Jump to content

Indian astronomy

From Wikipedia, the free encyclopedia

This is an old revision of this page, as edited by Oota~enwiki (talk | contribs) at 00:01, 24 May 2008 ('''COPERNICUS was POLISH'''). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

COPERNICUS was POLISH

Indian astronomy refers to the study of astronomy in the Indian subcontinent, as documented in literature spanning the Maurya (Vedanga Jyotisha, ca. 3rd century BCE) to the Mughal (such as the 16th century Kerala school) periods.

The astronomy and the astrology of ancient India (Jyotisha) is mainly based on a sidereal system of calculations. A tropical system has also been used in a few cases. For example, a tropical determination of the Uttarayana (Uttarāyana उत्तरायन) is found in the Mahabharata[citation needed], and also in the Vedanga Jyotisha of Lagadha,[1] but not in subsequent systems, which have been sidereal.

The first named authors writing treatises on astronomy emerge from the 5th century CE, the date when the classical period of Indian astronomy can be said to begin. Besides the theories of Aryabhata in the Aryabhatiya and the lost Arya-siddhānta, we find the Pancha-Siddhāntika of Varahamihira. From this time on, we find a predominance of geocentric models, and possibly heliocentric models, in Indian astronomy, in contrast to the "Merucentric" astronomy of Puranic, Jaina and Buddhist traditions whose actual mathematics has been largely lost and only fabulous accounts remain.[citation needed]

Literature

While the Vedanga Jyotisha of Ladaga documents the state of Indian astronomy in the Maurya period, astronomy of the classical Gupta period, the centuries following Indo-Greek contact, is documented in treatises known as Siddhantas (which means "established conclusions" [2] ).

Varahamihira in his Pancha-Siddhantika contrasts five fo these: The Surya Siddhanta besides the Paitamaha Siddhantas (which is more similar to the "classical" Vedanga Jyotisha), the Paulisha and Romaka Siddhantas (directly based on Hellenistic astronomy) and the Vasishta Siddhanta.

The work referred to by the title Surya Siddhanta has been repeatedly recast. There may have been an early work under that title dating back to the Buddhist Age of India (3rd century BC). The work as preserved and edited by Burgess (1858) dates to the Middle Ages.

Whitney classifies these ancient siddhāntas into four categories : "a revelation", "attributed to ancient and renowned sage", "works of actual authors", and "later texts of known date and authorship" . Only a few of these ancient siddhāntas can be adequately reconstructed and some of them might have been vitiated by later interpolators [3] . Whitney's list of these siddhāntas are as follows according to four categories of Whitney [4]:

  1. Revelations : (1)Brahma-siddhānta (a part of Viṣṇu-dharmottara-Purāṇa; now lost), (2)Surya-siddhānta, (3)Soma-siddhānta(Bentley said it followed the system of Surya Siddhānta), (4)Bṛhaspati-siddhānta (Whitney could not locate any extant version), (5)Nārada-siddhānta.
  2. By ancient sages : (6)Garga-siddhānta, (7)Vyāsa-siddhānta, (8)Parāśara-siddhānta, (9)Pauliśa-siddhānta, (10)Pulastya-siddhānta, (11)Vasiṣṭha-siddhānta.
  3. Ancient authors : (12)Laghu Arya-siddhānta, (13)Bṛihad-Arya-siddhānta, (14)Varāha-siddhānta, (15)Brahma-siddhānta (of Brahmagupta), (16)Romaka-siddhānta.
  4. Dated authors : (17)Bhoja-siddhānta, (18)Siddhānta-śiromani, (19)Siddhānta-sundara, (20)Graha-lāghava, (21)Siddhānta-tattva-viveka, (22)Siddhānta-sārvabhauma.

