ANALYSIS OF THE LUNAR ECLIPSE RECORDS FROM THE GORYEOSA

Abstract

In this paper, we study the lunar eclipse records in the Goryeosa (History of the Goryeo Dynasty), an official history book of the Goryeo dynasty (A.D. 918 - 1392). In the history book, a total of 228 lunar eclipse accounts are recorded, covering the period from 1009 to 1392. However, we find that two accounts are duplications and four accounts correspond to no known lunar eclipses around the dates. For the remaining lunar eclipses, we calculate the magnitude and the time of the eclipse at different phases using the DE406 ephemeris. Of the 222 lunar eclipse accounts, we find that the minimum penumbral magnitude was 0.5583. For eclipses which occurred after midnight, we find that some accounts were recorded on the day before the eclipse, like the astronomical records of the Joseonwangjosillok (Annals of the Joseon Dynasty), while others were on the day of the lunar eclipse. We also find that four accounts show a difference in the Julian dates between this study and that of Ahn et al., even though it is assumed that the Goryeo court did not change the dates in the accounts for lunar eclipses that occurred after midnight. With regard to the contents of the lunar eclipse accounts, we confirm that the accounts recorded as total eclipses are accurate, except for two accounts. However, both eclipses were very close to the total eclipse. We also confirm that all predicted lunar eclipses did occur, although one eclipse happened two days after the predicted date. In conclusion, we believe that this study is very helpful for investigating the lunar eclipse accounts of other periods in Korea, and furthermore, useful for verifying the calendar dates of the Goryeo dynasty.

1. INTRODUCTION

Many astronomical phenomena are recorded in Korean history books such as the Samguksagi (History of the Three Kingdoms), the Goryeosa (History of the Goryeo Dynasty), and the Joseonwangjosillok (Annals of the Joseon Dynasty). In addition, it is well known that astronomical accounts are useful for verifying the contents of such history books, for studying historical astronomical phenomena, and so forth. In particular, a historical solar eclipse is a powerful tool for estimating the first day in a lunisolar calendar, allowing the conversion of a lunisolar calendar date into a modern calendar one (e.g., Ahn et al. 2009a), and for studying the variation in the length of the day (e.g., Stephenson 2007), because the event takes place during the new moon, has a short duration, and, most importantly, can be accurately reproduced. However, a solar eclipse phenomenon is significantly dependent on the location of the observer. Therefore, it is important to have information about the observer’s location, usually the capital of a dynasty, when utilizing these historical solar eclipse accounts.

A lunar eclipse occurs when the Moon passes through the Earth’s shadow. The shadow cast by the Earth is composed of two cone-shaped components: penumbral and umbral shadows where the Earth blocks part and all of the sunlight, respectively, from reaching the Moon. Compared with a solar eclipse, a lunar eclipse takes place at full Moon, has a relatively longer duration, and is less dramatic. On the other hand, the circumstance of a lunar eclipse phenomenon is the same over all parts of the Earth provided that the Moon is visible. However, in the case of a penumbral eclipse, there is no distinct change during the process of the eclipse except that the Moon turns slightly red. Presumably due to these reasons, relatively little attention has been paid to historical lunar eclipse records compared with solar eclipse records. With regard to the study of the Korean historical lunar eclipse record, Stephenson (2008) investigated historical eclipses, including the period of the Goryeo dynasty. However, because he focused on estimating a ΔT (i.e., the difference between dynamical time and universal time: TD – UT) value, the lunar eclipse accounts of the Goryeo dynasty without an observation time were not utilized. Very recently, Lee et al. (2012b) studied the system of night hours using lunar eclipse accounts, but used the accounts of the Joseon dynasty in that work.

In this study, we analyze the the lunar eclipse accounts recorded in the Goryeosa based on modern astrodynamic calculations. This paper is organized as follows. In Section 2, we discuss the lunar eclipse accounts of the Goryeosa and describe the modern calculations for these eclipses. We present the results in Section 3 and summarize our findings in Section 4. In Appendix A, we present the full catalog of all lunar eclipses recorded in the Goryeosa.

