Investigating calendrical methods of calculating sunrise and sunset times in the Shixian calendar.

This article focuses on the Shixian calendar, a Chinese calendar influenced by Western astronomy and mathematics, implemented during China’s Qing dynasty (1636–1912) and Korea’s Joseon dynasty (1392–1910). It analyzes the astronomical and mathematical methods used in the Shixian calendar, particularly those detailed in the 1724 treatise *Yuzhi lixiang kaocheng* (Thorough Investigation of Calendrical Astronomy Imperially Composed), for calculating sunrise and sunset times. The study finds that the calendar employed measurements of latitude via Polaris observations and accounted for the Sun’s diurnal parallax, while using Western trigonometric functions and spherical triangle properties, supported by detailed trigonometric tables. Comparing calculated times with those recorded in Chinese and Korean Shixian almanacs reveals changes in the values of latitude and obliquity of the ecliptic used over time, with distinct shifts around 1726 in China and 1728 in Korea, as well as differences in the dates on which sunrise and sunset times were recorded. This research enhances understanding of the Shixian calendar’s computational methods and its historical application in East Asian calendrical almanacs.