ancient indian astronomy - sandhi.hss.iitb.ac.insandhi.hss.iitb.ac.in/sandhi/mathematics and...

Ancient Indian Astronomy Review and Scope

Aniket SuleAstrophysikalisches Institut Potsdam

14th November 2005

Outline

● Brief Chronology● Astronomy in the Indus Valley Civilization?● Vedic Astronomy● Division of the ecliptic and calender● Contribution of medieval astronomers● Scope of research and current projects

Paleothic and Charcolithic era (pre 5000 BC)● India was inhabited since at least 50,000 BC● Cave paintings from the era have been found in

Bhimbetka, central India.● Mehrgarh, now in western Pakistan, was a

farming community first established in 6500 BC. It is considered as possible precursor of Vedic civilization.

● Some pit paintings of moon and stars probably older than 6000 BC are found in Kashmir.

● Some stone henge like megaliths are found in Krishna – Kaveri basin in the peninsular India.

Neolithic era (5000 – 2000 BC)

● First Indus Valley sites appear in around 5000 BC.● First big towns at around 3500 BC.● The Indus valley civilization peaked around 2500 2000 BC.● The civilization flourished on the banks of two mighty rivers

Indus (Sindhu) and Saraswati and surrounding areas.● Total area covered was close to a million sq. km making it

biggest civilization of the era.● The legendary river Saraswati flowing close to present Ind

Pak border dried out in around 1900 BC.● Indus valley civilization disappeared by 1700 BC.

Evolution of Vedic culture (1800 – 500 BC) ● Not much evidence is available● Vedas were written certainly before decline of

Indus valley civilization But most of the post – vedic literatures like puranas etc. and epics like Ramayana and Mahabharata were probably composed in this period.

● The period stands out with it's appalling lack of methodical records.

● By 500 BC India was huge amalgamation of small kingdoms with not much trade outside subcontinent.

Later period

● History in later period is neatly recorded in various sources. Record keepers of Alexander, court historians of Indian kings, Arab traders etc.

● In medieval periods, Indian scholars gave precise dates of their works. Also crosschecked by Chinese scholars who traveled to India to study Buddhism.

Astronomy in the Indus valley?● Indus script has not been deciphered yet. There are

more than 50 unsuccessful attempts.● We have to rely on our imagination to interpret

various pictures seen on Indus seals.● There is no evidence to suggest that IndoAryans

were advanced enough prior to 2000 BC to do complicated astronomical observations but vedic texts contain such references. This is probably due to exchange of knowledge between Indus valley and IndoAryans.

● Essentially developed for navigational purposes and probably time keeping.

Vedic Astronomy

● The oldest Indian astronomical references are found in Rigveda compiled under the name “vedanga jyotishya” (division of vedas dealing with science of lights i.e. stars)

● The compiler gives his name as “Lagadha”.● Many similarities with Babylonian and Persian

texts. The discussion of equinoxes and motion of sun etc. has strong resemblance with Avesta, yet vedas are more detailed. Thus they must have been composed post Avesta (3000 BC).

● The text is dated by the clear reference that winter solstice point was close to α Delphini. This was a situation in around 1400 BC. Some argue the particular verse was a later addition.

● The vedanga jyotishya also deals with ecliptic, calender and motion of Sun through year.

● Clearly mentions true sidereal year is longer than 365 days but shorter than 366 days.

● Post vedic literature mostly concentrates on commenting vedic verses with only few additional information. Often these additions are not consistent with time line.

Mahabharat

● Greatest Indian Epic● It contains loads of astronomical references.● Few examples: There was a lunar eclipse followed

by total solar eclipse in just 13 days in the war zone, Planetary positions at the time of major events, culmination of all the planets with sun and moon 36 years after the great war etc.

● Probable dating : 1000 – 1450 BC. Work still going on.

Ancient Indian Calendar

● There are five important terms in Indian calendar– Tithi – day number = (angle between sun and moon at

sunrise) / 12– Vaara – Weekday– Nakshatra – lunar asterism– Yoga & Karana – mainly astrological purpose.

● 12 Zodiac signs are defined same as western signs called Raashi.

● Start of the month is when moon enters new moon phase before sunrise

● The name of month is derived from nakshatra of moon on the full moon day / nakshatra opposite to the sun just before new moon.

● Vedas mention each tithi is roughly equivalent to 610 / 603 lunar days (sidereal).

● When moon is in same tithi for two consecutive sunrises, the tithi is repeated.

● When a tithi is skipped between two sunrises, it is omitted.

● Similar principles are used for addition / deletion of months.

● Advantage of lunisolar calendar is with the constant addition / deletion, the start of year never deviates a lot from vernal equinox (assuming no precession).

