[논문]Analysis of Solar and Lunar Motions in the Seonmyeong Calendar

Lee, Ki-Won

doi:10.5140/jass.2019.36.2.87

Analysis of Solar and Lunar Motions in the Seonmyeong Calendar 원문보기

Journal of astronomy and space sciences, v.36 no.2, 2019년, pp.87 - 96

Lee, Ki-Won (Francisco College, Daegu Catholic University)

Abstract ▼ AI-Helper

We investigate solar and lunar motions in the Seonmyeong (SM) calendar that was compiled by Xu, Ang of the Tang dynasty (A.D. 618-907) in China and used for 71 years from 822 to 892. This calendar was also used in Korea during the Goryeo dynasty (A.D. 918-1392) and in Japan for 823 years from 862 to 1684, the longest time among the three countries. Referring to historical documents of China, Korea, and Japan, we analyze the calendrical methods of calculating the daily apparent movements of the Sun and Moon in the SM calendar, which were considered their unequal motions, and compare the movements with the results of modern calculations for three periods in the Goryeo dynasty: 919, 1155, and 1392 years (i.e., the beginning, middle, and ending of the dynasty, respectively). We find that a quadratic equation was employed to obtain the daily movement of the Sun using physical quantities on the instant of each solar term, which was tabulated in its calendar book such as the Goryeosa (History of the Goryeo Dynasty). For quantitative analysis, we compute the mean absolute difference (MAD) of the daily apparent movement between the SM calendar and modern calculations and obtain 0.33, 0.30, and 0.31 arcmin for the periods of 919, 1155, and 1392 years, respectively. Meanwhile, we find relatively large MAD values in the daily movement of the Moon: 0.217, 0.284, and 0.240 degrees for each corresponding year. An interesting point is that the MAD value in the lunar motion shows the maximum in 1155 years, and is the minimum in the solar motion. In conclusion, we believe that this study will facilitate in the understanding of the SM calendar further, particularly in the calendrical methods of calculating sunrise, sunset, and eclipse times.

주제어

표/그림 (7)

표 Table 1. Summary of astronomical constants in the SM calendar used in this study
표 Table 2. Ready reckoner in relation to the solar motion
표 Table 3. Ready reckoner in relation to the lunar motion
표 Table 4. Summary of the CJDJ (Cheonjeong-Dongji) instants of 919, 1155, and 1392 by the SM calendar and the perihelion passage times in those days by modern calculations
$Fig. 1. Differences in daily solar motion between the SM calendar, SSM, and modern calculations SMC: red solid, green dot, and blue short-dash lines represent the results for the periods of 919, 1155, and 1392, respectively. The horizontal axis is the elapsed dates since the CJDJ (Cheonjeong-Dongji) instant of each year and the vertical axis is <TEX>$S_{i}^{SM}$</TEX> (n) − <TEX>$S_{i}^{SM}$</TEX> (n ) i i S n S n in units of (modern) arcmin. The vertical dotted lines are the elapsed dates of the spring equinox, summer solstice, and autumn equinox, from left to right, since the CJDJ instant of each year.$ 그림 Fig. 1. Differences in daily solar motion between the SM calendar, S^SM, and modern calculations S^MC: red solid, green dot, and blue short-dash lines represent the results for the periods of 919, 1155, and 1392, respectively. The horizontal axis is the elapsed dates since the CJDJ (Cheonjeong-Dongji) instant of each year and the vertical axis is $S_{i}^{SM}$ (n) − $S_{i}^{SM}$ (n ) i i S n S n in units of (modern) arcmin. The vertical dotted lines are the elapsed dates of the spring equinox, summer solstice, and autumn equinox, from left to right, since the CJDJ instant of each year.
$Fig. 2. Differences in daily lunar motion between the SM calendar, MSM, and modern calculations, MMC : red solid, green dot, and blue short-dash lines represent the results for the periods of 919, 1155, and 1392, respectively. The horizontal axis is the day number since the instant of the apogee passage and the vertical axis is MSM (<TEX>$\bar{m}$</TEX>) −MMC (<TEX>$\bar{m}$</TEX>) in units of (modern) degrees, which are averaged over the 12 cycles of anomalistic month length for each day number.$ 그림 Fig. 2. Differences in daily lunar motion between the SM calendar, M^SM, and modern calculations, M^MC : red solid, green dot, and blue short-dash lines represent the results for the periods of 919, 1155, and 1392, respectively. The horizontal axis is the day number since the instant of the apogee passage and the vertical axis is M^SM ($\bar{m}$) −M^MC ($\bar{m}$) in units of (modern) degrees, which are averaged over the 12 cycles of anomalistic month length for each day number.
표 Table 5. Summary of the instants of CJAP (apogee passage immediately before the CJDJ) of 919, 1155, and 1392 by the SM calendar and the diferences with apogee passage times in those days by modern calculations

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문제 정의

However, the accuracy of the SM calendar has not been analyzed through comparison with modern calculations. The purpose of this study is to investigate the accuracy of the solar and lunar motions by the SM calendar. The remainder of this paper is structured as follows.

제안 방법

In this study, we analyzed the calendrical methods of solar and lunar motions in the SM calendar referring to the Xintangshu (New History of Tang Dynasty) of China, Goryeosa of Korea, and Senmyo (Senmyo Calendar) and Chokei-Senmyoreki-Sanpo (Calendrical Method for the Senmyo Calendar of the Chokei, shortly Sanpo) of Japan. With regard to Japanese literature, the former is preserved in the National Library of Korea and is known to be made of a Japanese woodblock in 1644 but the author is unknown.
, solar terms incurring the sign change in the value of AU% compared to each subsequent solar term). Subsequently, compute the following quantities: Ilcha (IC), Choryul (CR), Malryul (MR), Chojeongryul (CJR), and Maljeongryul (MJR).
Subsequently, we calculated the daily Moon movement during each anomalistic month length using the DE405 ephemeris. As indicated in Section 3.
To estimate the accuracy of the lunar motion in approximately one tropical year, we first determined 12 successive instants of the apogee passage in each year by accumulating the anomalistic month length to the CJAP instant. Subsequently, we calculated the daily Moon movement during each anomalistic month length using the DE405 ephemeris.

후속연구

In conclusion, we believe that this study will facilitate in the understanding of calendrical methods in the SM calendar, such as the sunrise and sunset times, eclipse times, and so forth.

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