[논문]Dating the Stars in the Calendrical Method Shoushili of the Yuan Dynasty

Sang-Hyeon Ahn

doi:10.5303/jkas.2023.56.2.137

[국내논문] Dating the Stars in the Calendrical Method Shoushili of the Yuan Dynasty 원문보기

Journal of the Korean astronomical society = 천문학회지, v.56 no.2, 2023년, pp.137 - 147

Sang-Hyeon Ahn (Theoretical Astronomy Center, Korea Astronomy and Space Science Institute)

Abstract ▼ AI-Helper

Shoushili was the official calendrical method promulgated in 1280 CE by the Yuan dynasty. It contains a list of the angular spans in right ascensions for the 28 lunar lodges. They are known to have been measured by Guo Shoujing with his advanced instruments with an unprecedented precision or reading error of 5'. Such precise data are useful to determine their observational epoch with an error range which is narrow enough to pinpoint on which historical occasion they were observed. Using the precise SIMBAD data based on eDR3 of GAIA and carefully identified determinative stars and considering the precession of equinoxes and proper motions, we apply linear regression methods to those data and obtain the observational epoch of 1271 ± 16 CE and the measurement error of 4.1'. We also have polar distances corresponding to declinations written in another manuscript of the Ming dynasty. Since the two data sets have similar significant digits, they were suggested to have the same origin. However, we obtain their observational epoch of 1364±5 CE and the measurement error of 5.7'. They must have been measured with different instruments and on a different occasion from the observations related to Shoushili. We review the history of the calendrical reform during the 13th century in the Yuan dynasty. We conclude that the observational epoch obtained from lodge spans in Shoushili agrees with the period of observations led by Guo Shoujing or 1276-1279 CE, which is also supported by the fact that the ecliptic lodge span values listed in Shoushili were calculated from the equatorial lodge spans.

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표/그림 (5)

표 Table 1. Lodge spans in Shoushili and Polar distances in San Yuan Lie She Ru Xiu Qu Ji Ji for the 28 lunar lodges.
표 Table 2. Results of linear regressions for the lodge spans in Shoushili and polar distances in San Yuan Lie She Ru Xiu Qu Ji Ji for 28 lunar lodges.
그림 Figure 1. Results of linear regressions for the lodge spans in Shoushili. The equatorial circumference is assumed to be 365.2575 du. Discarding three outliers, we obtain the observational epoch 𝑡_o = 1271.07 ± 15.97 and the measurement error in lodge spans 𝜎_L = 4.1'. In the middle panel, 1𝜎_L and 2𝜎_L measurement-error bars are shown as dashed and dotted lines, respectively. The three outliers are plotted as open dots.
그림 Figure 2. Results of linear regression analyses for the polar distances of the 28 determinative stars listed in San Yuan Lie She Ru Xiu Qu Ji Ji. The equatorial circumference is assumed to be 365.2575 du. Removing four outliers, we obtained the observational epoch t_o±𝜎_t = 1363.88 ± 4.95, the measurement error 𝜎_𝛿5.7', and the Y-intercept or the misalignment error A = 1.8'. The dashed and dotted lines in the middle panel show 1𝜎_𝛿 and 2𝜎_𝛿 measurement-error bars, respectively. The four outliers are plotted with open dots.
표 Table A.1. Six stars inserted in Ling Tai Mi Yuan as complements to the omissions.

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