● Disadvantage is a layman cannot easily comprehend the calendar.

Nakshatras

● The 0 point of nakshatra belt is usually taken as point directly opposite Spica (α Vir) on the ecliptic. It is by definition first point of Aries.

● There are other less popular definitions (e.g. 0 point at ζ Pis, moving first point of Aries etc.)

● There are 27 nakshatras, not currently equispaced, not all close to ecliptic.

● Ashvinī and Arietisβ γ● Bharanī 35, 39, and 41 Arietis● Krittikā Pleiades (M45)● Rohinī head of Taurus (V shape)● Mrighashīrsha , Orionisλ φ● Ārdrā γ Gem● Punarvasu Castor and Pollux● Pushya Cancri / M44δ● Āshleshā head of Hydra● Maghā Regulus● Pūrva Phalgunī and Leonisδ θ● Uttara Phalgunī Denebola● Hasta Corvus● Chitrā Spica

● Svātī Arcturus● Vishākhā , , and Libraeα β γ ι● Anūrādha , and Scorpionisβ δ π● Jyeshtha , , and Scorpionisα σ τ● Mūla tail of Scorpio● Pūrva Ashādhā and Sagittariiδ ε● Uttara Ashādhā and Sagittariiζ σ● Shravana , and Aquilaeα β γ● Shravishthā to Delphinisα δ● Shatabhishaj Aquariiγ● Pūrva Bhādrapada and Pegasiα β● Uttara Bhādrapada Pegasi and Andγ α● Revatī Pisciumζ

Kundali representation

● Nothing but positions of the Sun, the Moon, 5 planets and two nodes of lunar orbit in 12 Raashis.

● All dates can thus be uniquely identified + 500 years.● There is misconception that it can be used for

astrology only. But we can use it for dating events.

● We are at advantage with Indian people's mad craze for astrology, that enables us to get records which can pinpoint day accurately through kundalis.

● Kundalis are traditionally plotted at the time of birth, war, major construction etc. ==> Lots of astronomical data.

Architecture and Astronomy

Architecture and Astronomy

● Sun temples and their orientation

● There are many carvings at various temples attributed to astronomy but the convention of the sculptures is poorly understood.

● Burials in most ancient period were direction sensitive

● Stonehenge like Megaliths are found in peninsular India. 43 such sites are identified. None are as massive as the Stonehenge but unmistakably similar.

Siddhantic Astronomy (400 AD – 1700 AD)

● Roughly translated as “theoretical / textual astronomy”.

● It marks a whole new era in Indian Astronomy as many astronomy specific textbooks were written. Mathematics became just a tool for astronomy and it's development was driven by needs of astronomy.

● this new trend was probably started after interacting with the Greeks and realization of importance of mathematical astronomy.

Vriddha Garga (?)

● Oldest available astronomical text is by Aryabhatta (b 476 AD) called Aryabhatiya.

● He and various subsequent authors refer to the observations made by a certain “Vriddha (old) Garga” which were compiled into a text. No manuscript of this text is found.

● Some of the observations attributed to Vriddha Garga indicate his period as roughly 500 BC but there are also other spurious much older observations.

Aryabhatiya● Key findings were as follows

– Earth is spherical– Earth rotates (inferred from motion of stars)– Definitions of Solar year, Lunar month, sidereal day

etc.– Synodic periods of planets.– Heliocentric distances of planets.– Daily positions of the planets.– Invention of number “0”.– π = (104*8+62000)/20000 =3.1416– Sine table

•“The importance of the creation of the zero mark can never be exaggerated. No single mathematical creation has been more portent for the sheer force of intelligence and power”

–G B Halsted (1912)

••The Importance of this invention is more readily appreciated when one considers that it was beyond the two greatest men of antiquity: Archimedes and Apolonius”

–Laplace (1749 – 1827)

Other Contributions

● Varahamihira (b. 485 AD, Panchasiddhantika)– Measurement of diameter of the Sun and the Moon– Prediction of Eclipses

● Brahmagupta (b 598 AD, Khandakhadyaka & Brahmasphuta Siddhanta)– Mainly development of mathematics for astronomy– Second order interpolation, second order indeterminate

eqations– Taught astronomy to Arabs (ref: Al Beruni)

● Surya Siddhanta (probably 600 AD)– Compilation of all the available material– Original draft probably older than Aryabhatta– Author unknown.

● There was steady progress through many centuries from hereon.

● Theory of Limits (Bhaskara II, 12th century), Infinite series expansion of p, sin, tan (Madhavacharya, 14th century), Taylor expansions and basic calculus (Tantrasangraha, 15th century)

● Pinacle is reached in 16th century with Mahadeva discussing lunicentric planetary positions including the inclination of lunar orbit w.r.t. ecliptic.

