Vedanga Jyotisha (वेदाङ्गज्योतिषम्)
Vedanga Jyotisha (Samskrit : वेदाङ्गज्योतिषम्) is described as one of the six branches of knowledge called Shad Vedangas. Vedangas are the ancillary subjects of the Vedas and help in understanding the processes associated with the life in Vedic times. The purpose of the Jyotisha was to fix suitable times for performing different Yajnas and this involves knowledge of astronomy. Vedanga Jyotisha by Lagadha is a crucial text in giving us the picture of development of Astronomy in ancient Bharatavarsha. The text can be considered as the records of the essential astronomical knowledge needed for the day-to-day life of the people of those times. Although the text is said to belong to later date (1400 B.C.), the subject is said to be the culmination of the knowledge developed through years of observations, accumulated over thousands of years prior to 1400 B.C.
In modern common parlance, the word Jyotisha is used to mean predictive astrology (Phalita Jyotisha), however in Vedangas the word Jyotisha is associated with the science of Astronomy which includes mathematics (Ganita) also. This article primarily refers to Jyotisha as a part of Vedangas, hence the term Vedanga Jyotisha is used (which is also the name of the valuable text given by Maharshi Lagadha). Mathematics or Ganita Shastra (गणितशास्त्रम्) was regarded as a part of Vedanga Jyotisha as a discipline.
परिचयः || Introduction
Astronomy is the main subject of the text Vedanga Jyotisha. Even during Rigvedic times astral sciences were highly developed where people acquired knowledge of the movement of sun and moon for knowing the seasons which was important in performing yajnas such as Darsapurnamasa and Chaturmasya. Ancient people had knowledge of the calculations for eclipses, full moon (Amavasya) and new moon (Purnima) days, of nakshatras (stellar constellations) as it is required for determining the commencement of specific Yajnas.
Jyotisha in Vedas
Like many branches of knowledge, the beginnings of astronomy in Bharatavarsha have been traced back to the Vedas. Vedanga Jyotisha text is found in two recensions - Rigveda Jyotisha (called Archa-jyotisha) and Yajurveda Jyotisha (called Yajusha-jyotisha). Though the contents of both the recensions are the same they differ in the number of verses contained in them. Rigveda version contains only 36 verses whereas the Yajurveda version contains 44 verses, the difference attributed to the addition of explanatory verses given by the adhvaryu who used them.
Prof K. S. Shukla notes a third recension called the Atharva-jyotisha ascribed to Rshis Svayambhu and Bhrgu which belongs to a later date. This recension, consisting of 162 verses deals with both astronomy and astrology. It mentions the names of the seven grahas and the weekdays. And in addition to tithi, nakshatra and yoga which were already known, it gives the names of the seven karanas of the Hindu calendar.
यथा शिखा मयूराणां नागानां मणयो यथा । तद्वद्वेदाङ्गशास्त्राणां ज्योतिषं (गणितं) मूर्धनि स्थितम् ॥ १९ ॥ (Veda. Jyot. 4)
yathā śikhā mayūrāṇāṁ nāgānāṁ maṇayo yathā । tadvadvedāṅgaśāsrāṇāṁ jyotiṣaṁ (gaṇitaṁ) mūrdhani sthitam ॥ 19 ॥
Like the crests on the heads of peacocks, like the gems on the hoods of the snakes (cobras), astronomy (mathematics) is at the highest position of vedanga shastras (the six ancillary branches of knowledge).
Contents of Vedanga Jyotisha
Several important aspects related to Kala (Time) and astronomy are discussed in this text.
- The Solstices
- Increase and decrease of the durations of days and nights in the ayanas
- The solstitial tithis
- The seasons
- Omission of titihis
- Table of parvas
- Yogas (which later developed as one of the five limbs of the Panchanga)
- Finding parva nakshatras and parva tithis
- The vishuvats (equinoxes)
- The solar and other types of years
- The revolutions of the Sun and moon (as seen from the earth)
- The times of the Sun's and Moon's transit through a nakshatra
- The adhikamasa (intercalary month)
- The measures of the longest day and shortest day
The practical way of measuring the time is mentioned as the time taken by a specified quantity of water to flow through the orifice of a specified water-clock as one nadika i.e. 1/60 part of a day.
