A massive amount has been written about Indian astronomy—several thousand manuscripts (Pingree 1970/1981;
13 An entrance or vestibule to a temple or group of buildings.
Sarma 1990a,b,c,d). The best way for a western scholar to approach Indian astronomy at present is through the compilation and translation of selected sources by Subbrayappa and Sarma (1985) with guidance from Pingree (1978; 1981). In particular, Pingree (1978) summarizes the major features of Indian astronomy and its evolution. The relationships of astronomy to architecture and to mythology are hardly mentioned in this material but are the subjects of a great deal of additional literature. Michell (1977/1989) provides a useful introduction to architecture that keeps its cosmic features constantly in mind. Hopkins (1915/1969) provides a convenient guide to mythology but has no systematic consideration of astronomical features. Pingree (1978) describes Indian astronomy in terms of five chronological divisions:
Pingree thinks that there was no mathematically based astronomy during the Vedic period. The presence in Vedic literature of references to adhimasas (intercalary months) show that the problem of relating synodic months to the solar year was already a subject of study, but Pingree (1976/1996) doubts that any systematic form of intercalation was in use. The year was supposed to consist of 12 months of 30 days each, but how this was reconciled with synodic months and the tropical year is unknown. Reference points in the sky were provided by the 28 lunar mansions or aster-isms regarded as markers for the nightly movement of the Moon. The identities of the stars of these asterisms are first attested in the 5th century a.d. Pingree does not discuss the problem of identifying these asterisms during the Vedic period and seems to doubt that it is possible, but DHK thinks that perhaps 2/3 of these can be determined from identities of particular asterisms with those in cognate systems in China and Arabia. There were two kinds of month names: one descriptive, and one derived from the names of 12 of the 28 lunar mansions. The months begin either with Phalguna or, more commonly, with Caitra, as the first month of spring. The month Karttika, named after the first of the lunar mansions, is associated with the beginning of autumn. In an early period, there were three seasons, then five, and finally six. Two halves of the year were measured from the solstices. Lunar months were also divided into a period from new moon to full moon and from full to new moons. It is not known if the months began with new moon or with full moon. Pingree sees the further development of Indian astronomy as largely due to different foreign influences.
Indian astronomy seems to have had its roots in several sources. In addition to the ancient Vedic and Dravidian sources, much technical astronomy was derived from Babylonia, Greece, and Islam. Features of foreign origin in Indian astronomy are discussed in detail by Pingree (1963). Although there have been suggestions from time to time of a Babylonian origin for the 360-day year mentioned in the Vedas or for the naksatras, these are unconfirmed. The earliest intrusion of well-dated astronomical material occurred in the later 5th century b.c. Mesopotamian material can be discerned in a Sanskrit text, Lagadha's Jyotisavedanga. For example, an equivalent to the tithi, 1/30 of a lunar month, is mentioned in the Seleucid Babylonian texts, but there it refers to the mean synodic month (see §4.1.4); in the Surya Siddhanta, it is of fixed length, but in later Hindu astronomy, it became 1/30 of the true lunar month, and thus variable (see Neugebauer 1957/1969, pp. 128, 186, f.n.2). The material includes also a luni-solar calendar with a cycle of 62 synodic months; Pingree suggests it is a less accurate analog to an 8-years intercalary cycle proposed by the Greek Cleo-stratus of Tenedos (~6th century b.c.). The Lagadha calendar is mentioned also in a number of other works: in the Arthasastra of Kautilya (possibly from Maurya), in the Suryaprajnapti (a Jain work), and in the earliest versions of the Gargasamhita (~1st century a.d.?), and the Paitama-hasiddhanta, in which an epoch dated at 80 a.d. is given). Other Babylonian features from this time include a linear zig-zag function to describe the length of a noon shadow during the year, and a ratio of the length of the longest to the shortest day as 3:2 (a ratio appropriate to and used extensively in Babylon but applicable only to extreme NW India). See §4.1.1 and Table 4.1 for the connection between latitude and length of daylight.
By the end of the 3rd century a.d., Greek astronomical materials had been translated into Sanskrit, and formulas for the interrelations among various time intervals established. The work Yavanajataka, completed by Sphujidhvaja by 270 a.d., contains, among many Babylonian techniques, planetary phenomena (principally elongations) designated by Greek letters, like that described in Neugebauer (1957/1969, p. 126ff; §184.108.40.206). In classical sources, they are found in a Greek manuscript attributed to Rhetorius (Boll 1908, 213ff; Pingree 1968, 245ff).
