Cai Yong
After the death of his father, Liu Hong retired for a short time but returned to his work, collaborating with Cai Yong on the "Qian Xiang Li" (乾象曆; "Qian Xiang Calendar"), this was considered so advanced for its time that it was adopted by the Han government immediately. The calendar predicted the movement of the moon, the first time such considerations had been made in ancient China. This system marked the first appearance of the argument of periapsis, a means to calculate syzygy (the calculation between three celestial bodies), and a means of charting the moon through the seasons. His means of establishing the accuracy of the calendar was by the detection of eclipses.