A yuga of 5 solar years is mentioned which consists of 67 lunar sidereal cycles, 1830 days, 1835 sidereal days, 62 sinodic months, 1860 tithis, 135 solar nakshatras, 1809 lunar nakshatras and 1768 risings of the Moon. The text also mentions that there are 10 ayanas and 10 vishuvas and 30 rtus in a yuga. The names of the five years of a yuga being
- संवत्सरः॥ Samvatsara
- परिवत्सरः ॥ Parivatsara
- इडावत्सरः ॥ Idaavatsara
- अनुवत्सरः ॥ Anuvatsara
- इद्वत्सरः ॥ Idvatsara
The present day yuga system consisting of the chaturyugas and mahayugas (as seen in puranic references) is discussed under the heading Kala.
The Vedic astronomers also noted that the shortest day was at the winter solistice when the seasonal year Shishira began with Uttarayana and rose to a maximum at the summer solistice.
However, the Vedanga Jyotisha astronomy suffered from two main defects. Since there are actually 1826.2819 days in a yuga of five solar (sidereal) years and not 1830 as stated in the Vedanga Jyotisha, therefore if one yuga was taken to commence at a winter solstice the next one commenced about four days later than the next winter solstice and not at the next winter solstice. Similarly, since there are actually 1830.8961 days in a period of 62 lunar months and not 1830 as stated in the Vedanga Jyotisha, therefore there was a deficit of about one tithi in the yuga of five solar years. These discrepancies must have been rectified but we do not know when and how this was done.
A glossary is given in the last section to explain the astronomical terms used in this article.
According to Prof. Balachandra Rao, the astronomical calculations described in Vedanga Jyotisha were in practical use for a long time. Around the beginning of the Christian era, a new class of Indian Astronomical literature emerged namely the Siddhantas. The word 'siddhanta' has the connotation of an established theory. These siddhanta texts contain much more material and topics than the Vedanga Jyotisha.
While nakshatra system was existing, the twelve signs of the zodiac Mesha, Vrshabha etc were introduced. Computations for arriving at the precise values for different aspects such as the length of the solar year, motion of the grahas, solar and lunar eclipses, determination of mean and true positions of grahas formed the core content of these siddhantas. Mathematics was greatly developed to aid these calculations.
According to tradition there were principally 18 Siddhantas
- Lomasa (Romasa)
Among them only five siddhantas were extant during the time of Varahamihira namely, Saura (or Surya) Paitamaha (or Brahma), Vaishishta, Romaka and Paulisa. These five were ably collected by Varahamihira and preserved in his Panchasiddhantika text.
Glossary of Astronomical Terms
This section is a collection of few astronomical terms, fewer of which are used in this article.