Coordinate system

In Hindu Astronomy, the vernal equinox (the First Point of Aries) is often calculated at 23°From 0° Aries (1950 CE), i.e. about 7° Pisces.[5] The constellation that marks this vernal equinox is the Uttarabhadra. [citation needed]

In the time of the Puranas, the vernal equinox was marked by the Ashwini constellation (beginning of Aries), which gives a date of about 300-500 CE. The Vishnu Purana (2.8.63) states that the equinoxes occur when the Sun enters Aries] and Libra, and that when the sun enters Capricorn, his northern course (from winter to summer solstice) commences, and the southern course when he enters Cancer.The Brahmanas place the Equinox in Krittika (Pleidas) and the Rig Veda in Mrigasira (Orion). These would indicate a time of around 1900 BCE and 4000 BCE, respectively. [citation needed]

In the Surya Siddhanta, the rate of precession is set at 54" (it actually is 50.3"), which is much more accurate than the number calculated by the Greeks.[6]

The Hindus use a system of 27 or 28 Nakshatras (lunar constellations) to calculate a month. Each month can be divided into 30 lunar tithis (days). There are usually 360 or 366 days in a year. [citation needed]

It has been argued that Nilakantha Somayaji's (1444-1550) work shows a better equation of the center for Mercury and Venus "than was available either in the earlier Indian works or in the Islamic or European traditions of astronomy till the work of Kepler, which was to come more than a hundred years later."[7]

Computational planetary models

There are a large number of computational planetary models presently employed by almanac makers in India. Many Indian almanacs are now prepared on the basis of modern astronomy, including the Rashtriya Panchanga published by government, which no pandit buys. Surya Siddhānta, two Ārya Siddhāntas of two Āryabhattas and Brahma Siddhānta are major ancient theoretical models which form the basis of most of traditional almanacs. Of these Surya Siddhanta ("Saura") is the most important, which Vārāha Mihira had declared in ca. 550 AD to be the "most accurate" [8]. It is interesting to note that Vārāha Mihira did not include Aryabhatiya among the five major siddhantas dealt by him, although Āryabhatiya had been written just half a century before Pañcasiddhāntika.

Āryabhatan model

Main article: Aryabhatiya

Aryabhata (476–550), in his magnum opus Aryabhatiya, propounded a computational system based on a planetary model in which the Earth was taken to be rotating on its axis and the periods of the planets were given with respect to the Sun. Some have interpreted this to be a heliocentric model,[9][10][11] but this view has been disputed by others.[12][13][14] He recognized that the light from the Moon and the planets was reflected from the Sun and accurately calculated many astronomical constants, such as the periods of the planets, times of the solar and lunar eclipses, and the instantaneous motion of the Moon (expressed as a differential equation).[15][16] The first major astronomer to attack the Aryabhatiya was Varahamihira.[17] Brahmagupta was the greatest critic of Aryabhatiya; he devoted an entire chapter 'Tantra Parikshā' in his treatise Brāhm-Sphuta-Siddhānta to criticizng the Aryabhatiya in the harshest of terms.[18]

Bhaskara II (1114–1185) expanded on early models in his astronomical treatise Siddhanta-Shiromani, where he mentioned the law of gravity, discovered that the planets don't orbit at a uniform velocity, and calculated many astronomical constants based on this model, such as the solar and lunar eclipses, and the velocities and instantaneous motions of the planets.[19][20]

Arabic translations of Aryabhata's Aryabhatiya, known as Jije Al Arzbahar by al-Khwarizmi, were available from the 8th century but is not available now, while Latin translations were available from the 13th century,[21][22] before Copernicus had written De revolutionibus orbium coelestium. In 1030, al-Biruni had also discussed the theories of Aryabhata, Brahmagupta and Varahamihira in his Ta'rikh al-Hind (Indica in Latin; Chronicles of India in English), often quoting Brahmagupta's Brahmasiddhānta for authoritative statements. Regarding whether the earth was at rest or revolving, the latter being the view of Aryabhata, he wrote:[23]

As regards the resting of the earth [...] this, too, is a dogma with the Hindu astronomers. Brahmagupta says in the Brahmasiddhānta: "Some people maintain that the first motion (from east to west) does not lie in the meridian, but belongs to the earth. But Varāhamihira refutes them by saying: 'If that were the case, a bird would not return to its nest as soon as it had flown away from it towards the west.' And, in fact, it is precisely as Varāhamihira says.

