It is widely accepted that Indian mathematical astronomy changed drastically under the influence of Greek astronomy around the 3rd century CE. One of the points to be noted is that although Greek elements are evident in Sanskrit texts on astronomy, they all belong to the time before Ptolemy and nothing is found of the innovations initiated by him: for instance, the second anomaly of the moon, the ‘equant’ of the planetary model, and spherical trigonometry. Thus there were attempts to search for the origin of geometrical models of Indian astronomy in the Hellenistic astronomy before Ptolemy. But a paucity of documents has prevented satisfactory explanation of the link between the Mediterranean area and India. The first Sanskrit text that deals with planetary theory using geometrical models is the Āryabhaṭīya of Āryabhaṭa (born 476 CE). We regard this text as the endpoint of the long process of sanskritizing Greek astronomy. The planetary theory is found in the last eight verses of Chapter 3 (Kālakriyāpāda), where the basic units of time and the elements of calendar are described. In India the position of planets was a topic of calendar to be used for casting horoscopes. The text of the Āryabhaṭīya is expressed in very condensed verses and difficult to understand without the help of commentaries. The eight verses under discussion are also expressed in very terse wording and allow different kinds of interpretation. We took resort to the oldest surviving commentary by Bhāskara I written in 629 CE, although we are not very sure whether he conveyed the true meaning of Āryabhaṭa. It seems that he wanted to convince the reader by claiming that he was the true follower of Āryabhaṭa’s school. However, commenting on Āryabhaṭa’s planetary theory, Bhāskara refers to the opinion of ‘others’, showing that already in his time there were different interpretations. In the Indian planetary theory two epicycles play an essential role. They are called manda-vṛtta and śīghra-vṛtta and were used to explain eccentricity and anomalistic motion, respectively. It was also known that a manda epicycle produces the same result as an eccentric circle (pratimaṇḍala) . According to Bhāskara, these models are only upāyas (artificial means) by which to express reality. Upon this a question arises: how was the reality conceived and where were the true planets thought to be located? Another point of discussion is whether Indian astronomers could totally dismiss traditional cosmology.