gives eclipses with features described in these records, whendataareavailable Wehavedetermined T s for 19 solar eclipses in this way and shown these i
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1 Preprint N 2003/3/6 8 1, 2 2, 1 :, 2 : Time variation of the moment of inertia of the Earth derived from Chinese and Japanese records of ancient solar eclipses Kin-aki KAWABATA 1,KiyotakaTANIKAWA 2 and Mitsuru SÔMA 2 1 : Nagoya University (Emeritus Prof, 2 : National Astronomical Observatory kawabata-nagoya@jcomhomenejp Abstract Time variation of the Earth s rate of rotation from BC 709 through AD 975 is obtained from Chinese and Japanese records of solar eclipses Chinese records employed in the present article are the Ch unch iu focusedonlu affairs, the chronological tables of the Shih-chi (chap 15, the Han-shu (chap 27, the Hou-han-shu of conjunction in solar and lunar ecliptic longitude on BC 34/8/24 is andthenthesunisnot eclipsed in the conjucntion The sun on Yuan-chia reign period, 30th year, 7th month, day hsin-ch ou, the first day of the month (453/8/20 was eclipsed in the region from South Atlantic Ocean through the Indian Ocean and then the eclipse recorded as a total solar eclipse and stars were seen in the Song-shu (chap 28, San-kuo-chih (chap 4, the Chinshu (chap 12, the Song-shu (chap 34, Liang-shu (chap 3, Nan-shi (chap 2, 6, 7, the Sui-shu (chap 4, the Chiu-t ang-shu (chap 6, and the Hsin-t ang-shu (chap 32 Japanese records employed in the present article are the Nihongi (chap 22, the Sandai Jitsuroku (chap 34 could not be observed in China Therefore the eclipse was recorded in the book according to a prediction In two eclipses recorded in the Han-shu (BC 2/2/5 and the San-kuo-chih (243/6/5, the sun was totally eclipsed in an area far from the capital at that time but in the Chinese territory (the Veritable Records of the Three On tidal term versus T plane ( T = TT Reigns , (chap 24 and the Nihonkiryaku (Outlines of the Annals of Japan, Chronicle up to 1036 (chap 6 We have selected 31 records of solar eclipses with descriptions of one of words of total, complete, or stars were seen in these Chinese books Japanese records of candidates of total eclipses employed in the present article are from the list (3 of eclipses in the list appear to be total by Ogura (1916 Except a solar eclipse recorded in the Han-shu (chap 27 as Chien-chao reign period, 5th year, 6th month, day jen-shen, the last day of the month, a solar UT, we plot an area of parameters which gives total/annular eclipse in the capital of the dynasty Since the tidal term and T will not change significantly within short period, we expect substantially the same values of these paramaeters for two succsesive total/annular eclipses occurring within a period of 60 years When we plot such belts for two successive eclipses occuring within a period shorter than 60 years, these two belts cross at the tidal term of 13 arcsec/cy 2 We can clearly see the feature in Figures 17, 21, and 22 The result agrees well with ( 1294 ± 025 arcsec/cy 2 obtained by Dickey et al eclipse, not complete and like a hook (1994 by LLR (lunar laser ranging In other cases, (BC 34/8/23, 33 eclipses are identified with eclipses in the table of Canon of Eclipses by Th Ritter Oppolzer (translated by Gingerich The longitude of the moon measured from the ascending node of the lunar orbit at the time two belts are more or less parallel and then we can not determine the tidal term In the next, we determine a range of T for pairs of eclipses occuring within a period shorter than 60 years in such a way that T in the range 1