Brahmagupta says in another place of the same book: "The followers of Aryabhata maintain that the earth is moving and heaven resting. People have tried to refute them by saying that, if such were the case, stones and trees would fall from the earth."

But Brahmagupta doe not agree with them, and says that that would not necessarily follow from their theory, apparently because he thought that all heavy things are attracted towards the center of the earth. He says: "On the contrary, if that were the case, the earth would not vie in keeping an even and uniform pace with the minutes of heaven, the prāṇas of the times."

Nilakanthan model

In 1500, Nilakanthan Somayaji (1444-1544) of the Kerala school of astronomy and mathematics, in his Tantrasangraha, revised Aryabhata's model for the planets Mercury and Venus. His equation of the centre for these planets remained the most accurate until the time of Johannes Kepler in the 17th century.[24]

Nilakanthan Somayaji, in his Aryabhatiyabhasya, a commentary on Aryabhata's Aryabhatiya, developed his own computational system for a partially heliocentric planetary model, in which Mercury, Venus, Mars, Jupiter and Saturn orbit the Sun, which in turn orbits the Earth, similar to the Tychonic system later proposed by Tycho Brahe in the late 16th century. Nilakantha's system, however, was mathematically more effient than the Tychonic system, due to correctly taking into account the equation of the centre and latitudinal motion of Mercury and Venus. Most astronomers of the Kerala school of astronomy and mathematics who followed him accepted his planetary model.[24][25]

Calendars

Further information: Hindu calendar

In the Vedanga Jyotisa, the year begins with the winter solstice.[26] Hindu calendars have several eras:

Interactions with foreign traditions

Hellenistic astronomy

Further information: Greek astronomy
Greek equatorial sun dial, Ai-Khanoum, Afghanistan 3rd-2nd century BCE.

Hellenistic astronomy is known to have been practiced near India in the Greco-Bactrian city of Ai-Khanoum from the 3rd century BCE. Various sun-dials, including an equatorial sundial adjusted to the latitude of Ujjain have been found in archaeological excavations there.[28] Numerous interactions with the Mauryan Empire, and the later expansion of the Indo-Greeks into India suggest that some transmission may have happened during that period.[29]

Several Greco-Roman astrological treatises are also known to have been imported into India during the first few centuries of our era. The Yavanajataka ("Sayings of the Greeks") was translated from Greek to Sanskrit by Yavanesvara during the 2nd century CE, under the patronage of the Western Satrap Saka king Rudradaman I.

Later in the 6th century, the Romaka Siddhanta ("Doctrine of the Romans"), and the Paulisa Siddhanta ("Doctrine of Paul") were considered as two of the five main astrological treatises, which were compiled by Varahamihira in his Pañca-siddhāntikā ("Five Treatises").[30] Varahamihira wrote in the Brihat-Samhita: "The Greeks, though impure, must be honored since they were trained in sciences and therein, excelled others....."[31] The Garga Samhita also says: "The Yavanas are barbarians, yet the science of astronomy originated with them and for this they must be reverenced like gods."

Islamic astronomy

Further information: Islamic astronomy

Early Islamic astronomy was greatly influenced by Indian astronomy, particularly the Surya Siddhanta and the works of Aryabhata and Brahmagupta, which were translated from Sanskrit into Arabic. These works were compiled as the Zij al-Sindhind, based on the Surya Siddhanta and the works of Brahmagupta, which were translated by Muhammad al-Fazari and Yaqūb ibn Tāriq in 777. Sources indicate that the text was translated after an Indian astronomer visited the court of Caliph Al-Mansur in 770.

