Timeline Aryabhata: Pioneer of Indian Astronomy

Aryabhata: Pioneer of Indian Astronomy 18

• 476 Aryabhata is born Birth year inferred from his own statement in the Aryabhatiya Aryabhata states that he was 23 when 3,600 years of the Kali Yuga had passed, which corresponds to 499 CE and gives a birth year of 476. His birthplace is uncertain, with Kusumapura (near Pataliputra) and Ashmaka both proposed.
• 499 Aryabhata calculates the Earth's sidereal rotation period About 23 hours, 56 minutes and 4.1 seconds His figures for the Earth's rotation give a sidereal day of about 23 hours, 56 minutes and 4.1 seconds. This is very close to the modern value.
• 499 Aryabhata calculates the length of the sidereal year 365 days, 6 hours, 12 minutes and 30 seconds Aryabhata gives the sidereal year as 365 days, 6 hours, 12 minutes and 30 seconds, about 3 minutes longer than the modern value.
• 499 Aryabhata composes the Aryabhatiya A compact treatise of 121 verses on mathematics and astronomy At the age of 23, Aryabhata completed the Aryabhatiya in Sanskrit verse. It has four sections, the Gitikapada, Ganitapada, Kalakriyapada and Golapada.
• 499 Aryabhata describes the kuttaka method A recursive procedure for linear indeterminate equations Aryabhata gives the kuttaka, or pulverizer, a method for solving linear Diophantine equations. It is closely related to the Euclidean algorithm.
• 499 Aryabhata divides time into Yugas and dates the Kali Yuga A Mahayuga of 4,320,000 years used as the basis for planetary cycles Aryabhata uses a Mahayuga of 4,320,000 years as the basis for his planetary revolution numbers. He also dates his work by the 3,600 years elapsed since the start of the Kali Yuga.
• 499 Aryabhata explains eclipses as shadows Eclipses attributed to the Earth's and Moon's shadows rather than a demon Aryabhata explains lunar eclipses as the Moon entering the Earth's shadow and solar eclipses as the Moon's shadow falling on the Earth. He gives methods for computing them.
• 499 Aryabhata gives an accurate approximation of pi The circumference of a circle with diameter 20,000 is given as 62,832 In the Aryabhatiya, Aryabhata gives the ratio of circumference to diameter as 62,832 to 20,000, or 3.1416. He describes the value as approximate.
• 499 Aryabhata gives methods for square and cube roots Root extraction in a place-value system The Aryabhatiya explains procedures for extracting square and cube roots. They depend on the decimal place-value structure of numbers.
• 499 Aryabhata gives rules for sums of series Formulas for sums of squares and cubes of natural numbers The Ganitapada gives rules for the sums of arithmetic progressions and for the sums of squares and cubes of the natural numbers.
• 499 Aryabhata models planetary motion with epicycles Planetary positions computed with epicycles and eccentric circles Aryabhata computes planetary positions with a system of epicycles. His model is a geometric tool for calculating the planets' motion across the sky.
• 499 Aryabhata presents a table of sines Sine differences given at 3.75-degree intervals The Aryabhatiya contains a table of sine differences at intervals of 3.75 degrees. This is among the earliest surviving sine tables, and Aryabhata called the function jya.
• 499 Aryabhata presents spherical astronomy in the Golapada Geometry of the celestial sphere and the Earth The Golapada, the last section of the Aryabhatiya, applies spherical geometry to the celestial sphere, the Earth and the motions of heavenly bodies.
• 499 Aryabhata proposes that the Earth rotates on its axis Daily motion of the stars explained by a spinning Earth Aryabhata states that the apparent westward motion of the stars is caused by the Earth rotating. He compares it to a person in a boat who sees stationary objects moving backward.
• 499 Aryabhata sets out his alphabetic numeration in the Gitikapada Letters used to encode large numbers in a place-value scheme In the opening section of the Aryabhatiya, Aryabhata encodes numbers with Sanskrit syllables in a place-value system. He uses it to state astronomical constants compactly in verse.
• 499 Aryabhata states that the Moon shines by reflected sunlight The Moon and planets are lit by the Sun The Aryabhatiya says that the Moon and the planets shine by reflected sunlight. This is correct and was a clear break from older explanations.
• 499 Aryabhata states the area of a triangle Plane geometry in the Ganitapada Aryabhata gives the area of a triangle as half the base multiplied by the height. The Ganitapada also treats the areas of other plane figures and shadow problems.
• 550 Aryabhata dies Traditional estimate of about 550 CE Aryabhata is traditionally said to have died around 550 CE, though the exact date and place are not recorded. His work became the foundation of an Indian school of astronomy.