2 gives eclipses with features described in these records, whendataareavailable Wehavedetermined T s for 19 solar eclipses in this way and shown these in Figure 28 by thick vertical lines 7 eclipses are separated from the others more than 60 years apart and then T are determined from a single solar eclipse and these are shown by thin vertical lines in Figure 28 Remaining 4 eclipses are recorded as not complete Our calculation for each eclipse indicates that the sun is not totally eclipsed at the latitude of the capital at that time but the magnitude of 3 eclipses among 4 is high Therefore the descriptions in these books can be justified for these 3 eclipses These eclipses are, however, omitted from our analysis because our method can not be applied for these eclipses Figure 28 and 29 show T versus year and O C versus year plot of our results, respectively Here C means the parabolic fitting by Stephenson (1997 The solid curve in Figure 28 shows the tidal components T tidal of T, for the tidal term of 130arcsec/cy 2 obtained by Stephenson (1997 The long dashed curve in Figure 28 is the one obtained by a parabolic fiting by Stephenson (1997 For a convenience of comparison of our results with Stephenson s one, his spline fitting is also shown by a short dashed line These figures show irregular variation of T with a time scale of years is added to the parabolic line (long dashed curve Nontidal components of T, T nontidal = T T tidal, are due to variations of the moment of inertia of the earth Suppose that glaciers in polar regions melt and then the sea level rises by 1 m When we take into account that the total area of the sea is 2/3 of the earth surface, the total mass of melted ice becomes gr 1 Stephenson (1997 Immanuel Kant 1754 Kant 2000,, θ 2 (θ 36525, 10 arcsec/cy 2 18, arcsec 40 arcsec, arcsec Laplace arcsec/cy 2, Adams 1853 Laplace, 578 arcsec/cy 2 Chapront ( arcsec/cy 2 19, Hansen ( arcsec/cy 2, (Lasker arcsec/cy 2 Oppolzer (1887 Hansen (1857 Leverrier (1858,BC AD ,000 5,200 Canon der Finsternisse ,, Ginzel, Cowell, Newcomb, Radau, Fotheringham, Schoch, (1979 Putting the radius of the earth to R, weadoptan approximation that the mean square distance of the Fotheringham ( arcsec/cy 2, mass from the rotation axis of the earth is 2 3 R2 We 15arcsec/cy 2 assume that the mean square distance of glaciers before melting is negligibly small comparing with 2 3 R2, Thentheincreaseofthemomentofinertiaofthe 134 earth is by a factor of 10 7 when the sea level rises 1 15arcsec/cy = 201arcsec/cy 2 m due to melting of glaciers The length of the day increases by 10 ms in this case Supposing that the sealevel continues to rise over 1000 years in a constant rate, T increases by 30 min Therefore, the variation of the sea level due to the variation of atmospheric temperature in the polar region is a probable cause of the variation of the length of the day in hundreds 60arcsec/cy 2 261arcsec/cy 2 Fotheringham 108arcsec/cy 2, Fotheringham 261arcsec/cy 2 153arcsec/cy 2 of years or in a millenium 2
