Ancient Indian astronomy may be classified into two main categories: (1) the vedic astronomy and (2) the post vedic astronomy. The vedic astronomy is the astronomy of the vedic period i.e. the astronomy found in the vedic saṃhitas and brāhmanas and allied literature. The principal avocation of the people in the vedic times being the performance of the vedic sacrifices at the times prescribed by the śastras, it was necessary to have accurate knowledge of the science of time so that the times prescribed for performing the various vedic sacrifices could be correctly predicted well in advance. Astronomy in those times, therefore, was essentially the science of time-determination. It centred round the Sun and Moon and its aim was to study the natural divisions of time caused by the motion of the Sun and Moon, such as days, months, seasons and years, special attention being paid to the study of the times of occurrence of new moons, full moons, equinoxes and solstices.

A system of 27 asterisms, or nakṣatras, plays an important role in Indian astronomy and calendrical science. The present convention is that the ecliptic is divided into 27 equal parts each 13°20' long commencing from one initial point. These arcs are called nakṣatras. Again a bright or prominent star of each division is called yogatārā bearing the name of the are division e.g., Kṛttikā as nakṣatra means an are division and as a yogatārā it means the star η Tauri of the Pleiades group.

The origin of this asterism system is very old. The names of these stars appearin Vedic litrature. The Taittirīya, Kāṭhaka, Maitrāyaṇī Saṃhitas and the 19th book of Atharva Veda, each has given a list of 27 nakṣatras (the last two have included an additional star, Abhijit (αLyrae), making a total of 28 nakṣatras). All these lists always begin with the name kṛttikas (the star group Pleiades), and order of names of stars are more or less the same. Some of the stars changed their names in different hands; but they are always either star groups or single stars, and never arc divisions.

The present paper restricts to the analysis of some passages from the Vedic literature, viz. Śatapatha Brāhmaṇa and Vedāṅga Jyautiṣa, from the view point of mathematical astronomy.

The Śatapatha Brāhmaṇa in 2.1.2.1 to 2.1.2.5, refers to some ritual in which some fire has to be set up. It recommends Kṛttikā as the nakṣatra or the lunar asterism under which to set up the fire. For, there are some special features that Śatapatha-Brāhmana obviously considers as good points. According to the text, one good point about Kṛttikā is that it is ′the most numerous′; secondly, it rises ′in the east′.

What are the characteristics of ancient China’s astronomy? Many scholars have discussed the problem. In 1939 Herbert Chatley summed up fifteen points. Joseph Needham(1959) in his great work Science and civilisation in China concentrated it into seven points.

1. 1 the elaboration of a polar and equatorial system strikingly different from that of the Hellenistic peoples;

2. 2 the early conception of an infinite universe, with the stars as bodies floating in empty space;

3. 3 the development of quantitative positional astronomy and star catalogues two centuries before any other civilisation of which comparable works have come down to us;

4. 4 the use in these catalogues of equatorial coordinates, and a faithfulness to them extending over two millennia;

5. 5 the elaboration, in steadily increasing complexity, of astronomical instruments, culminating in the 13th century invention of the equatorial mounting, as an ‘adapted torquetum’ or ‘dissected’ armillary sphere;

6. 6 the invention of the clock drive for that forerunner of the telescope, the sighting tube, and a number of ingenious mechanical devices ancillary to astronomical instruments;

7. 7 the maintenance, for longer continuous periods than any other civilisation, of accurate records of celestial phenomena, such as eclipses, comets, Sunspots, etc.

In recent years a number of auroral catalogues have been compiled from Oriental records, but the auroral identifications given vary greatly from one catalogue to another. This is due to the fact that, up to now, no reliable criteria have been found which could help us discriminate between auroral and non-auroral ancient records. In this paper two new criteria are propounded and their usefulness illustrated by the solution of a few currently much debated questions.

