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