2018 marks the 400th anniversary of the controversy over the comets between Orazio Grassi and Galileo Galilei. The appearance of three comets in 1618 initiated a scientific and polemical exchange between the two. A central issue of the debate was the location of the comets, either above or below the lunar sphere, and the role of observational evidence in contemporary cosmology and natural philosophy. The debate over the comets had implications for the substance of the heavens, the existence of change and corruption in the celestial region, as well as the utility of mathematical demonstrations for natural philosophy. However, historians of science have not fully explored the religious, political and scientific import of this episode in the history of science. The most glaring omission in the historiography is the ease with which historians of science have glossed over Grassi’s final response the Galileo, his Ratio ponderum librae simbellae (1626 Paris, 1627 Rome), for example Drake and O’Malley excluded any translation of Grassi’s last response to Galileo and instead chose to include a translation of Kepler’s Hyperaspistes in their 1960 publication The Controversy on the Comets of 1618. In this paper I will explore the connections between the scientific, religious and political aspects of the controversy with special emphasis on its import for the history of Jesuit science and the role of the Society of Jesus in the development of early modern mathematics.and natural philosophy.