Indian astronomy and other countries

The astronomy of India was exchanged with other countries for a long period of time.

Indian astronomical ideas traveled to China, especially from 581-907 AD.

The Vedic calendar system was used in Nepal, Tibet, Thailand, Java, and elsewhere.

The Arabic astronomists of the Islamic caliphates, such as al-Khwārizmī, al-Ḥasan, al-Nairizi, and ibn aṣ-Saffar, were heavily influenced by Indian astrononmy. Caliph al-Mansūr personally ordered the translation of two of Brahmaguptas works, which became the Sindhind and the Arkand. It is through this channel that jyā became mangled in translation into Latin as 'sine', which it came to be known by in Europe. al-Baruni went to India circa the 1000s AD and wrote the famous T a'rikh al-Hind.

In the 1700s, Maharaj Sawai Jai Singh II consulted extensively with Jagannātha Samrāṭ on astronomical projects. Part of this involved Samrāṭ learning Arabic and Persian so that he could perform translations. Jai Singh also was in contact with Jesuit missionaries regarding matters astronomical. He also used a telescope which had been invented in Europe in the 1600s.

Pingree's periods
David Pingree, in his History of Indian Literature attempted to classify the periods of Indian astronomy as follows:

B. V. Subbarayappa, K. V. Sarma discuss Mr. Pingree's viewpoint in their work Indian Astronomy, emphasizing that Indian astronomy produced many of it's own innovations, and was not entirely based upon ideas imported from other cultures.