3 Preprint N 2003/3/6 8, Calame and Mulholland ( 123 ± 25 arcsec/cy 2 Fotheringham, Spencer Jones Dickeyet al (1994 Spencer Jones ( ( 1294 ± 025 arcsec/cy 2,,, 2 r, n, n 2 r 3 =const, (1916 ṙ r = 2 Opppolzer,628 ṅ 1183, 3 n r = m, n = arcsec/cy 628/4/10, 873/7/29, 975/8/10, ṅ arcsec/cy 2, ṙ m/cy, Hansen, Oppolzer, Ginzel, Cowell,, ṙ = 0148ṅ ṅ Newcomb, Radau,, 13 arcsec/cy 2 2 ṅ = 26 arcsec/cy, 385 m/cy,1940 1,0038 sec/cy BC sec, (1979 Schoch,BC 20, 801 AD E 150 E, 10 N 50 N IAU (UT,, 1967 SI, SI (TT 1979,1994, T =TT UT, (1942, T T tidal (1975, (1992,, 20 T nontidal = T T tidal Stephenson, (1997 Christodoulidis et al (1988 ṅ, ω T SI 19 ω T =(+49± 3ṅ arcsec/cy 2, 13 arcsec/cy 2 SI T tidal =(44± 2t 2 20 sec ( t 1820 T T nontidal = T T tidal T , (Calame and Mulholland /365 3
4 1: 1910 T ( Stephenson (1997 parabola , : T (Stephenson 1997 : Babylonia (solar and lunar < 25deg, : Babylo-, nia (solar > 25deg, : Ancient Greek,?: Arab : T tidal : parabola, : spline, 2 Stephenson (1997, (2002 T 19 (616/5/21 20,, 9 Fotheringham (628/4/10, BC 1063, BC 763, BC 648, BC 585, BC 463, BC 15 arcsec/cy 2, T 3000 sec, 431, BC 310, BC 129, 29, 71, 364 (1979, Oppolzer Ginzel T, Oppolzer,,, 71,590,733,840,878,891,939,968,, 1030, 1093, 1133, 1147, 1178, 1185, 1187, 1191, 1207, 1239, 1241, 1267, 1330, , 20 2 Stephenson (1997,, (2001, Tanikawa and Sôma (2001 (1979 (1992 (2000,,,,, 13 arcsec/cy 2, T =2000sec, 15 arcsec/cy 2, T =3000sec 4
5 Preprint N 2003/3/6 8 3, T < 16 arcsec/cy 2, Kawabata, Tanikawa, and Sôma (2003, Stephenson (1997, arcsec/cy 2 = 13 arcsec/cy 2,2728sec< T <2959 sec, T 3: /5/21 3 Kawabata, Tanikawa, and Sôma (2003, BC 700 AD 1000, (1916,,, T,,, (1979 (1994,, Oppolzer,,,, 1, 1, 9, 6, 2 (2002 T 5 11, T, Opp: Oppolzer JD: 13 arcsec/cy 2, T = 2000sec,,,,, T, - T 5
6 9 BC 89/9/29 Opp: 2661 JD: 1,689,188 1: ( E N E N E N E N E N BC 80/9/20 Opp: 2684 JD: 1,692, E N ( E 32 3 N E 32 3 N E 32 3 N 11 BC 34/8/ E N E N ( E N BC 34/8/ E 35 1 N BC 28/6/19 Opp: 2813 JD: 1,711,366 ( 16 1 BC 709/7/17 Opp: 1176 JD: 1,462, BC 2/2/5 Opp: 2879 JD: 1,720,728 ( ( 12 2 BC Opp: 1449 JD: 1,502,171 ( 6, /11/23 Opp: 2888 JD: 1,722, BC 549/6/19 Opp: 1582 JD: 1,521,071 ( /12/16 Opp: 3050 JD: 1,745, BC Opp: 1842 JD: 1,559,549 ( /1/18 Opp: 3184 JD: 1764,905 Oppolzer ( BC 198/8/7 Opp: 2402 JD: 1,649,322 ( /6/5 Opp: 3470 JD: 1,809, BC 188/7/17 Opp: 2425 JD: 1,652,954 7, 18, /7/27 Opp: 3611 JD: 1,833,032 7 BC 181/3/4 Opp: 2441 JD: 1,655, /8/28 Opp: 3730 JD: 1,852,788 8 BC 147/11/10 Opp: 2523 JD: 1,668,
7 Preprint N 2003/3/ /12/12 Opp: 3888 JD: 1,878,096 ( /8/20 Opp: 3942 JD: 1,886,748, /8/10 Opp: 3944 JD: 1,887,103 4: BC 442/3/11, [ ], 20 ( /4/18 Opp: 4092 JD: 1,909, /6/25 Opp: 4685 JD: 1,996, /6/10 Opp: 4107 JD: 1,911, /10/28 Opp: 4690 JD: 1,997,488 21, /11/23 Opp: 4110 JD: 1,912, /8/5 Opp: 4701 JD: 1,999, /5/21 Opp: 4345 JD: 1,946, ( /4/10 Opp: 4374 JD: 1,950, /7/28 Opp: 4955 JD: 2,040, /9/26 Opp: 4561 JD: 1,977, /8/10 Opp: 5184 JD: 2,077,398 22, /10/27 Opp: 4626 JD: 1,987,
8 5: 7: 8: 6:, 28, 29, 30 T (No 4 BC 443,BC Oppolzer BC 444 BC 442, (1992, No 11 BC 442 (BC 34/8/24 4 BC 442,,, , 46,, BC 444,, 8
9 Preprint N 2003/3/6 8 9: 11: 18, (No 17 (No 31 2,,, 7 (1995,1965,, ,, 10: 11 T < 3000 sec T =3000sec (09:51 UT 087, T = 3500 sec 09:47 UT, :52 UT 15, 33, (No 8 (No 13, (No 21 9, (No 20, 9