Scope of the research

● Chronology of India– What happened to Indus valley culture?– When vedas were composed? Are they oldest human

texts?– Were the epics Ramayana and Mahabharata real?

● Identification of the Nakshatras– Nakshatras are ill defined– We have their identification by traditional knowledge

but no explicit proof.– The traditional identification has problems as some

nakshatras are far for ecliptic, some are very faint, some are both.

● Indus valley Astronomy?– They are bound to be good astronomers as they needed

stars for navigation. But no conclusive information is found.

● Prajapati?– There is a mythical constellation of “king of

nakshatras” elaborately explained. – Covers most of the area of Virgo, Libra, Bootis,

Scorpio– All stars are properly identified except a bright star at

the position of heart which is missing.

Historical “New Stars”?

Flamsteed ? not seen ?Cas ACas1667

Johannes Kepler's SNKepler SNR3Oph1604

Tycho Brahe's SNTycho SNR4 Cas 1572

Aql1230

0Sco1203

Chinese and Japanese3C 581Cas1181

Chinese, North American (?); also Arab, Japan M1 6Tau1054

Arabic; also Chinese, Japanese, EuropeanSNR 10069+1Lup1006

0Cas

902

10Sco/Oph827

Gem437

ChineseSNR 3933 Sco 393/396

Chinese 386

Chinese 369

ChineseSNR 1852Cen185 AD

Chinese; "first such record“ 352 BC

Dubiously listed in some source102241 BC

The Saptarshi Calendar(Sule, Vahia, Joglekar & Bhujle, Indian J. for History of Science, Sub.)

● Saptarshi (seven sages) represents Ursa Major.● It is said in various puranas that first two stars of

saptarshi visit every nakshatra every 100 years.● The effect is caused by precession.● The observation is significant as the motion is very

small, almost unnoticable.● The fact that it is in Puranas, means it is older

than 400 BC.

mçHlç<ççÇ&Cççb lçá ³ççÌ HçÓJççÌ& o=Mîçílçí nîçáçÆolççÌ çÆoçÆJç ~mçHlç<ççÇ&Cççb lçá ³ççÌ HçÓJççÌ& o=Mîçílçí nîçáçÆolççÌ çÆoçÆJç ~lç³ççímlçá cçOîçí vç#ç$çb o=Mîçlçí ³çlmçcçb çÆvççÆMç ~~105~~lç³ççímlçá cçOîçí vç#ç$çb o=Mîçlçí ³çlmçcçb çÆvççÆMç ~~105~~lçívç mçHlç<ç&³ççí ³çákçwlçççÆmlç<þvl³çyoMçlçb vçæ=Cççcçd ~lçívç mçHlç<ç&³ççí ³çákçwlçççÆmlç<þvl³çyoMçlçb vçæ=Cççcçd ~lçí lçá HççjçÇçÆ#çlçí kçÀçuçí cçIççmJççmççÆvJopççíllçcç: ~~106~~lçí lçá HççjçÇçÆ#çlçí kçÀçuçí cçIççmJççmççÆvJopççíllçcç: ~~106~~lçoç ÒçJç=Êç½ç kçÀçÆuçÜç&oMççyoMçlççlcçkçÀ: ~~107~~lçoç ÒçJç=Êç½ç kçÀçÆuçÜç&oMççyoMçlççlcçkçÀ: ~~107~~

Take two stars of Take two stars of SaptarshiSaptarshi which are seen first after the rise. which are seen first after the rise. The The nakshatranakshatra which is seen in the middle of it at night, ||105|| which is seen in the middle of it at night, ||105|| Is said to be residence of Is said to be residence of Saptarshi Saptarshi for 100 years of man's life.for 100 years of man's life.Oh great Oh great brahminbrahmin, they were in , they were in MaghaMagha at the time of at the time of Parikshit Parikshit ||106|| ||106|| The 1200 year long The 1200 year long Kali YugaKali Yuga started from that time. ||107|| started from that time. ||107||

Magha Nakshatra is same as the sickle in the constellation Leo.Magha Nakshatra is same as the sickle in the constellation Leo.

Sri Sri Vishnu Purana, Geeta Press, Gorakhpur (1922)The Vishnu Purana, H. H. Wilson (1961)

Why a primitive observer would bother?

● Bright constellations like saptarshi were used for timekeeping in the ancient era.

● From 8000 – 3000 BC, the first two stars of saptarshi were in culmination with Pollux and Castor (another bright pair).

● Thus one can calibrate time even when view of UMa is blocked, using the other pair.

● After 3000 BC, the precession ensured that the two pairs were no longer in culmination.

● So natural course would be to measure speed of the drift.

