魏晋时期行星算法及精度分析

Planetary Theory and Its Accuracy in the Uranic Manifestation System and Luminous Inception System of Wei and Jin Periods

曹魏天文学家杨伟所制《景初历》,自魏明帝景初元年(237)开始,沿用至刘宋元嘉二十一年(444)。据《晋书·律历志》载,西晋末“永嘉南渡”(307)后,《景初历》五星算法逐渐粗疏,东晋初便用《乾象历》推五星算法替代了《景初历》的推五星术。在详细释读《乾象历》和《景初历》行星算法基础上,利用Python语言模拟这两部历法中的行星算法,讨论了两部历法307—336年的行星计算精度。结果表明,永嘉南渡后三十年,《景初历》行星计算精度均要优于《乾象历》,这一结果与《晋书·律历志》所载并不相符。

Luminous Inception System produced by Yang Wei,an astronomer from Wei Period,has been in use since the first year of Ching Chu in 237 and has been in use until the 21st year of Yuanjia in Liu Song Period(444).According to the Treatise on mathematical harmonics and astronomy of the Jin Book,after the incident of“Yongjia Nandu”(307)at the end of Western Jin Dynasty,the planetary theory in the Luminous Inception System was gradually deficient,and the planetary theory in the Uranic Manifestation System was used to replace the planetary theory in the Luminous Inception system at the beginning of Eastern Jin Dynasty.In this paper,Python language was used to simulate the planetary theory in the two systems,and in the errors of calculating the planetary position in the first 30 years and307-336 years of the two systems were discussed.The results show that the error of calculating the planetary position in the Luminous Inception System is smaller than that in the Uranic Manifestation System,whether at the early stage of the promulgation of the two calendars or thirty years after Yongjia’s southern crossing.