This thesis aims to elucidate the changing forms of engagement between Europeans and Indians in relation to astronomy in India between 1784 and 1876. It seeks to trace the evolving contexts in which knowledge of astronomy was developed and to provide a nuanced characterisation of the resultant cognitive interface between Europeans and Indians, focusing in particular on Bengal and Bombay. The defining features of this period saw Europeans exploring the history of Indian astronomy, before establishing observatories and colleges to foster modern Western astronomy, while Indians turned to rethink how the history of Indian astronomy (and astrology) fitted with modern science. Yet while recent historiographical interventions have drawn attention to the more philosophical forms of engagement, this thesis contends that such a concentration has elided a much more practical engagement between Europeans and Indians in relation to modern (Western) astronomy in India. This engagement was not about a constant process of Indians rationalising participation in modern science, or looking backwards while moving forwards. In addition, it was premised more on collaborative and experiential constructions of knowledge, without express awareness of fixed "Western" or "Indian" paradigms. There was evidence of such engagement in the observatory and in the field, as well as in certain college settings, and in some parts of India more than others. However, racialised colonial institutions and attenuated educational schemas could at length hinder such possibilities, leaving the spotlight on the more philosophical forms of engagement. This thesis hence aims to address a lacuna in the history of science in colonial India by reappraising the significance of astronomy during these years. Through drawing on a range of written texts and physical objects in relation to astronomy, as well as on inter-disciplinary perspectives, it seeks to reflect the heterogeneous nature of the Indian intellectual climate in the colonial period.