 

2. LUNAR ECLIPSES

2.1. Goryeosa Accounts

We surveyed lunar eclipse accounts from the Goryeosa and compared them with the database of Korean historical astronomical records provided by the Korea Astronomy and Space Science Institute (hereafter, KASI). The KASI database lists the lunar eclipse accounts of the Goryeo dynasty together with other historical documents such as the Goryeosajeolyo (Abridged History of the Goryeo Dynasty, shortly Jeolyo), the Jeungbomunheonbigo (Revised and Enlarged Edition of the Reference to Old Books, shortly Bigo), and so forth. However, we found that the eclipse accounts recorded in this other literature are also all included in the Goryeosa. In addition, we found that three accounts from the year 1134 that are classified as lunar eclipse events in the KASI database are not eclipse phenomena but occultation ones, and one account from the year 1154 is omitted. Hence, there are a total of 228 lunar eclipse accounts from the Goryeo dynasty. The first lunar eclipse account appeared in 1009, approximately 90 years after the Goryeo dynasty was established, and the last one appeared in 1392, the year the dynasty fell.

The Goryeo court had adopted Chinese lunisolar calendars, and in the Goryeosa the day is recorded with sexagenary cycles, similar to other historical documents. In this paper, we express the cycles using an Arabic number together with the symbol #, following the work of Lee et al. (2012a). As an example, day #06 refers to the 6th of the sixty sexagenary cycles. We refer to the works of Han (1987, 2001) and Ahn et al. (2009b) to determine the Julian calendar date that corresponds to the lunisolar calendar date from the Goryeosa account.

Of the 228 lunar eclipse accounts, we find that nine accounts have a difference of more than three days from the known Julian date for the lunar eclipse; we summarize those accounts in Table 1. In the table, columns 1, 2, and 3, and 4, 5, and 6 are the lunisolar calendar dates from the Goryeosa and the Julian calendar dates from Ahn et al. (2009b), respectively. Throughout this study, all dates are given in units of the Julian calendar, except for those expressed using the sexagenary cycles (i.e., the Arabic number together with the symbol #), unless otherwise mentioned. In the seventh column, we present our classification of the event according to the characteristics of the account: Class I and II are the cases in which no eclipse occurred around the determined Julian date and a typographical error in the date is suspected, respectively, and Class III is the case where the recorded date is different by a few days from the date of calculated lunar eclipse. In the last column, we include notes relating to the content of the account.

Table 1Summary of lunar eclipse accounts showing over three days difference in date compared with known lunar eclipses

In Class I, the first day of 1106 March is #30 (Ahn et al. 2009b), hence #37 is the 8th day. However, there is a large difference in time between this day and the full moon day, in general the 15th or 16th day in the lunisolar calendar.

In the first Class II case, the account from 1030 February #05 states that a lunar eclipse was expected but did not occur; however, there is no #05 day in February of that year. On the other hand, the account from 1030 April #22 states that “According to last year (i.e., 1029) almanac of the Song dynasty, December was Daejin (Large Month, i.e., a month with 30 days) but it was Sojin (Small Month, i.e., a month with 29 days) in our almanac. In addition, a lunar eclipse was predicted for January 15th of this year but did not occur”. The sexagenary cycle of 1030 January 15 (i.e., 1030 February 19) is #05. Due to the similarity in the content and the agreement in the sexagenary cycle, we believe that 1030 February #05 is a typo for 1030 January #05. In addition, it is known that 1029 December was Sojin in the Song dynasty (Hung 2004) and that there was a total lunar eclipse on the next day (i.e., 1030 February 20) in units of UT.