● As angles are much complex thing to define (think about 3000 BC), primitive observers expressed motion as period of stay in each nakshatra.

● The nakshatra next to Punarvasu is Pushya which is pretty small. Saptarshi indeed were in culmination with Pushya for roughly 100 years.

● This may be the origin of the legend of 100 year Saptarshi transition.

Year = 7000 BCYear = 7000 BC

Hasta11

U. Falguni10

P. Falguni9

Magha8

Hydra7

Ashlesha6

Pushya5

Punarvasu4

UMa3

Thuban2

Polaris1

Hasta11

U. Falguni10

P. Falguni9

Magha8

Hydra7

Ashlesha6

Pushya5

Punarvasu4

UMa3

Thuban2

Polaris1


Hasta11

U. Falguni10

P. Falguni9

Magha8

Hydra7

Ashlesha6

Pushya5

Punarvasu4

UMa3

Thuban2

Polaris1

Year = 0 ADYear = 0 AD

Hasta11

U. Falguni10

P. Falguni9

Magha8

Hydra7

Ashlesha6

Pushya5

Punarvasu4

UMa3

Thuban2

Polaris1


● by simulation of the sky we found that this 100 year transition happened in 2200 – 2100 BC.

● Reference to rising of U Ma points to the possibility that observations were done from a place below tropic of cancer.

● Both of these conclusion together point that if this was real observation, it must have been done by the Indus valley civilization.

● It is also relevant to them as the culmination had timekeeping significance.

● On the other hand, pastoral community like Aryans, won't have much use for timekeeping during nights.

The concept of Yuga

● Yuga is considered one of the longest units of time amongst Indians.

● Different possible definitions exist. Some associate it with synchronization of the calendar with the tropical year. It leads to either 5 year or 19 year yuga period. This definition is found in Vedas.

● Some say yuga starts when all 7 astronomical bodies (sun, moon, 5 planets) are in culmination. This is also supported by Siddhantic astronomers.

● The culmination is ill defined and can have various possible periods from 60 years to 432,000 years depending on tightness of culmination.

● Traditionalists like to believe in 432,000 year period first mentioned by Varahamihira.

● Further this period is supposed to represent shortest of the 4 yugas. And the other yugas are supposed to be in the ratio 1:2:3:4. This means length of yuga cycle is 4,320,000 years, which is absurd.

● We propose 1200 year period which gives sufficiently tight culmination.

● The Kali yuga is supposed to have started 36 years after the Mahabharata war which happened roughly in 1250 BC.

● The period of yuga cycle then turns out to be 12,000 years.

● We show that the yuga cycle represents important stages of evolution of IndoAryans.

YugaYuga Transitions Transitions• Satya YugaSatya Yuga begins 12,000 BC begins 12,000 BC

13,000 BC = End of the last ice age. 13,000 BC = End of the last ice age. • Treta YugaTreta Yuga begins 7,200 BC begins 7,200 BC

First permanent settlements appear in Mesopotamia and community farming starts at about First permanent settlements appear in Mesopotamia and community farming starts at about 7,000 BC.7,000 BC.

Early Mehrgarh settlement 6500 BC – 6000 BC.Early Mehrgarh settlement 6500 BC – 6000 BC.• Dwapar YugaDwapar Yuga begins 3,600 BC begins 3,600 BC

Sahara desert starts forming, Sumerian kings take over Mesopotamia, Indo – Iranians enter Sahara desert starts forming, Sumerian kings take over Mesopotamia, Indo – Iranians enter Afghanistan in roughly 3500 BC.Afghanistan in roughly 3500 BC.

• Kali YugaKali Yuga begins 1,200 BC begins 1,200 BC MahabharatMahabharat war, major loss of life occurs between 1250 – 1050 BC. war, major loss of life occurs between 1250 – 1050 BC.

• Kali Yuga intensifies (chaotic situation, peril, grief) 200 BCKali Yuga intensifies (chaotic situation, peril, grief) 200 BC Death of Death of AshokaAshoka 236 BC, Overall chaos 236 BC, Overall chaos

• Kali YugaKali Yuga ends 50 BC ends 50 BC 56 BC = Start of the 56 BC = Start of the Vikram SanvatVikram Sanvat, Reign of , Reign of Shakari VikramadityaShakari Vikramaditya (?), End of chaos which (?), End of chaos which

was had been abundant since was had been abundant since Ashoka’s Ashoka’s death.death.

Summary

● Not much is known about chronology of ancient India. Astronomy can help in big way.

● Medieval Indian astronomers had achieved unmatched accuracy in predicting planet positions but apparently not much interested in other transient phenomena in the sky (e.g. comets, supernovae etc.)

● There are lots of open problem in the field which require professional handling.

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