Pingree (1996, p. 127) points out that the Panchasiddhan-tika gives the longitude difference between Alexandria and Ujjain as 7;20 nadis (44°; the modern difference is 45;50) and between Alexandria and Varanasi as 9 nadis (54°; modern 73;7). He thinks that the only way values that close to reality could have been obtained would have been from simultaneous observations of a lunar eclipse from both places, which implies scientific cooperation between astronomers in Alexandria and Ujjain.
Pingree (1978, p. 534) recognizes five main schools (paksas) of astronomy, each associated with slightly different parameters and computing methods. The dates of origin and principal areas of influence of these paksas are as follows:
(3) Ardharatrikapaksa, ca. 500 a.d., Rajasthan, Kashmir, Nepal, Assam
Brahmagupta of the first of these schools wrote the Brahmasphuta-siddhanta, in 628 a.d., which formed the basis for the Mahasiddhanta, which, in turn, was largely adopted by al-Fazarl [Islamic astronomer, late 8th century] in his Zij-al-Sindhind. This was translated by Adelard of
Bath in 1126, and it was the primary source of Hindu influence on European astronomy (Pingree 1978, p. 580). Among the distinguishing characteristics of the different schools were somewhat different definitions of the positions of the Yogataras or junction stars. Other distinctions included the following:
(1) The time intervals used in calculating planetary, solar, and lunar periods
(2) The parameters used in the calculations
(3) The particular form of epicyclic theory that underlay the calculations
(4) The techniques of computation, in some of which the Indian scholars made substantial improvements over their sources
Although the Indians invented the system of decimal numbers, they preserved much of their astronomical information in verse. For this purpose, they used a large number of synonyms for numbers. Usually, these had a small number of other meanings. Thus, there are 40 words for "1," all of which also meant "Earth" and "Moon." The equivalents for some of the numbers are as follows:
7 = Horse, Mountain 8 = Elephant, Serpent 11 = Siva 12 = Sun 14 = Indra 27 = Star, Asterism
Such a way of representing numbers with such consistent associated meanings would lend itself easily to iconographic interpretation. We know of no direct evidence that this occurred, but the possibility should be kept in mind when studying Indian art.
Roger Billard's (1971) work L'astronomie Indienne, despite its name, is not a history of astronomy in India but an attempt to date the principal canons of astronomy on the basis of internal structural evidence. The work is ingenious, textually and historically, and statistically sophisticated, but ultimately unconvincing. His evidence suggests that Mercury was systematically omitted from the observations on which the canons are based (in his view). He offers no suggestion why careful observers, who included Mercury parameters in their corrections, should not have had an observational basis for these parameters. When all the mean longitudes, excluding those of Mercury, converge to indicate a particular date that is within an appropriate historical range, the technique seems fairly convincing. However, when one looks, for example, at Billard's (1971, p. 154) analysis of the parameters included in the revised version of the Suryasiddhanta, one finds that some parameters are said to be based on observations of 955 a.d., some on observations of 1031 a.d., one on observations of 1185 a.d., and others on observations of 1230 to 1273 a.d. This is certainly not a consistent set of observations, and only consistent sets could provide satisfactory evidence that they are indeed based on observations. The premise of an observational basis controls the interpretation of such inconsistencies. There has been some criticism also of Billard's historical placement of the canons (Pingree 1976, 1996). From the standpoint of consistency, probably the least satisfactory of all conclusions would be that the parameters of some canons were based on observations and others were not.
Mercier (1985), who used slightly different modern parameters than did Billard for checking the ancient parameters but accepted Billard's premises, verified Billard's dates and showed that the use of the meridian at Ujjain for the observations optimized the results for most canons. He showed that the Romakasiddhanta, which he dates to 505 a.d., seems to be based on observations at Alexandria. Mercier, like Billard, thinks that the Kaliyuga era base of 3102 b.c. was "defined and fixed as a direct consequence" of Aryabhata's work of 499 a.d., equivalent to the year 3600 of the Kaliyuga. We certainly agree that the year 3600 of the Kaliyuga era would have seemed important to any Indian astronomer, whether it was created at that time or was preexistent. Possibly, a preexistent era base was modified by Aryabhata. Pingree (1996) has demonstrated that the role of observation in establishing corrections was normally limited to providing a choice among long-established parameters.
Around the beginning of the 6th century, Aryabhata14 of Kusumapura (b. 476 a.d.), one of the greatest Indian astronomers, argued for the plausibility of a rotating Earth and was thus one of a select company prior to Copernicus to whom such a notion seemed reasonable. Aryabhata's works were written in Sanskrit verse and began with an invocation to Brahma. They were divided into three sections: mathematics, time and astronomy, and the celestial sphere. In the mathematics section, units are defined, using as numbers the consonants of the Sanskrit alphabet.15 In astronomy and spherics, Aryabhata proposed that Sun and Moon moved in epicycles, of size 13.5 and 31.5 units (of 360), respectively, and that planets had two epicycles, which expand and contract with time. Aryabhata obtained a value of the obliquity of the ecliptic of 24°; he developed a procedure for calculating the magnitude and duration of eclipses, given the Moon's latitude, and he described a model of a celestial sphere that was rotated by means of a hydraulic mechanism.