With regard to the other Class II cases, the accounts of 1120 August #19 and 1122 August #29, we suggest that these may be typos for 1120 September #49 (1120 October 8), one month later, and for 1122 August #39 (1122 September 18), ten days later, respectively. The lunar eclipse of 1120 September #49 is also recorded in the Goryeosa. Therefore, according to this study, the lunar eclipses on 1030 February #05 and 1120 August #19 are duplications of those on 1030 January #05, stated in the account of 1030 April #22, and 1120 September #49, respectively. Considering the possibility of additional typographical errors, we would like to point out that the dates of the Class I accounts from 1291 May #48 and 1294 September #59 may contain errors in the recorded month and thus in fact be typos for two months later accounts, specifically, 1291 July #48 (1291 August 11) and 1294 November #59 (1294 December 4), even though the former dates are classified as cases with no eclipses in this study. There were lunar eclipse events on the latter dates and the events were observable in the Goryeo dynasty.

Finally, for the accounts of 1078 June #51 and 1082 October #7 in Class III, we believe that the dates should be 1078 July 27 and 1082 November 8, respectively, in the Julian calendar.

2.2. Modern Calculation

We calculated the times of the lunar eclipses based on the algorithms of Liu & Fiala (1992) and Meeus (1998) but using the DE406 ephemeris of Standish et al. (1997). The type of the lunar eclipse depends on the radii of penumbra (fp) and umbra (fu), which are given by

where πs and πm are the solar and lunar parallaxes, respectively, and rs is the radius of the Sun. If we denote L as the apparent separation of the centers of the Moon and the antisolar point and rm as the lunar radius, then the conditions for each lunar eclipse type are as follows:

In practice, however, the atmosphere and non-sphericity of the Earth have an effect on lunar eclipses. Hence, we adopted the lunar parallax adjusted by Danjon (1951) , πs, which is given by (1+1/85−1/594)πs. For further details on lunar eclipse calculations, see the works of Liu & Fiala (1992) and Urban & Seidelmann (2013).

According to our calculations, there were a total of 1160 lunar eclipses across the world during the period of the Goryeo dynasty, i.e., from 918 to 1392. To verify our calculations, we compared the eclipse times from this study with those provided by the NASA1, in units of TD. We found that the average differences are 8.45 ± 0.11 s for the time of greatest eclipse and −0.78 ± 0.02 and −4.78 ± 0.17 s in the durations of the penumbral and partial phases, respectively. However, according to this study the lunar eclipse on 1001 March 12 was a total one with a duration of 2.4 min, but it is classified as a partial one in the NASA lunar eclipse catalog. Except for this eclipse, we found that the average difference in the duration of the totality is −5.38 ± 0.30 s. We believe that these differences are likely caused by the adoption of different ephemerides. It is known that the times in the NASA catalog are derived using the VSOP87 (Bretagnon & Francou 1988) and ELP 2000-82 (Chapront-Touzé & Chapront 1983) ephemerides for the Sun and the Moon, respectively, whereas we use the DE406 ephemeris of Standish et al. (1997) as noted above. However, for the purpose of this study, the amounts of these differences are negligible.

Since the ephemeris uses the uniform time scale TD, conversion into the real, nonuniform time scale known as UT is required to study historical astronomical phenomena. We referred to the ΔT values of Morrison & Stephenson (2004), tabulated at intervals of 100 years, and used a cubic spline interpolation method (Press et al. 1992) to obtain the ΔT value for a given year. In this study, we assume that the observer’s location in the Goryeo dynasty was Gaeseong, one of capitals of the dynasty, with 37° 59′ N and 126° 33′ E as its latitude and longitude. In addition, we reduce all times in units of the apparent solar time at Gaeseong using this assumed longitude and correcting the equation of time.

 

