Aryabhata's system of astronomy was called the audAyaka system, in which days are reckoned from uday, dawn at lanka or "equator". Some of his later writings on astronomy, which apparently proposed a second model (or ardha-rAtrikA, midnight) are lost but can be partly reconstructed from the discussion in Brahmagupta's khanDakhAdyaka. In some texts, he seems to ascribe the apparent motions of the heavens to the Earth's rotation.

Mosi sistem suria

Aryabhata appears to have believed that the earth rotates about its axis. This is indicated in the statement, referring to Lanka , which describes the movement of the stars as a relative motion caused by the rotation of the earth:

"Like a man in a boat moving forward sees the stationary objects as moving backward, just so are the stationary stars seen by the people in Lanka (or on the equator) as moving exactly towards the west." [achalAni bhAni samapashchimagAni – golapAda.9]

But the next verse describes the motion of the stars and planets as real movements: "The cause of their rising and setting is due to the fact that the circle of the asterisms, together with the planets driven by the provector wind, constantly moves westwards at Lanka."

As mentioned above, Lanka (lit. Sri Lanka) is here a reference point on the equator, which was the equivalent of the reference meridian for astronomical calculations.

Aryabhata described a geocentric model of the solar system, in which theSun and Moon are each carried by epicycles. They in turn revolve aroundthe Earth. In this model, which is also found in the Paitāmahasiddhānta (ca. CE 425), the motions of the planets are each governed by two epicycles, a smaller manda (slow) and a larger śīghra (fast).[22] The order of the planets in terms of distance from earth is taken as: the Moon, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the asterisms."[3]

The positions and periods of the planets was calculated relative to uniformly moving points. In the case of Mercury and Venus, they move around the Earth at the same speed as the mean Sun. In the case of Mars, Jupiter, and Saturn, they move around the Earth at specific speeds, representing each planet's motion through the zodiac. Most historians of astronomy consider that this two-epicycle model reflects elements of pre-Ptolemaic Greek astronomy.[23] Another element in Aryabhata's model, the śīghrocca, the basic planetary period in relation to the Sun, is seen by some historians as a sign of an underlying heliocentric model.[24]

Gerhana

Aryabhata states that the Moon and planets shine by reflected sunlight. Instead of the prevailing cosmogony in which eclipses were caused by pseudo-planetary nodes Rahu and Ketu, he explains eclipses in terms of shadows cast by and falling on Earth. Thus, the lunar eclipse occurs when the moon enters into the Earth's shadow (verse gola.37). He discusses at length the size and extent of the Earth's shadow (verses gola.38–48) and then provides the computation and the size of the eclipsed part during an eclipse. Later Indian astronomers improved on the calculations, but Aryabhata's methods provided the core. His computational paradigm was so accurate that 18th century scientist Guillaume Le Gentil, during a visit to Pondicherry, India, found the Indian computations of the duration of the lunar eclipse of 1765-08-30 to be short by 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.[3]

Aryabhata's computation of the Earth's circumference as 39,968.0582 kilometres was only 0.2% smaller than the actual value of 40,075.0167 kilometres. This approximation was a significant improvement over the computation by Greek mathematician Eratosthenes (c. 200 BCE), whose exact computation is not known in modern units but his estimate had an error of around 5–10%.[25][26]

Tempoh sidereal

Considered in modern English units of time, Aryabhata calculated the sidereal rotation (the rotation of the earth referencing the fixed stars) as 23 hours, 56 minutes, and 4.1 seconds; the modern value is 23:56:4.091. Similarly, his value for the length of the sidereal year at 365 days, 6 hours, 12 minutes, and 30 seconds is an error of 3 minutes and 20 seconds over the length of a year. The notion of sidereal time was known in most other astronomical systems of the time, but this computation was likely the most accurate of the period.

Heliosentrisme

As mentioned, Aryabhata claimed that the Earth turns on its own axis, and some elements of his planetary epicyclic models rotate at the same speed as the motion of the Earth around the Sun. Thus, it has been suggested that Aryabhata's calculations were based on an underlying heliocentric model, in which the planets orbit the Sun.[27][28] A detailed rebuttal to this heliocentric interpretation is in a review that describes B. L. van der Waerden's book as "show[ing] a complete misunderstanding of Indian planetary theory [that] is flatly contradicted by every word of Aryabhata's description."[29] However, some concede that Aryabhata's system stems from an earlier heliocentric model, of which he was unaware.[30] It has even been claimed that he considered the planet's paths to be elliptical, but no primary evidence for this has been found.[31] Though Aristarchus of Samos (3rd century BCE) and sometimes Heraclides of Pontus (4th century BCE) are usually credited with knowing the heliocentric theory, the version of Greek astronomy known in ancient India as the Paulisa Siddhanta (possibly by a Paul of Alexandria) makes no reference to a heliocentric theory.