ASTRONOMY

ASTRONOMY There are astronomical references of chronological significance in the Vedas. Due to precession of Earth, the seasons shift at a rate of about a month every two thousand years. Some Vedic notices mark the beginning of the year and that of the vernal equinox in Orion; this was the case around 4500 b.c. There are other astronomical references from the subsequent millennia, which indicates the memory of a long period over which astronomy developed into a science. Fire altars, with astronomical basis, have been found in the third millennium cities of India. The texts that describe their designs are conservatively dated to the first millennium b.c., but their contents appear to be much older.

Vedic ritual was based on the times for the full and the new moons, the solstices and the equinoxes. There were two years: the ritual year started with the winter solstice (mah?vrata), and the civil one started with the spring equinox (vishuva). The passage of the rising of the sun in its northward course from the winter solstice to the summer solstice (vishuvant) was called gav?m ayana, or the sun's walk. The solar year was divided into two ayanas: in the uttar?yana, the sun travels north; in the dakshin?yana, it travels south.

The movement of the moon was marked by its nightly conjunction with one of the 27 or 28 nakshatras (stars or star clusters). The Rig Veda 1.164 also speaks of another tradition of dividing the zodiac into twelve equal parts. It appears that these divisions were called the ?dityas.

The incommensurability between the lunar and the solar reckonings led to the search for ever-increasing cycles to synchronize the motions of the sun and the moon. This is how the yuga (world cycle) astronomical model was born. In the lunar month, there were separate traditions of counting the beginning of the month by the full-moon day and the new-moon day.

During the earliest times in India, there existed a centennial calendar with a cycle of 2,700 years. Called the Saptarshi calendar, it is still in use in several parts of India. Its current beginning is taken to be 3076 b.c. Notices by the Greek historians Pliny and Arrian suggest that, during the Mauryan times, the calendar used in India began in 6676 b.c. It is very likely that this calendar was the Old Saptarshi calendar with a beginning at 6676 b.c. Other major Indian eras are that have wide currency are Kaliyuga (3102 b.c.), Vikrama (58 b.c.), and Shaka (a.d. 78).

The shifting of seasons through the year and the shifting of the North Pole allow us to date several other statements in the Vedic books. Thus the Shatapatha Br?hma?a statement that the Krittik?s never swerve from the east corresponds to 2950 b.c.

The Maitr?yaniya Br?hma?a Upanishad refers to the winter solstice being at the midpoint of the Shravishth? (Delphini) segment and the summer solstice at the beginning of M?gha. This indicates 1660 b.c. The Ved?nga Jyotisha, the text that describes some of the astronomical knowledge of the times of altar ritual, has an internal date of circa 1350 b.c.

Astronomical Ritual

The year was known to be somewhat more than 365 days and a bit less than 366 days. In one tradition, an extra eleven days were added to the lunar year of 354 days. According to one text, five more days are required over the nominal year of 360 days to complete the seasons.

The central idea behind the Vedic system is the notion of bandhu (connections) between the astronomical, the terrestrial, and the physiological. The connections were represented in sacred ritual and sacred books. This knowledge was also coded in the organization of the Rig Veda, which was taken to be a symbolic altar of hymns. The examination of the Rig Veda is of unique significance since this ancient book has been preserved with incredible accuracy.

Vedic ritual was generally performed at an altar. The altar design was based on astronomical numbers related to the reconciliation of the lunar and solar years. The fire altars symbolized the universe, and there were three types of altars representing the earth, the space, and the sky. The altar for the earth was drawn as circular, whereas the sky (or heaven) altar was drawn as square. The geometric problems of circulature of a square and that of squaring a circle are a result of equating the earth and the sky altars. These problems are among the earliest considered in ancient geometry.

The fire altars were surrounded by 360 enclosing stones; of these, 21 were around the earth altar, 78 around the space altar, and 261 around the sky altar. Thus the earth, the space, and the sky are symbolically assigned the numbers 21, 78, and 261.

The main altar was built in five layers. The basic square shape was modified to several forms, such as that of a falcon and a turtle. These altars were built in five layers, of a thousand bricks of specified shapes. The construction of these altars required the solution to geometric and algebraic problems. The main altar was an area that was taken to be equivalent to the nominal year of 360 days.

The altar ritual dealt with the difference between the two years: lunar, which is a fraction more than 354 days (360 tithis); and solar, which is in excess of 365 days (between 371 and 372 tithis). A well-known altar ritual says that altars should be constructed in a sequence of 95, with progressively increasing areas. The residual excess in 95 years adds up to 89 tithis; it appears that this was distributed in some manner over the 95-year period. The 95-year cycle corresponds to the tropical year being equal to 365.24675 days.

The Vedic astronomical system as given in the Ved?nga Jyotisha is a luni-solar system. It considers a five-year yuga, employing two intercalary lunar months, with the condition that at the beginning of each yuga both the sun and the moon would be at the Shravishth? nakshatra, and it will be the winter solstice. For these conditions to be met, several corrections had to be made at the end of the yuga. For example, an additional day was needed to make sure that the new yuga would start with the new-moon day.

Nature of the Planetary System

The ?ryabhat?mya of ?ryabhata (b. a.d. 476) is a milestone of astronomy for two reasons. In it Earth is taken to spin on its axis, and the orbits of the planets are considered with respect to the sun. This idea of a spinning Earth causing night and day was a major advance in astronomy. Since the inner planets were already seen close to the sun, it made it easy to refer their orbital motions with respect to the sun. In contrast to this, in the Greek view the planets and stars were on concentric crystalline spheres centered on Earth. Each planet, the sun, and the moon were on their own sphere; the stars were placed on the largest sphere surrounding all of the rest.