3. RESULT

3.1. Catalog of Lunar Eclipses

In Appendix A, we list the times of the eclipse at different phases for the full lunar eclipse accounts recorded in the Goryeosa, except for six accounts (i.e., the four categorized as Class I and the two duplications categorized as Class II). For the Class III accounts, we use the estimated date given in the last column of Table 1. In the appendix, column 1 (No) is the sequential number, and columns 2, 3, and 4 are the Julian date from Ahn et al. (2009b). Column 5 is the eclipse (Ecl.) type, where “Pe” is penumbral, “Pa” is partial, and “To” indicates a total eclipse. Columns 6 (P1) and 7 (U1) are the first external contact times of the penumbra and umbra, respectively. Columns 8 (U2) and 10 (U3) are the first and last internal contact times, respectively, of the umbra. Columns 11 (U4) and 12 (P2) are the last external contact times of the umbra and penumbra, respectively. Column 9 (TGE) is the time of greatest eclipse. All times are given in units of the apparent solar time at Gaeseong; hence, the durations of each phase are slightly different compared to those given in units of TD. In the last column, we provide some additional notes. P and N indicate accounts where the lunar eclipse was predicted but it was unobservable (primarily due to bad weather) and where the eclipse was not reported (or predicted) but it occurred, respectively. Particularly, those accounts strongly suggest that the lunar eclipse accounts in the Goryeosa are recorded on the basis of actual observations not theoretical calculations. T and E denote cases where the lunar eclipse is recorded as a total one and where the estimated date is used, respectively.

Since it is known that the royal court of the Joseon dynasty (A.D. 1392 – 1910), the next dynasty after the Goryeo, did not change the date in the records, in particular, of astronomical phenomena which were observed after midnight (Ahn & Park 2004), we use positive and negative signs on the hour instead of changing the date. The plus and minus signs on the hours represent the next day or previous day, respectively, with reference to the Julian date given in columns 2, 3, and 4. If the time is over one day, we added 24 hours. As an example, for the first external contact time (P1) of the eclipse on 1030 February 19 (no. 14), +27 h 59 min means 03 h 58 min on February 21.

3.2. Characteristics of the Eclipse Accounts

As can be seen in Appendix A, for a lunar eclipse that occurred after midnight, some accounts (e.g., nos. 6, 18, etc.) show a change in the observation date while others (e.g., nos. 9, 12, etc.) show no change; this is different from the accounts in the Joseonwangjosillok (Lee et al. 2012b), a representative history book of the Joseon dynasty. Moreover, those accounts do not provide a definite reference hour for the change of the observation date. In addition, we found that several accounts show a difference in date from modern calculations even after taking the observation date change into consideration. We summarize those accounts from Appendix A in Table 2. In the table, the meaning of each column is the same as that in Appendix A, except for the last column. In that column, we note the sequential number of the eclipse as listed in the appendix. According to this study, the Julian dates of 1087 June #05 and 1107 November #05 should be one day later and those of 1156 September #31 and 1172 June #08 one day earlier than the dates from Ahn et al. (2009b), i.e., 1087 July 18, 1107 December 31, 1156 October 30, and 1172 July 09, respectively. For the reason of the date differences in these cases including the Class III cases, we suggest that further studies are needed to identify the reasons for this discrepancy in the dates.

Table 2Summary of the lunar eclipse accounts that present a date difference according to this study

We assume that a Goryeo astronomer could recognize any magnitude of lunar eclipse. In practice, however, it might be difficult to observe some eclipses, particularly a low magnitude penumbral eclipse. It is outside the scope of this study to estimate the lower limit of the magnitude above which a lunar eclipse is observable. Instead, we calculated the penumbral magnitude for the lunar eclipses recorded in the Goryeosa, and found that the eclipse of 1011 August 16 exhibited the least magnitude, 0.5583. Hence, we may conjecture that the royal astronomer of the dynasty could observe any lunar eclipse phenomenon magnitude brighter than a 0.5583, in the penumbral phase. For the purpose of illustration, we depict the progress of that lunar eclipse in Figure 1. In the figure, the large gray and small red circles represent the diameters of the penumbra and umbra, respectively. The dashed line through the center of the circles (i.e., marked by the yellow cross) is the plane of the ecliptic. We also present the first and last external contact times (P1 and P2) together with the time of greatest eclipse (TGE). The abbreviations “D. Pen.” and “Pen. M.” at the bottom of the figure represent the duration of the penumbral phase and the penumbral magnitude, respectively.

Figure 1.Systematic diagram showing the progress of the lunar eclipse of 1011 August 16. The large gray and small red circles represent the diameters of the penumbra and umbra, respectively. The dashed line passing through the center point is the ecliptic.