10 14: BC : BC sec < T < sec BC 188 T sec,094, BC188 4 T =TT UT, ( , 13:,, 30 (No 30, T,, 2 T T, T, T 10
11 Preprint N 2003/3/6 8 15: 17: 18: T, 13 arcsec/cy 2 15, 13 arcsec/cy 2 16: T 2 AD2 T = T 8510 sec,bc2 084, 01:19 UT,,, T 28, T,702,628 17, 21, 22, 2: BC 89 BC 80 T 13 arcsec/cy 2, (UT T BC 89/9/29 BC 80/9/20 s, : : : : , 13 arcsec/cy 2 11
12 19: 21: 20: T < T <3254 sec 22: < T = 2959sec, T < 2728 sec,702, , 2728 < T < 3254 sec 08:12 UT < T < 2959 sec, (632/1/27, Opp: < T <2959 sec 628 T 2728 < T 628 < 2959 sec 22, T, 628 T > 1851 sec 628 T 231 sec < T 628 < 2959 sec Kawabata, Tanikawa, 692 sec 3, and Sôma (2003 T =2959sec, 017, (1992 (
13 Preprint N 2003/3/6 8 25: 24: 23: 761, 702,616, ,616,628,702,729,761 T 729 5, 2 T =2840sec 088, 3 25, 26 T = 2959sec, T,702 (1979, ( , 09, 27 (681/11/3 34 arcsec, (2002,, 13
14 3: T =2840sec UT LT 628/4/10 00:49 09: /1/27 08:24 17:27 016, 08:38 UT, /3/31 23:44 08: LT 637/4/1 680/11/27 03:30 12: /11/16 01:22 10: : 34 arcsec,,, 26: 099,,, 5 T 28 T,,, Stephenson (1997 Table A1 T T (1979 T tidal, T tidal, Ginzel 563/10/2 1331/11/29 50,,, 9zoll Stephenson (1997, T, 6zoll zoll, zoll, 6 7,1 2 T 9zoll,6zoll 075, 05 5,7 8 T 016, Stephenson (1997 T,
15 Preprint N 2003/3/6 8 28: T : Babylonia (Stephenson 1997, Table A1 Stephenson T Stephenson 29: T 28 : Babylonia (Stephenson 1997, Table A1 15
16 30: T T tidal : Babylonia (Stephenson 1997, Table A1 Stephenson T 1m T gr 29 T, T R, 2 O C C 3 R2, Stephenson (1997 T Cal =31t 2 20 sec, t AD T ms 1000, 1m, T T 28 T T tidal, m, T,,,, Stephenson T,,,, 6 (Kawabata, Tanikawa, and Sôma T 2003, 1m,, T,,,, 13 arcsec/cy 2, 2/3, T 16
17 Preprint N 2003/3/6 8, Kawabata, K, K Tanikawa, and M Sôma, 2003, T, Proceedings of ICHA/IAU International Conference on Astronomical Instruments and Archives from the Asia-Pacific Region, Cheongju, Korea, 2 5 July 2002, YonseiUniv Press(Korea,in, press, Lasker, J, 1986, Astron Astrophys, 157, Leverrier, U J J, 1858, Ann de l Obs de Paris, 4, Oppolzer, Th Ritter von, 1962, Canon of Eclipses, translated by O Gingerich, Dover Publications, INC, New York Originally published as vol 52, of the Memoirs, Mathematics Natural Sciences 10 Class of the Imperial Academy ofsciences in Vienna ( Jones, H S, 1939, Mon Not R Ast Soc, 99,, , Stephenson, F R, 1997, Historical Eclipses and Earth s Rotation, Cambridge University Press 46 Tanikawa, K, and M Sôma, 2001, Proceedings of International Conference on the 770th Birth An-, niversary of Guo Shoujing and the History of Time Apparatus, Xingtai,China,18 22October 2001 (in press (Kawabata, Tanikawa,, Sôma, 2002, (Report of the National Astronomical Observatory of Japan, 5, (Mori, 2000,, (Ogura, 1916, (The Astronomical Herald published by the Astronomical Society of Japan, 9, 13 18, 25 29, 39 43,52 55, Calame, O and and D Mullholand, 1978, Science, 199, (Saito and Ozawa, 1992, Chapront-Touze, M and J Chapront, 1983, Astron Astrophys, 124, Christodoulidis, D C et al, 1988, J Geophys Res, 93, Dickey,JOet al, 1994, Science, 265, , (Sugimoto and Mori, 1995,, 1, (Suzuki, 1942,, 6, 143 (Tanikawa and Sôma, 2001,, 95, Fotheringam, J K, 1920, Mon Not R Ast Soc, 81, Hansen, P A, 1857, Tables de la Lune construites d apres le Principe Newtonien de la Gravitation Universelle H M Stationery Office, London (Uchida, 1975,, (Watanabe, 1979,, 17
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