Fragments of texts during this period indicate that Arabs adopted the sine function (inherited from Indian trigonometry) instead of the chords of arc used in Hellenistic mathematics.[32] Another Indian influence was an approximate formula used for timekeeping by Muslim astronomers.[33]

Nearly a thousand years later in the 17th century, the Mughal Empire saw a synthesis between Islamic and Indian astronomy, where Islamic observational instruments were combined with Hindu computational techniques. While there appears to have been little concern for planetary theory, Muslim and Hindu astronomers in India continued to make advances in observational astronomy and produced nearly a hundred Zij treatises. Humayun built a personal observatory near Delhi, while Jahangir and Shah Jahan were also intending to build observatories but were unable to do so. After the decline of the Mughal Empire, however, it was a Hindu king, Jai Singh II of Amber, who attempted to revive both the Islamic and Hindu traditions of astronomy which were stagnating in his time. In the early 18th century, he built several large observatories in order to rival Ulugh Beg's Samarkand observatory and in order to improve on the earlier Hindu computations in the Siddhantas and Islamic observations in Zij-i-Sultani. The instruments he used were influenced by Islamic astronomy, while the computational techniques were derived from Hindu astronomy.[34][35]

The seamless celestial globe invented in Mughal India, specifically Lahore and Kashmir, is considered to be one of the most impressive astronomical instruments and remarkable feats in metallurgy and engineering. All globes before and after this were seamed, and in the 20th century, it was believed by metallurgists to be technically impossible to create a metal globe without any seams, even with modern technology. It was in the 1980s, however, that Emilie Savage-Smith discovered several celestial globes without any seams in Lahore and Kashmir. The earliest was invented in Kashmir by Ali Kashmiri ibn Luqman in 998 AH (1589-90 CE) during Akbar the Great's reign; another was produced in 1070 AH (1659-60 CE) by Muhammad Salih Tahtawi with Arabic and Sanskrit inscriptions; and the last was produced in Lahore by a Hindu metallurgist Lala Balhumal Lahuri in 1842 during Jagatjit Singh Bahadur's reign. 21 such globes were produced, and these remain the only examples of seamless metal globes. These Mughal metallurgists developed the method of lost-wax casting in order to produce these globes.[36]

European astronomy

Through Islamic astronomy, Indian astronomy had an influence on European astronomy via Arabic translations. During the Latin translations of the 12th century, Muhammad al-Fazari's Great Sindhind, which was based on the Surya Siddhanta and the works of Brahmagupta, was translated into Latin in 1126 and was influential at the time.[37]

Some scholars have suggested that knowledge of the results of the Kerala school of astronomy and mathematics may have been transmitted to Europe through the trade route from Kerala by traders and Jesuit missionaries.[38] Kerala was in continuous contact with China and Arabia, and Europe. The existence of circumstantial evidence[39] such as communication routes and a suitable chronology certainly make such a transmission a possibility. However, there is no direct evidence by way of relevant manuscripts that such a transmission took place.[38]

Later in the early 18th century, Jai Singh II of Amber invited European Jesuit astronomers to his observatory, who had bought back the astronomical tables compiled by Philippe de La Hire in 1702. After examining La Hire's work, Jai Singh concluded that the observational techniques and instruments used in European astronomy were inferior to those used in India at the time. It is uncertain whether he was aware of the Copernican Revolution via the Jesuits, but it appears Indian astronomers were not concerned with planetary theory, hence the theoretical advances in Europe did not interest them at the time.[40]

Terminology

  • purvapaska (new moon to full moon period)
  • uttarayana: period when sun moves north (winter to summer solstice)
  • visuva: spring equinox
  • visuvant: summer solstice

Seasons

  • madhu, madhava in vasanta: spring
  • sukra, suci in grisma: summer
  • nabha, nabhasya in varsa: rains
  • isa, urja in sarada: autumn
  • saha, sahasya in hemanta: winter
  • tapa, tapasya in sisira: freeze

