There are very many references to the Sun, Moon, stars, planets, meteors, etc., in Vedic literature before 1500 BCE. The Sun is the Lord of the universe, and the Moon shines by the Suns light. The Earth is described as a sphere.

Even casual observations of the sky would reveal that there are three clear time-markers in the sky, namely, a day, a lunar month and a year. All the major civilisations tried to understand the correlations among these time units. A verse in Rigveda says: The wheel (of time) formed with 12 spokes, revolves round the heavens, without wearing out. O Agni, on it are 720 sons (that is, days and nights).

So, a year has 12 months and 360 days. Later in Taittireeya Samhitaa, there is a clear mention of a solar year of 365 days. The names of the 12 months are given in this Samhitaa as: Madhu, Maadhava, Shukra, Shuci, Nabhas, Nabhasya, Isha, Urjaa, Sahas, Sahasya, Tapas and Tapasya. Now a lunar month is nearly 29.5 days, and 12 lunar months make 354 days. To align the lunar months and the solar year, there would be an extra intercalary month or adhika maasa called samsarpa in some years.

In the Rigveda, it is stated that God Varuna charted a broad path for the Sun in the sky. This obviously refers to the ecliptic, which is the path of the apparent motion of the Sun around the Earth in the sky, in the stellar background. It is inclined to the celestial equator, which is a large circle in the sky in the plane of Earths equator. This is depicted in the picture above.

Here S1, S3 are the equinoxes, S2 is the summer solstice, and S4 is the winter solstice. Vedic literature describes the apparent half-yearly northern (Uttaraayana; from S4 to S2), and southern (Dakshinaayana; from S2 to S4) motions of the Sun, and equinoxes in Taittireeya Samhitaa, Aitareya Braahmana and other texts.

The Moons sidereal period is nearly 27 days, and its path is only slightly inclined to the ecliptic. Then it is convenient to divide the ecliptic into 27 equal parts called nakshatras. This concept is essentially Indian, and the names of the 27 nakshatras, Ashvini, Bharani, ... Revati are also listed in the Taittireeya Samhitaa. The Samhitaa also refers to a five-year yuga cycle, wherein the Sun and the Moon return together at the same position in the sky after five years. All in all, there are rudiments of a calendar with 12 months in a year, inclusion of intercalary months appropriately, and 27 nakshatras as markers of the Moons movement. But it is not formulated mathematically and there are no clear rules.

It is in Vedaanga Jyotisha, ascribed to sage Lagadha, that we have a quantitative calendrical system, with a five-year yuga. One of the verses in it says: When the Sun and Moon occupy the same region of the zodiac together with the asterism of Vaasava (Shravishthaa), at that time begins the yuga, the synodic month of Maagha, the solar month called Tapas, the bright fortnight (of Maagha) and their northward course (Uttaraayana). So, winter solstice is at the beginning of Shravishthaa (Delfini) constellation. This corresponds to some time between 1370 BCE and 1150 BCE, though the text could have been composed a little later.

In the Vedaanga Jyotisha calendar, one has a yuga with five years, 60 solar months, 62 lunar months and 1,830 civil days. There are two adhikamaasas in five years. The concept of a tithi, which is 1/30 of a lunar month, is mentioned, perhaps for the first time. Vedaanga Jyotisha is the first text in India to give simple arithmetical algorithms in calendrical astronomy for finding tithi, nakshatra, the positions of the Sun and the Moon in the sky, and so on. There is nothing on planetary motion.

Compared to the actual value of 365.2564 days for a sidereal year, the Vedaanga Jyotisha value is 366 days. It has been suggested that this was for ease of calculations, with corrections introduced appropriately.

The Vedaanga Jyotisha gives a formula for the duration of day time (sunrise to sunset), according to which it is 12, 15 and 18 muhoortas, when the Sun is at the winter solstice, equinox and summer solstice respectively (one muhoorta is 48 minutes). The formula is reasonably correct for a latitude around 28.

The Kaatyaayana Sulbasutra (composed around 5th century BCE) describes the determination of the east and west directions from the shadows of a gnomon. Data for the annual and diurnal variations of a gnomon-shadow, given in Arthashastra and many Jaina and Buddhist texts around 300 BCE, seem to be based on observations. Recent research indicates that an eclipse cycle of nearly 18 years was in vogue even before the Vedaanga Jyotisha.

There is a long gap between 300 BCE and Aryabhateeya, the first extant text on full-fledged mathematical astronomy in India, composed in 499 CE. However, there were 18 siddhaantas earlier, five of which were summarised in Varaahamihiras Pancasiddhaantikaa composed around 520 CE. Exciting research on pre-Aryabhatan astronomy is going on.

M S Sriram

Theoretical Physicist & President,Prof. K.V. Sarma Research Foundation

(This is the fourth article in the series on Indias contributions to science and technology)

(sriram.physics@gmail.com)

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The wheel with 12 spokes: Astronomy in ancient India - The New Indian Express