A Study on the Calculation and Accuracy of Solar Eclipses in the Tibetan Shixian System ( rgya rtsis ): A Case Study of the Ma yang rgya rtsis snying bsdus

The Shixian System ( Shixian li 時憲曆) of the Qing dynasty is a calendrical framework that integrated traditional Chinese mathematical astronomy with Western astronomy. From the eighteenth century onward, it was introduced into the Tibetan regions in two forms: One is the imperially composed Tibetan translation Rgya rtsis chen mo , the others, the Tibetan-compiled Ma yang rgya rtsis snying bsdus series. This study focuses on the solar eclipse algorithms found in these two series of texts, focusing on their textual sources, numerical tables, and astronomical models. The Rgya rtsis chen mo derives its eclipse algorithms from the Suan qizheng jiaoshi lingfan fa 算七政交食淩犯法. A comparison between the earliest and latest version in the Tibetan Shixian system shows that the eclipse limit values and solar motion tables are derived from the Yuzhi lixiang kaocheng houbian 御製曆象考成後編, while the remaining numerical tables are sourced from the Yuzhi lixiang kaocheng biao 御製曆象考成表. The main procedures and astronomical models are based on the Yuzhi lixiang kaocheng 御製曆象考成. Therefore, the Tibetan Shixian system represents an adaptation of the Yuzhi lixiang kaocheng series. This study employs Python programming to simulate the moments of solar eclipses for the period between 1744 and 1844, the average errors for three phases of solar eclipses are approximately 40 minutes, and the mean error in eclipse magnitude is 0.12.