See also

Notes

  1. ^ Pingree(1978)
  2. ^ Cf. Burgess, Appendix by Whitney p. 439.
  3. ^ Cf. Burgess, Appendix by Whitney p. 441-444.
  4. ^ Cf. Burgess, Appendix by Whitney p. 439-444.
  5. ^ (Frawley 1991:148)[unreliable source?]
  6. ^ (Frawley 1991:148)[unreliable source?]
  7. ^ Ramasubramanian et al. 1994, cited in Subhash Kak. Birth and Early Development of Indian Astronomy. In Astronomy across cultures: The History of Non-Western Astronomy, Helaine Selin (ed), Kluwer, 2000
  8. ^ cf. G. Thibaut, Pañcasiddhāntika, chapter 1, verse 4.
  9. ^ B. L. van der Waerden (1970), Das heliozentrische System in der griechischen,persischen und indischen Astronomie, Naturforschenden Gesellschaft in Zürich, Zürich: Kommissionsverlag Leeman AG. (cf. Noel Swerdlow (June 1973), "Review: A Lost Monument of Indian Astronomy", Isis 64 (2), p. 239-243.)
    B. L. van der Waerden (1987), "The heliocentric system in Greek, Persian, and Indian astronomy", in "From deferent to equant: a volume of studies in the history of science in the ancient and medieval near east in honor of E. S. Kennedy", New York Academy of Sciences 500, p. 525-546. (cf. Dennis Duke (2005), "The Equant in India: The Mathematical Basis of Ancient Indian Planetary Models", Archive for History of Exact Sciences 59, p. 563–576.).
  10. ^ Thurston (1994), p. 188.

    "Not only did Aryabhata believe that the earth rotates, but there are glimmerings in his system (and other similar systems) of a possible underlying theory in which the earth (and the planets) orbits the sun, rather than the sun orbiting the earth. The evidence is that the basic planetary periods are relative to the sun."
  11. ^ Lucio Russo (2004), The Forgotten Revolution: How Science Was Born in 300 BC and Why It Had To Be Reborn, Springer, Berlin, ISBN 978-3-540-20396-4. (cf. Dennis Duke (2005), "The Equant in India: The Mathematical Basis of Ancient Indian Planetary Models", Archive for History of Exact Sciences 59, p. 563–576.)
  12. ^ Noel Swerdlow (June 1973), "Review: A Lost Monument of Indian Astronomy" [review of B. L. van der Waerden, Das heliozentrische System in der griechischen, persischen und indischen Astronomie], Isis 64 (2), p. 239-243.

    "Such an interpretation, however, shows a complete misunderstanding of Indian planetary theory and is flatly contradicted by every word of Aryabhata's description."
  13. ^ David Pingree (1973), "The Greek Influence on Early Islamic Mathematical Astronomy", Journal of the American Oriental Society 93 (1), p. 32.

    "The reader should note that, in writing this survey, I have disregarded the rather divergent views of B. L. van der Waerden; these have been most recently expounded in his Das heliozentrische System in der griechischen, persischen und indischen Astronomie, Zürich 1970."
  14. ^ Dennis Duke (2005), "The Equant in India: The Mathematical Basis of Ancient Indian Planetary Models", Archive for History of Exact Sciences 59, p. 563–576 [1].