We also examined 20 accounts that are recorded in the Goryeosa as total lunar eclipses (i.e., the eclipses marked with a T in the last column of Appendix A), and found 18 of those accounts to be accurate. However, the partial eclipses of 1252 September 19 and 1388 May 22 were very close to total eclipses, with umbra magnitudes of 0.8868 and 0.9244, respectively. In the case of the account for 1089 June 26, the lunar eclipse is recorded as follows: “there was the phenomenon that the Moon was hidden”. At that time, the lunar eclipse was total; thus we can presume that this is another expression for a total lunar eclipse.

Finally, we verified the accounts where a lunar eclipse was predicted (i.e., the eclipses marked with a P in the last column of Appendix A) and found that all forecasted eclipses occurred except for that of 1030 February 19 (i.e., 1030 January #05, no. 14 in Appendix A). There was no lunar eclipse on that date but there was one on 1030 February 21 (or February 20), as presented in Appendix A, and it was a total eclipse. In Figure 2, we present the lunar eclipse map for 1030 February 21. As can be seen in the figure, the eclipse was visible at Gaeseong during the time when the Moon was rising, if the weather was fine. If we assume that Goryeo astronomers made a mistake in the length of the lunar December of 1029 (that is, if the month was Daejin not Sojin), as mentioned in Section 2.1, and that they did not change the date for astronomical phenomena which occurred after midnight, we could say that their prediction was correct.

Figure 2.Lunar eclipse map of 1030 February 21 showing the visibility area of the eclipse at different phases: P1, U1, U2, U3, U4, and P2 (see the text for details). The darkest shaded area indicates the region of the Earth in which the eclipse was not visible, whereas all phases of the eclipse were visible in the unshaded region.

 

4. SUMMARY

Along with solar eclipses, lunar eclipses are astronomical phenomena whose occurrence can be accurately calculated not only for future events but also past ones using a modern ephemeris. Hence, eclipse data are very useful for verifying historical records. However, less attention has generally been paid to accounts of lunar eclipses than to those of solar eclipses.

In this paper, we investigated the lunar eclipse accounts of the Goryeo dynasty. Although lunar eclipse phenomena are recorded in several documents, including the Jeolyo, Bigo, and so on, we found that all eclipse accounts are also recorded in the Goryeosa. Thus, we surveyed the lunar eclipse accounts from the Goryeosa and found a total of 228 accounts, including four unfulfilled and two duplicated ones. We constructed a catalog for 222 lunar eclipses using the DE406 ephemeris of Standish et al. (1997), the ΔT values of Morrison & Stephenson (2004), and the algorithms of Liu & Fiala (1992), Meeus (1998), and Urban & Seidelmann (2013). For the conversion of the lunisolar date to the Julian date, we basically referred to the works of Han (1987, 2001) and Ahn et al. (2009b). However, for some accounts we estimated the dates and used these estimated dates in our catalog.

First, we found that a Goryeo astronomer could recognize a lunar eclipse phenomenon provided that the eclipse had a magnitude brighter than 0.5583 in the penumbral phase. Second, we found that all accounts recorded as total lunar eclipses are accurate, except for two accounts. However, we found that in those two cases, both eclipses were also very close to total. Third, we confirmed that all predicted lunar eclipses in the accounts actually occurred, except for one eclipse on 1030 February 19. However, if we assume that the Goryeo dynasty made an error in the number of days in the preceding month, we may say that this was also correctly identified and dated. Finally, we found that the Goryeo court changed the date in some accounts but not in others for lunar eclipses that occurred after midnight, different from the records of the Joseon dynasty. We also found four accounts showing a difference between the dates determined using the work of Ahn et al. (2009b) and the dates derived from the results of this study, even when taking into consideration the date change for events that occurred after midnight.

In conclusion, we believe that this study is very helpful for understanding the astronomical records of the Goryeo dynasty, particularly the lunar eclipse records. For further work, however, we suggest that more studies are needed on the accounts that exhibit a difference in the Julian dates derived from this study as compared with previous ones.