|Adhikamasa : Additional (intercalary) lunar month in a lunar year||Lagna : Orient ecliptic point; point of intersection of the ecliptic with the eastern horizon|
|Aksha (akshamsa) : Terrestrial latitude||Lanka : Place on the earth's equator through which the prime meridian|
|Amavasya : New moon day||Madhya ratra : Midnight|
|Ardharatra : Midnight||Madhya rekha : Central meridian of the earth passing through Lanka, Ujjaiyini, Kurukshetra, and Mount Meru|
|Ayanamsa : Amount of precession of equinoxes (in degrees)||Madhyahna : Mid day|
|Ardharatrika : Calculations from the midnight||Manda : Slow|
|Ayananta : Solistice||Masa : Conjunctions of grahas; yuti, yoga|
|Bhachakra : Zodiac (consisting of 27 nakshatras or twelve rashis)||Meru : Earth's pole|
|Bhagana : Revolutions of a celestial body in a long period of time (like Mahayuga)||Muhurta : A unit of time; 30 muhurtas = 1 day; 1 muhurta = 2 ghatikas = 48 minutes|
|Bhaga : One degree of arc; amsa||Nakshatra dina : Sidereal day|
|Bhugola : Terrestrial globe||Nimesha : A unit of time; according to the siddhanta siromani, 1 day = 9,72,000 nimeshas|
|Chakra : Circle, cycle, 3600||Paada : A quarter; quadrant|
|Chakramsa : Degrees in a circle, 3600||Paksha : Forthnight; half of a lunar month|
|Chandrakala : 1/16th of the moon's disc||Pala : A unit of time; Vinadi|
|Chaturyuga : Great age of 43,20,000 years; Mahayuga||Praahna : Forenoon; purvahna|
|Chaadya : Eclipsed body ; Graahya||Praana : A uit of time; 4 seconds of sidereal time; asu|
|Chakralipta : Minutes of arc in a circle; 3600 x 601 = 21,6001||Pratipat : The first tithi (lunar day) of either bright or dark half of a lunar month|
|Chandra : The moon||Purnima : Fullmoon; opposition of the sun and the moon|
|Chandramasa : The lunar month||Rahu : Ascending node of the moon; paata of the moon; Tamas|
|Chaadaka : Eclipser ; Grahaka||Rashi : Zodiacal constellation; each 300 extent|
|Chaaya : Shadow||Rtu : Season; a year consists of six rtus|
|Dakshinayana : Southern course of Sun||Sauradina : Solar day|
|Darsa : Conjunction of the sun and the moon||Sauravarsha : Solar year|
|Dhruva : Pole Star ; fixed||Saavana dina : Civil day; kudina; bhudivasa|
|Dinagana : Civil days; Ahargana||Sparshakala : Time of the first contact of an eclipse|
|Dinardha : Half day||Sraavishta : Dhanishta constellation|
|Gati : Motion||Suklapaksha : Bright half of a lunar month|
|Ghana : Cube||Tantra : Indian astronomical texts which adopt the beginning of Kaliyuga as the epoch|
|Ghatika : A unit of time; 1/60th part of a day (24 minutes); naadi, nadika, ghati||Tithi : Lunar day; 1/30th of a lunar month|
|Grahana : Eclipse||Uttarayana : Northern course of the Sun along the ecliptic|
|Hora : One hour; 1/24th of a day||Vikalaa : One second of arc; 1/3600th of a degree; Vilipta, Vilipti|
|Ketu : Descending node of the moon; 1800 - Rahu||Vinaadi : 1/60th of a nadi; 24 seconds; Pala, Vighati|
|Krishnapaksha : Second half of a lunar month||Vipala : 1/60th of a pala|
|Kshana : A unit of time; 2 ghatis (according to Surya Siddhanta)||Vishuva (Vishuvat) : Equinox; Krantipaata|
|Kona : Angle||Vyasa : Diameter of a circle; Vishkambha|
|Lipta : Minute of arc; Kalaa||Vyasardha : Radius of a circle|
- Balachandra Rao, S. (2014) Indian Astronomy. Concepts and Procedures. Benguluru : M.P. Birla Institute of Management
- Kolachana, Aditya & Mahesh, Kaluva & Ramasubramanian, K.. (2019). Main characteristics and achievements of ancient Indian astronomy in historical perspective. 10.1007/978-981-13-7326-8_24.
- K. S. Shukla, Astronomy in ancient and medieval India, Indian Journal of History of Science, Vol.4, Nos. 1-2 (1969), pp.99-106.
- B.B. Datta and A. N. Singh (1962) History of Hindu Mathematics, A Source Book, Parts 1 and 2. Bombay: Asia Publishing House. (Page 7)
- Kuppanna Sastry, T. S. and Sarma, K. V. (1985) Vedanga Jyotisa of Lagadha in its Rk and Yajus Recensions with the translation and notes of Prof. T. S. Kuppanna Sastry. New Delhi : Indian National Science Academy
- Balachandra Rao, S. (2017 Third Edition) Indian Mathematics and Astronomy. Benguluru : Bhavan's Gandhi Center of Science & Human Values