Aryabhatta, the pioneer of astronomy

Aryabhatta

Aryabhatta or Aryabhatta I (476–550 CE) was the first of the major mathematician astronomers from the classical age of Indian mathematics and Indian astronomy. He was born in 476 in Ashmaka, the region between the Narmada and Godavari rivers in central India.

He went to Kusumapura (Pataliputra, modern Patna) for advanced studies and lived there for some time. He was the head of an institution (kulapa) at Kusumapura and might have been the head of the Nalanda University.

Works:

Aryabhatta is the author of several treatises on mathematics and astronomy, some of which are lost. His works include-

1.          Aryabhatiyam and
2.          Arya-siddhanta.
   

Aryabhatiyam:

The Aryabhatiyam is also known as Ashmakatantra (the treatise from the Ashmaka) and Arya-shatas-asta (literally, Aryabhata's 108). It was extensively referred to in the Indian mathematical literature. It presented a number of innovations in mathematics and astronomy in verse form, which were influential for many centuries. The extreme brevity of the text was elaborated in commentaries by his disciple Bhaskara I and by Nilakantha Somayaji in his Aryabhatiya Bhasya. The text consists of the 108 verses and 13 introductory verses, and is divided into four Pādas or chapters:

1. Gitikapada (13 verses): It consists of-

·         Large units of time which present a cosmology:

                                                                                i.            Kalpa

                                                                              ii.            Manvantra

                                                                            iii.            Yuga

·         A table of sines (Jya)

·         The duration of the planetary revolutions during a mahayuga, given as 4.32 million years.

2. Ganitapada (33 verses): It consists of-

·        Mensuration (Kṣetra vyāvahāra)

·         Arithmetic and geometric progressions

·         Gnomon / shadows (Shanku-Chhaya)

·         Simple, quadratic, simultaneous and indeterminate equations (Kuṭṭaka)

·         Trigonometry:

                                                                                i.          Sine (Jya)

                                                                              ii.            Cosine (Kojya)

                                                                            iii.            Versine (Utkrama-jya)

                                                                            iv.            Inverse sine (Otkram jya)

3. Kalakriyapada (25 verses): It consists of-

·         Different units of time

·         A method for determining the positions of planets for a given day,

·         Calculations concerning the intercalary month (Adhikamasa, Kshaya-tithis)

·         A seven-day week with names for the days of week

4. Golapada (50 verses): It consists of-

·         Geometric/trigonometric aspects of the celestial sphere

·         Features of the ecliptic, celestial equator, node

·         Shape of the earth

·         Cause of day and night

·         Rising of zodiacal signs on horizon

·         A few colophons

Arya-siddhanta:

The Arya-siddhanta, a lost work on astronomical computations, is known through the writings of Aryabhata's later mathematicians including Varahamihira, Brahmagupta and Bhaskara I. This work appears to be
 based on the older ‘Surya Siddhanta’ and uses the midnight
-day reckoning, as opposed to sunrise in Aryabhatiya. It also contained a description of several astronomical instruments:

1.   The gnomon (Shanku-yantra)
2.   A shadow instrument (Chhaya-yantra)
3.  Angle-measuring devices:

a.      Semicircular(Dhanur-yantra)

b.      Circular (Chakra-yantra)

·            4.  A cylindrical stick (Yasti-yantra)

·         5. An umbrella-shaped device (Chhatra-yantra)

·         6. Water clocks of two types:

                                                  i.            Bow-shaped and

                                                           ii.            Cylindrical.

Contributions of Aryabhatta in Mathematics & Astronomy:

1.             Aryabhatta worked out the value of pi.
2.           He worked out of the area of triangle. His wrote that “for a triangle, the result of a perpendicular with the half side is the area.”
3.             He discussed the idea of sin.
4.             He worked on the summation of series of squares and cubes (square-root and cube-root).
5.            He talks about the “rules of three” which is to find the values of x when three numbers a,b and c is given.
6.            Aryabhatta calculates the volume of a sphere.
7.        He described the model of the solar system, where the sun and the moon are each carried by epicycles that in turn revolve around the earth. He also talks about the number of rotations of the earth, describes that the earth rotating on its exis, the order of the planets in terms of distance from earth.
8.            He described the solar and lunar eclipse scientifically.
9.            He describes that the moon and the planets shine by light reflected from the sun.
10.         He calculated the sidereal rotation which is the rotation of the earth with respect to the stars as 23 hours, 56 minutes and 4.1 seconds.
11.          He calculated the lenth of the sidereal year as 365 days, 6 hours, 12 minutes and 30 seconds. The actual value shows that his calculation was an error of 3 minutes and 20 seconds over a year.

Honours for Aryabhatta:

• India's first satellite named after Aryabhatta.
• An Institute for conducting research in astronomy, astrophysics and atmospheric sciences is the Aryabhatta Research Institute Of Observational Science (ARIES) near Nainital, India.
• The inter-school Aryabhatta Math Competition is also named after him.
• Bacillus aryabhata, a species of bacteria was discovered in the stratosphere by ISRO scientists in 2009 and named after him. ,,

       I.