    "Thus for both outer and inner planets, the mean motion given is the heliocentric mean motion of the planet. There is no textual evidence that the Indians knew anything about this, and there is an overwhelming amount of textual evidence confirming their geocentric point of view. Some commentators, most notably van der Waerden, have however argued in favor of an underlying ancient Greek heliocentric basis, of which the Indians were unaware. See, e.g. B. L. van der Waerden, “The heliocentric system in greek, persian, and indian astronomy”, in From deferent to equant: a volume of studies in the history of science in the ancient and medieval near east in honor of E. S. Kennedy, Annals of the new york academy of sciences, 500 (1987), 525-546. More recently this idea is developed in about as much detail as the scant evidence allows in L. Russo, The Forgotten Revolution (2004)."
  15. ^ Joseph (2000) [page needed]
  16. ^ Thurston (1994).
  17. ^ Varahamihira, Panchsiddhāntikā-3.6-7, translation and commentary by G.Thibaut and Sudhakar Dwivedi.
  18. ^ Gunākar Mule, Itihāsa, p.31.
  19. ^ Joseph (2000) [page needed]
  20. ^ Bhaskaracharya's Siddhantashiromani (Golādhyāya, Bhuvanakośa,6), p. 180-181.
    आकृष्टिशक्तिश्च मही तया यत् खस्थं गुरु स्वाभिमुखं स्वशक्त्या ।
    आकृष्यते तत्पततीव भाति समे समन्तात् क्व पतत्वियं खे ॥६॥
    Jain (2000) p. 116 [unreliable source?] interpreted Bhāskarāchārya to the effect that "Earth has a force of attraction, from this force Earth pulls nearby things towards herself; this force of attraction is greater in the vicinity of Earth and lesser as distance increases ... and heavier objects do not take longer time to fall"
  21. ^ The Arabic numeral system
  22. ^ Indian Astronomy Through Ages
  23. ^ Edward Sachau (tr. and ed.), Alberuni's India, Indialog Publications, New Delhi, ISBN 81-87981-42-3, p.207-8
  24. ^ a b George G. Joseph (2000), p. 408.
  25. ^ K. Ramasubramanian, M. D. Srinivas, M. S. Sriram (1994). "Modification of the earlier Indian planetary theory by the Kerala astronomers (c. 1500 AD) and the implied heliocentric picture of planetary motion", Current Science 66, p. 784-790.
  26. ^ Bryant 2001:253
  27. ^ Cunningham, A. 1883. A Book of Indian Eras.
  28. ^ "Afghanistan, les trésors retrouvés", p269
  29. ^ "Les influences de l'astronomie grecques sur l'astronomie indienne auraient pu commencer de se manifester plus tot qu'on ne le pensait, des l'epoque Hellenistique en fait, par l'intermediaire des colonies grecques des Greco-Bactriens et Indo-Grecs" (French) Afghanistan, les trésors retrouvés", p269. Translation: "The influence of Greek astronomy on Indian astronomy may have taken place earlier than thought, as soon as the Hellenistic period, through the agency of the Greek colonies of the Greco-Bactrians and the Indo-Greeks.
  30. ^ "the Pañca-siddhāntikā ("Five Treatises"), a compendium of Greek, Egyptian, Roman and Indian astronomy. Varāhamihira's knowledge of Western astronomy was thorough. In 5 sections, his monumental work progresses through native Indian astronomy and culminates in 2 treatises on Western astronomy, showing calculations based on Greek and Alexandrian reckoning and even giving complete Ptolemaic mathematical charts and tables. Encyclopedia Britanica Vol12, p269 Source
  31. ^ ":Mleccha hi yavanah tesu samyak shastram idam sthitam
    Rsivat te api pujyante kim punar daivavid dvijah
    -(Brhatsamhita 2.15)
  32. ^ (Dallal 1999, p. 162)
  33. ^ (King 2002, p. 240)
  34. ^ Sharma, Virendra Nath (1995), Sawai Jai Singh and His Astronomy, Motilal Banarsidass Publ., pp. 8–9, ISBN 8120812565
  35. ^ Baber, Zaheer (1996), The Science of Empire: Scientific Knowledge, Civilization, and Colonial Rule in India, State University of New York Press, pp. 82–9, ISBN 0791429199
  36. ^ Savage-Smith, Emilie (1985), Islamicate Celestial Globes: Their history, Construction, and Use, Smithsonian Institution Press, Washington, D.C.
  37. ^ G. G. Joseph, The Crest of the Peacock, p. 306.
  38. ^ a b Almeida, D. F., J. K. John, and A. Zadorozhnyy. 2001. "Keralese Mathematics: Its Possible Transmission to Europe and the Consequential Educational Implications." Journal of Natural Geometry, 20:77-104.
  39. ^ C. K. Raju (2001). "Computers, Mathematics Education, and the Alternative Epistemology of the Calculus in the Yuktibhasa", Philosophy East and West 51 (3), p. 325-362.
  40. ^ Baber, Zaheer (1996), The Science of Empire: Scientific Knowledge, Civilization, and Colonial Rule in India, State University of New York Press, pp. 89–90, ISBN 0791429199

