandiya Brahman1.5.5 mentions as 

ऊध्वं सप्त ऋषीनुपतिष्ठस्व ॥।

~" Worship the seven sages above"~

Almost all the stars in the Nakshatras are, either the biggest, brighter, twin stars or as a group visible and easily identifiable.
A remarkable feat of Vedic people. It has been proved by various scholars that this Nakshatra system is a Hindu creation. Contrary to the popular belief that it was borrowed from the Chinese system. In fact, it is the other way around. 





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References
1. SB Dixit " Bhartiya Jyoti's Shastra" Part 1
2. William Brennand " Hindu Astronomy"
3. Ancient Indian Astronomy by RN Iyengar.
4. Ancient Astronomy by Prof TS Kuppanna Shastry
5. Research on Nakshatras by Dr Arjun Pai
6. Mythology of Nakshatras by Arvind Bhagwath

Siddhant Period

5 Siddhantas Astronomical knowledge was very well developed during the Vedic and Vedang periods and was further developed and updated in sub...