In Chinese ancient times the Sun worship was in vogue. Mainly there were two sorts of the worship rites: 1) for rising and setting Sun; 2) for solar eclipses. Many evidences for Sun worship have been found in Chinese ancient books and bone inscriptions (Xu Zhentao et al.1985).

The everyday worship to the Sun certainly caused spontaneous observations for solar phenomena. Since the ancients only had a limited knowledge they could not understand what were these phenomena and they, however, created many wonderful myths to describe them. These myths about Solar phenomena have vividly been expressed in the works of art of the Han Dynasty recently unearthed. So analysing the works of art we may trace the original phenomena of solar activity.

The instruments of measuring time have been closely related to astronomy, especially to astrometry. In ancient China, before mechanical clocks were imported from European countries, accurate Water Clocks, main tools for measuring time, had been developed two thousand years ago.

In this paper the sizes (mainly the height) of five single vessel-type Clocks of Western Han Dynasty (206 B.C.-25 A.D.), which were either unearthed in recent years or recorded in some historical documents, are taken as a sample for studying the scaling of indicator-rods and precision of Clock.

In Europe it has been customary to regard the ancient Greeks as our intellectual ancestors. Greek science was seen as the fountainhead from which modern European science ultimately derived both its existence and its characteristic features. This was not a completely empty idea. Each time a modern astronomer mentions a planet, the perigee and apogee of its orbit, its periods and their various anomalies, he is using so many Greek words. Moreover, until about a hundred years ago the extant works of the Greeks were the earliest scientific texts known to European scholars so that Greek science acquired a unique position in the European mind,and that ancient Greek culture in general became ‘classical’ and thus an ideal model or pattern for civilization as such. In consequence, the traditional European History of Science became an account of how science arose among the Greeks, how it penetrated into other cultural areas, and how it was sometimes eclipsed and again reborn in one of the so-called ‘renaissances’ of which European historians are so fond to speak.

Among the historians of Indian astronomy, John Bentley seems to be first to stress, nearly two hundred years ago, that yuga and kalpa, which form the basic time-divisions used for traditional astronomical computations in India, are not historical but astronomically interpolated. Bentley says that a division of time simply into the four yugas, viz. Krta, Tretā, Dwāpara and Kali, was introduced in 204 B.C. “It appears,” as Bentley surmises, “that at, or about this period (204 B.C.), improvements were made in astronomy; new and more accurate tables of the planetary motions and positions were found, and equations introduced. Beside these improvements, the Hindu history was divided into periods, for chronological purposes....The period immediately preceding the inventor was called the first, or Kali yuga; the secojid or next, was called the Dwāpara Yuga; the third was called the Tretā Yuga; and the fourth, or furthest back from the author, was called Kṛta Yuga and with which the creation began. The end of the first period, called Kali was fixed by a conjunction of the Sun, Moon and Jupiter, in the beginning of Cancer, on the 26th June 299 B.C. This was called the Satya Yuga, or true conjunction, and is the radical point from which the calculation proceeds” (Bentley 1823, p.61-62).

Astronomical constants such as the length of the solar year, sidereal and synodic periods of revolutions of the Moon and five brighter planets have been computed using the system of astronomy in ancient and mediaeval India and a comparison made with their modern values. The modern values of the Moon’s inequalities have been compared with that of the earlier Hindu astronomical reckonings. Also, the Equation of the Centre of the Sun as determined in the period 500 A.D. to 1150 A.D. has been discussed in relation to corresponding modern values.

The first treatise on calendric astronomy was compiled C1300 B.C.and is known as “The Vedāṅga Jyautiṣa. It gives rules for framing calendar covering a five-year period, called a ‘Yuga’. In this yuga-period calendar, there were 1830 civil days, 60 solar months, 62 synodic lunar months, and 67 sidereal lunar months. The calendar was luni-solar, and the year started from the first day of the bright fortnight when the Sun returned to the Delphini star group. Corrections were made, as required, to maintain this stipulation to the extent possible. The Vedāṅga calendar was framed on the mean motions of the luminaries, the Sun and the Moon, and was based on approximate values of their periods. Vedāṅga Jyautiṣa calendar remained in use for a very long time from C 1300 B.C. to C 400 A.D. when Siddhānta Jyautiṣa calendar based on true positions of the Sun and the Moon came into use and gradually replaced totally the Vedāṅga calendar.