References

editions of primary texts
  • Ebenezer Burgess. "Surya-Siddhanta, Text with English Translation and Notes",Edited by S.Jain,Oriental Book Centre,Delhi,2005, ISBN 81-8315-017-9, pp.552 plus editorial 52 pages.
  • Ebenezer Burgess. "Translation of the Surya-Siddhanta, a text-book of Hindu Astronomy", Journal of the American Oriental Society 6 (1860): 141–498.
  • Surya Siddhānta,with Hindi commentary by Dr Rāmchandra Pāndey (Head of Department of Jyotiṣa, BHU University),Chowkhambā,Vārānasi.
  • Śāstri, Hargovinda (1978), Amarkoṣa with Hindi commentary, Vārānasi: Chowkhambā Sanskrit Series Office
  • G.Thibaut and Sudhakar Dwivedi."Panchasiddhantika",Chowkhambha,Varanasi, India,1888,reprint 1997
  • Gunākar Mule,Shruti-Smriti Paramparā and Ganitajna-Jyotishi Aryabhatta, published in Itihāsa,vol.3, Jan-Dec 1994, Research magagine of 'Indian Historical Research Council',35 Firoze Shah Road, New Delhi.
  • Bhāskarāchārya, Siddhāntaśiromani, published by Chowkhambā Sanskrit Sansthāna, Vārānasi, 3rd reprint 1999.
  • Burgess, Ebenezer (tr.) The Surya Siddhanta. Delhi: Motilal Banarsidass, 1989 (1860)
  • Kuppanna Sastry, T.S., Vedanga Jyotisha of Lagadha. Indian National Science Academy, Delhi 1985.
  • Vidyalankara, V. Satapatha Brahmanastha Agnicayana Samiksa. Bahalgarh, 1985.
  • Rāmniwās Rāi, Āryabhatiya,with Hindi commentary, published by Indian National Science Academy, Bahādurshāh Zafar Mārg, New Delhi,1976 (published on the occasion of 1500th birth anniversary of Āryabhata).
secondary literature
  • J.M. Roberts, The Hutchinson History of the World, BI Publications, 54 Janpath, New Delhi-1 (In association with Hutchinson Publishing Group of 3 Fitzroy Square, London W.1).
  • Billard, R. L'Astronomie Indienne. Ecole Francaise d'Extreme Orient, Paris, 1971.
  • Template:Harvard reference
  • Duke, Dennis. 2005. "The Equant in India: The Mathematical Basis of Ancient Indian Planetary Models." Archive for History of Exact Sciences 59: 563–576[2].
  • Filliozat, Jean. 1969. "Notes on Ancient Iranian and Indian Astronomy." Journal of the K.R. Cama Oriental Research Institute 42:100-135.
  • Sri Yukteswar Giri. The holy science. Los Angeles, Ca: Self-Realization Fellowship, 1984.
  • Joseph, George G. (2000). The Crest of the Peacock: Non-European Roots of Mathematics, 2nd edition. Penguin Books, London. ISBN 0691006598
  • Kak, Subhash C. (2000). 'Birth and Early Development of Indian Astronomy'. In Selin, Helaine (2000). Astronomy Across Cultures: The History of Non-Western Astronomy (303-340). Kluwer, Boston. ISBN 0-7923-6363-9.
  • Template:Harvard reference
  • Kramrisch, S. The Presence of Siva. Princeton University Press, Princeton 1981.
  • Pingree, David (1978). "History of Mathematical astronomy in India." Dictionary of Scientific Biography, vol. 15, pp. 533–633, New York: Charles Scribner's Sons.
  • Pingree, David (1996). "Astronomy in India." in Christopher Walker, ed., Astronomy before the telescope, pp. 123-142. London: British Museum Press. ISBN 0-7141-1746-3.
  • Sen, S.N., and K.S. Shukla, eds. 1985. History of Astronomy in India. New Delhi: Indian National Science Academy.
  • Thurston, Hugh (1994). Early Astronomy. Springer-Verlag, New York. ISBN 0-387-94107-X
  • Nemichandra (Śāstri) Jain, Bhāratiya Jyotiṣa, published by Bhāratiya Jñānpith, New Delhi, 31rst reprint 2000, ISBN 81-263-0003-5.[unreliable source?]
Retrieved from "https://en.wikipedia.org/w/index.php?title=Indian_astronomy&oldid=214531579"