Varahamihira's (6th century) Panca Siddhantika is a collection of five treatises on astronomy, placed by Pingree in what he calls the "Greek" period. The treatises are as follows:
(1) The Surya Siddhanta
(2) The Romaka Siddhanta
(3) The Paulisa Siddhanta
(4) The Vasishtha Siddhanta
(5) The Paitamaha Siddhanta, one of several Brahma Siddhantas16
14 Translated by Clark (1937, cited in Neugebauer 1957/1969, p. 183) and by Shukla and Sarma (1976). See Pingree (1970/1981: 1, 308-310).
15 The first 25 consonants correspond to the numbers 1-25 (e.g., k = 1, kh = 2, g = 3, gh = 4,.. .);the next 8 consonants indicate tens from 30, 40,.. . 100. The nine vowels indicate multiplication by powers of 100. Thus, a = x1;i = x100; u = x10,000;r = 1,000,000;. = x108; e = x1010; o = x1012; ai = x1014; au = x1016. Thus, the combination khuyughr = 4,320,000 (the number of years in a Yuga).
16 Others are (a) the Brahma (unfortunately, referred to as the
Paitamaha) Siddhanta, a short prose treatise dealing with a later phase of Indian astronomy than Varaha Mihira's work (it is part of a longer work, the Vishnudharmottara), (b) The Sphuta Brahmasiddhanta
Among other things, the treatises contain solar and lunar theories, linear planetary theory, and rote methods for the computation of eclipses, using pre-Ptolemaic operations and geometry imported into India from the west.17 Greek influence is explicit:
The Greeks indeed are foreigners, but with them this science is flourishing.
The title Romaka Siddhanta indicates a reference to "Romans" (probably, as Neugebauer surmised, Greeks of the Roman or Byzantine empires). The Paulisa Siddhanta was attributed by al Biruni to an astrologer named Paulus Alexandrinus (fl. ~380 a.d.). The Surya Siddhanta was considered by Varahamihira to be the most important of the five and today is still considered the main canon of Hindu astronomy (Neugebauer 1957/1969, p. 174). Dating from the early 5th century, some manuscripts contain the command of the Sun (Surya) to Maya Asura:
Go therefore to Romaka-city, your own residence; there, undergoing incarnation as a barbarian, owing to a curse of Brahma, I will impart to you this science.
See §7.5 for a discussion of the Panca Siddhantika in the context of the transmission of ideas from Greece and Babylonia.
An interesting feature of Indian astronomy was the concept of the periodicity of comets already by the 6th century a.d. (Sharma 1987). Unfortunately, we do not know how this was established. Perhaps it was an inference from the observation that most celestial bodies reappear periodically, or perhaps it was suggested by details from cometary orbits. We do know that Varahamihira already recognized that some comets at different apparitions could be the same despite appearing in different directions. Sharma suggests that "The periods might have been determined by noting velocity over the visibility period." The 6th-century astronomer Bhadrabahu is quoted as saying, the maximum period of disappearance of a comet is 36 years; the average period is 27 years; and the minimum period is 13 years.
The 10th-century astronomer Bhattotpala, on the other hand, cited particular named comets having periods between 100 and 1500 years. These statements show clearly that the concept of cometary periodicity was present, but hardly ensures that any of the periods was correctly determined. The difficulty with the assertions is that the apparent trajectories of comets, even those with similar orbital elements, differ from apparition to apparition because of different distances from Earth and locations in the sky. The length of a tail at perihelion, for example, will be much greater if the comet is on the same side of the Sun as the Earth than if it is on the far side. If one could assess the time of perihelion by the relative angular velocity and, somehow, written by Brahmagupta, which is based on (a), and (c) the Brahma Siddhanta known as the S'akalya Siddhanta.
17 One of the interesting developments stemming from the theory of epicycles was the invention of power series for sine and cosine by Madhava in the 14th century, and according to Pingree, in Europe, these were first established by Newton (Pingree 1978, p. 632, f.n. 60).
could establish the distance from Earth at that time, some comparison in properties, such as the perihelion distance to the Sun, could be established. However, the angular size of the tail alone is not a sure guide because the tail development is determined by the intrinsic length of the tail and this in turn depends on the amount of material in the comet and on the number of previous passes. A classical work describing the state of Indian astronomy in the Middle Ages is al Birunis India (translated by Sachau 1910), dating from ~1030 a.d.
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