The canons of Sanskrit astronomy depend on mean motions which are normally postulated to refer to the central meridian of Ujjain. The present work is a statistical analysis of these mean motions designed to discover the optimum position of the meridian, by comparison with modern mean motions. This follows earlier work done by Billard in determining the optimum year. The results confirm that from the time of Aryabhata all the canons were referred to meridians lying well within India, and in many cases clearly identifiable with Ujjain within the statistical bounds.

Apparitions of comets were thought to be a bad omen in earlier times in almost all the old civilizations. This led to correlating these apparitions with some particular events which took place simultaneously. Although the information was collected and recorded merely for astrological purposes, yet these records are in no way less important from astronomical points of view. Ancient Indian astronomers like Garga, Marīci, Asita, Devala and others made cometary studies and recorded their trajectories(Bṛhat-saṃhitā, Chapter on Ketucārādhyāya).

In earlier times there was a notion that the comets were heavenly bodies and their apparitions, paths, rising and setting in the sky, could not be found out by mathematical calculations as is clear from the following śloka(Bṛhat-saṃhitā, Chapter on Ketucārā dhyāya).

The origin and development of planetary theories in India are still imperfectly understood. It is generally believed that fullfledged planetary theories capable of predicting the true positions of the Sun, Moon and Star-planets appeared in India along with the emergence of the siddhāntic astronomical literature. Before this siddhāntic astronomy there had existed the Vedāṅga Jyotiṣa of Lagadha, prepared around circa 400 B.C. in the Sūtra period more or less on the basis of astronomical elements developed in the time of the Saṃhitās and the Brāhmaṇas. This Jyotiṣa propounded a luni-solar calendar based on a five-year period or yuga in which the Sun made 5 complete revolutions. Moreover, this quinquennial cycle contained 67 sidereal and 62 synodic revolutions of the Moon, 1830 sāvana or civil days, 1835 sidereal days, 1800 solar days and 1860 lunar days. An important feature of the Jyotiṣa is its concept of the lunar day or tithi which is a thirtieth part of the synodic month. The tithi concept was also used in Babylonian astronomy of the Seleucid period. To trace the motion of the Sun and the Moon and to locate the positions of fullmoons and newmoons in the sky a stellar zodiac or a nakṣatra system coming down from the times of the Saṃhitās and the Brāhmaṇas was used. The Jyotiṣa was acquainted with the solstices and equinoxes, the variation in day-length of which a correct ratio was given. It is, however, silent about the inclination of the ecliptic, the non-uniform and irregular motion of the Sun and the Moon and various other important elements.

The Hsiu-yao Ching ( HYC) is a Chinese text on Indian astrology composed in the middle of the eighth century. Its full title can be rendered as 'Good and bad time and day and beneficient and maleficient mansions and planets promulgated by Bodhisattva-Mañjuśrī and other sages'. As the title shows the book is ascribed to the legendary Mañjuśrī and other sages, but the actual author is the Buddhist monk Amoghavajra (A.0.705-774) whose native place was somewhere in north India. His Chinese name Pu-k'ung Ching-kang is a literal translation of the Sanskrit name. Like most of the texts on Buddhist astrology and astronomy, HYC is contained in Vol.21 of the Taisho Tripitaka compiled by the Japanese Buddhist scholars during the Taisho Period (1912-1926). From many corruptions in the texts it seems that the compilers were not much interested in Buddhist astrology and astronomy in general, and that they did not try to secure better manuscripts either. Specifically in the case of HYC they simply based their edition on the text of the Korean Tripitaka and put in the footnotes the variant readings found in the Chinese Tripitaka of the Ming Dynasty.