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Astronomy, with which Astrology and Mathematics (Ganita-sastra) are closely connected, was required both for Vedic sacrifices (dharma) as well as for various needs of practical life (kama). In the Jyotisha Vedanga preserved in two versions for the Yajurveda and Rigveda we find a calendar arranged on the basis of a five-year Yuga, with a 266 day year, and notices of the position of the sun and the moon at the solstices, and at new and full moon with regard to the Nakshatras. Some further development is found in works like the Garga-Samhita of which only fragments are extant, the Vridda-Girga-Samhiti, Weber Ms of Panshkarasadin, the Nakshatras and other Parisishtas of the Atharva Veda, the Paitamaha-Siddhanta recorded by Varahamihira, pradipa, Rasayamala, Rasa-kaumudi. Chemistry also forms part of medical and other texts like the Ashtanga.hridaya, Jogichara.bhu mi Sastra, Rasa nakshatra malika, Dhatu-ratna mali, Dhatu.kriya, Bhava prakasa, Anka-prakasa, samgadhara samgraha, etc,

the Jain Surya-prajnapti, the Epic, the Puranas, and the Smritis of Parasara and others. Varahamihira (550-587) preserved in his PanchaSiddhantika, the contents of five Siddhantas, viz. Paitamaha, Romaka (connected with Rome), Paulisa (probably associated with Paulus Alexandrinus), Surya (revealed by Surya to Asura Maya) and Vasistha. The Romaka-siddhanta of course need not be interpreted as an allusion to Rome, the knowledge probably came from Alexandria which was included in the Roman empire. The Romaka-Siddhanta adcpts a non-Indian Yuga system, viz., the Metonic period of nineteen years multiplied by 150 which gives the smallest Yuga exactly divisible into integral numbers of lunar months and civil days, and it makes calculations for the meridian of Yavanapura. The Paulisa Siddhanta does not adopt a constant Yuga but operates with specially constructed short periods of time and gives the difference in longitude between Yavanapura and Ujjain. The Surya-siddhanta accepts the Kalpa system and operates with sidereal revolutions of the sun as in the Paulisa Siddhanta but unlike the tropical revolutions in the Romaka-siddhanta. "It alone gives a general rule for the equation of the centre, and its full treatment of eclipses conforms with the meagre rules of the Romaka and the rough formulae of the PaulisaSiddhanta. The Vasishtha-siddhanta like the Paulisa has taken some note of planetary anomalies, though exactly what is uncertain". None of these five Siddhantas exist in their original form. A Brahmasiddhanta forms part of the Vishnu dharmottara-purana on which Brahmagupta's Spbuta Brahma siddhanta is based. The Sakalya-siddhanta presents the orthodox modern doctrine. The Romaka was touched by Lala (about 505) and revised drastically by Srisena. The Vasishtha Siddhanta was first revised by Vijaya. Nandin before Brahmagupta, and then by Vishnu-chandra. The Laghu Vasishtha Siddhanta is not connected with the original or the revision, and the Vriddha Vasishtha Siddhanta in Mss. seems equally far removed. The extant Suryasiddhanta in fourteen chapters of Vanas is modernised from the original possibly by Lala. The treatises of the famous Aryabhatta (476-499) of Kusumapura show great development in the field of Astronony and Mathematics.

His extant works include his Aryabhatiya in the Aryastanzas, Dasagitikasutra which mentions his numerical notation, and Aryashta-Sata of 108 verses which is divided into the section of Ganita (mathematics) in 33 verses, of Kilakriya (measurement) of time in 25 verses, and Gola (sphere) in 50 verses. His other works are lost. He is commended for the brevity and elegance of his composition. 'His is the first work to show a distinct chapter on mathematics in relation to astronomy and the division of Astronomical topics was effective." He held that the earth was a sphere and rotated on its axis, which was not approved by Varaha-mihira or Brahmagupta. He equated the four Yugas despite traditional difference of length. He ascribed elipses not to the operation of Rahu but to the moon and shadow of the earth. There was a second Aryabhatta who wrote the Arya-siddhanta (about 550) which differs in its numerical notation from the earlier Aryabhatta. The works of Simha, Pradyumna and Vijayanandin mentioned by Varahamihira appear to be lost The Pancha-siddhantika of Varahamihira is very important. He also declines to accept the conjunction of planets as explaining eclipses. Much more important was Brahmagupta of Billamalla near Multan, who wrote his Sphuta-siddhanta in 628, and in 665 he wrote the Khanda-kandyaka, a practical treatise (karana) giving materials for astronomical calculation which was based on a last work of Arya-bhatta. He is systematic and complete. He devotes one chapter to solving astronomical problems. Lalla came later and wrote the Sishya-dhivriddhi-tantra to increase the pupils' intelligence, which Was commented on by Bhaskara. The Raja-mriganka (1042), a Karana (practical) work, is ascribed to Bhoja, and the Bhavati, also a Karana, to Satananda (1099). The Siddhanta-siromani of Bhaskaracharya (1150) is divided into four parts, riz., the Lilavati and Bijaganita (algebra) devoled to mathematics, the Grahaganita on planets, and the Gola (sphere) dealing with astronomy proper. The Gola chapter contains a section on astronomical problems, a treatise on the astronomical instruments (? telescope, etc), and a description of the seasons. His Karana-kutuhula with practical instructions dates from 1178. Later came the more practical works like the tables.

of Tithyudipalin of Markanda (1478), and the Grahalaghava of Ganesa (1520). "The advent of Persian and Arabic influences has left Indian Astronomy unchanged, nor has it ever been extinguished by Western science" as declared by Professor A. B Keith. The unique achievements of the Hindus in Astronomy may be briefly summerized. Bhaskaracharya took in consideration the minuest time known as krati equalling 34,000 th part of a second. The Vedic sages knew that the Sun illuminates the Moon, and that the Moon comes back to the same position in its rotation after 27-28 th day. The month was counted of 30 days after noticing the number 30 of the Sun rise from one full or new moon to another full cr new moon. The year was counted of 365 days. But it was found out that 12 lunar months of 30 days each do not make up 365 days. Hence to maintain the accuracy between the lunar and the solar year they added a mala-masa at every 3 years. That the rotation of the earth causes the distinction between the day and the night was first discovered by Aryabhatta (950). Nearly a 1000 years later Coparnic discovered this in Eu one. Aryabhatta, who knew the causes of the solar and the lunar eclipses, declared that the moon and other planets have no light of their own and are illuminated by the Sun, that these planets like the earth rotate round the Sun, and that their path of rotation is not circular but epicycle or ellipe (dirghavritta). The circular shape of the earth is established by Bhaskaracharya by pointing that the dawn appears before the Sun rise. Bhaskaracharya and Brahmagupta have fixed the diameter of the earth at 15-1 and 1600 yojanas respectively. Taking one yojana of 3200 cubits or 911 miles the diameter of the earth is 7905 miles, which approximate the modern calculation of 7918 miles. The aerial extent over the earth calculated as 12 yojanas or 55 miles is almost the same as the modern calculation of 50 miles. Long before the discovery of the centre of gravity by Newton (1642-1727) it was stated in the Siddhanta-siromani of Bhaskaracharya (1150) that heavy things fall on earth on account of earth-attraction (madhyakarshana).' 1 A krishti saktis cha mahi taya yat khastham guru svabhi mukham sva-saktya akrishyate tat patati iva bhati.

It, therefore, means that the earth, planets, stars. moon, and sun attract each other and owing to mutual attraction each remains to its own orbit.