A pure heliocentrism is to be found in the following statement in the Vishnu Pur??a: "The sun is stationed for all time, in the middle of the day. The rising and the setting of the sun being perpetually opposite to each other, people speak of the rising of the sun where they see it; and, where the sun disappears, there, to them, is his setting. Of the sun, which is always in one and the same place, there is neither setting nor rising."

By examining early Vedic sources, the stages of the development of the earliest astronomy become apparent. After the Rig Vedic stage comes the period of the Br?hma?as, in which we place the Ved?nga Jyotisha astronomy. The third stage is early Siddh?ntic and early Pur??ic astronomy.

The concepts of the sh?ghrocca and mandocca cycles are peculiar to Indian astronomy. They indicate that the motion of the planets was taken to be fundamentally around the sun, which, in turn, was taken to go around Earth. The mandocca, in the case of the sun and the moon, is the apogee where the angular motion is the slowest; in the case of the other planets, it is the aphelion point of the orbit. For the superior planets, the sh?ghrocca coincides with the mean place of the sun, and in the case of an inferior planet, it is an imaginary point moving around Earth with the same angular velocity as the angular velocity of the planet around the sun; its direction from Earth is always parallel to the line joining the sun and the inferior planet.

The mandocca point serves to slow down the motion from the apogee to the perigee and speed up the motion from the perigee to the apogee. It is a representation of the nonuniform motion of the body, and so it can be seen as a direct development of the idea of the non-uniform motion of the sun and the moon. The sh?ghrocca maps the motion of the planet around the sun to the corresponding set of points around Earth. The sun, with its winds that hold the solar system together, is, in turn, taken to go around Earth. The antecedents of this system can be seen in the earlier texts.

Astronomical Siddh?ntas

In these standard texts of Indian astronomy, which became popular about two thousand years ago, the calculations are not done with respect to the nakshatras but rather with respect to the twelve signs of the zodiac. There is speculation that this change arose out of the interaction with the Greeks, but the twelve-division zodiac was a part of the early Indian astronomical tradition.

The mean longitudes were computed from the number of days elapsed from the beginning of long periods called the kalpa and the yuga, with the current yuga (Kaliyuga) having commenced on 17/18 February 3102 b.c. Planetary motions were computed using epicyclic and eccentric circles. Eclipses were computed more accurately by applying corrections due to parallax. Computations were based on arithmetic, geometric and algebraic techniques; plane and spherical trigonometry was also used.

The problems dealt with in the siddh?ntas include: the determination of the longitudes of the planets and also of the ascending and descending nodes of the moon; corrections of these computations with the passage of time; lunar and solar eclipses; problems relating to the shadow; the phases of the moon; helical rising and setting of the planets; occultation of stars and planets; and astronomical instruments.

The astronomical texts may be divided into three types: siddh?ntas, karanas, and koshthakas. While the siddh?ntas are comprehensive and commence the calculations from the kalpa or a yuga, the karanas are practical manuals to facilitate calculations from a specific epoch with zero corrections at that point. The koshthakas or saranis are astronomical tables for the casting of horoscopes by astrologers. There are also texts that focus only on instruments.

The prominent astronomers after ?ryabhata include his later rival Brahmagupta (seventh century), Bh?skara II (b. 1114), and the many mathematician-astronomers of the Kerala school that flourished during the years of the Karnataka (Vijayanagara) empire. The two most prominent names of this school are M?dhava (c. 1340–1425) and N?lakantha (c. 1444–1545). Their contributions include power series for trigonometric functions, demonstration that ? is irrational, and contributions to calculus. N?lakantha presented an improved version of the ?ryabhata's scheme in which the five planets orbit the sun and in turn they all orbit Earth.

Size of the Universe

The Br?hma?as consider noncircular motion of the sun and, by implication, of the moon, and the sun is taken to be about 500 Earth diameters away from Earth. Much later, ?ryabhata considers the orbit of the sky as 4.32 million times greater than the orbit of the sun. Clearly, this was inspired by cosmological ideas. The Pur??as consider the size of the universe to be 500 million yojanas (or over 4.5 billion miles). They also speak of other universes beyond ours. The conception of such a large size, and the noncentrality of Earth for the universe sets this tradition apart from Western astronomy.

Subhash Kak

See also?ryabhata ; ?ryabhat?ya ; Br?ma?as ; Upanishadic Philosophy ; Ved?nga Jyotishta

BIBLIOGRAPHY

Billard, Roger. L'Astronomie Indienne. Paris: École Française d'Extrême Orient, 1971.

Kak, Subhash. "Astronomy of the Vedic Altars." Vistas in Astronomy 36 (1993): 117–140.

——. "The Astronomy of the Age of Geometric Altars." Quarterly Journal of the Royal Astronomical Society 36 (1995): 385–396.

——. The Astronomical Code of the Rgveda. New Delhi: Munshiram Manoharlal, 2000.

——. "Birth and Early Development of Indian Astronomy." In Astronomy across Cultures: The History of Non-Western Astronomy, edited by H. Selin. Dordrecht: Kluwer Academic Publishers, 2000.

Rao, S. Balachandra. Indian Astronomy: An Introduction. Hyderabad: Universities Press, 2000.