New reductions of orbits based upon Chinese ancient cometary records

Planer. Space Sci., Vol. 45, No. 12. pn. 1551~1555. 1997 :c: 1998 %evier Science Ltd All rights reserved. Printed in Great Britain 0032-0633/‘97 $17.00+0.00 PII: SOO32-0633(97)OOlSl-5

Pergamon

New reductions of orbits based upon Chinese ancient cometary records* Hongnan Zhou,’ Weifeng Zhuang’ and Yu Wang3 ‘Physics Department, Nanjing Normal University. 210097, Nanjing, P.R.C. ‘Library, Shantou University, 5 15063. Shantou, P.R.C. ‘Department of Astronomy. Nanjing University, 210093, Nanjing, P.R.C. Received 20 August 1996: revised 25 August 1997; accepted 2 September 1997

are shown in Section 3. In Section 4 we discuss the results and give some concluding remarks.

2. The reduction of observation data in Chinese ancient cometary records Usually, Chinese ancient following contents :

records

include

the

(I) The date of observation in the Chinese calendar system ; (II) The positions (or constellations) of the appearance and disappearance of comet ; (III) The moving direction of the comet in the sky; (IV) The visual brightness and morphology of the comet.

1. Introduction In Chinese history, there are a lot of astronomical observation records. A Compilation of Chinese Ancient Records qf’ Celestial Phenomena (Beijing Observatory, 1988) is a summary of all ancient and medieval astronomical observation records in China. Among all these old recorded data there are several comet observations. The orbits of some of these comets have been already determined with the use of the old recorded observations (Ho, 1962; Kiang, 1972 ; Yeomans, 1977 ; Chang, 1979 ; Hasegawa, 1979. 1995; Marsden et al., 1996). In this study, we reduced 363 cometary observations belonging to 88 different comets (from 146 B.C. to 1760 A.D.) to a consistent set of observations. In Section 2, the process of reduction on the Chinese ancient cometary observation data were explained and listed. The orbital determination of all more than three times recorded comets have been carried out using the numerical method of N-body problem. Especially, for thirty different comets, new orbits are presented for the first time. The method and results, of orbital determination of recorded comets

*Supported by the National China and Jiangsu Province.

cometary

Natural

Science Foundation

of

For example, the original records of cometary observations in 1106 was given as follows (Beijing Observatory, 1988) :

We translated

Chinese into English, it means as follows :

On the evening of Feb. 10, 1106, a comet appeared in the western sky. Its size was larger than a cup, and its ray was 6 zhang (60”) in length, 3 chi (3”) in width. It pointed to northeast, passed from TKui through tLo, tWei, tMaia into tPi, then it entered the horizon and went out of sight. “Song Shi, Tian Wen 9”. Vol. 56, 1228.

t The name of the Chinese ancient constellation.

H. Zhou rt ul. : Reductions

1552

Fig. 1. The apparent positions of old comet 1106 corresponding to the original the Huang-Yu Star Map (1 : Kui ; 2 : Lo ; 3 : Wei ; 4 : Maia; 5 : Pi)

According to the original records, we could reduce the observation data with the following steps: firstly, the apparent positions (or constellations) of the comet in correspondence with the observation time were drawn on the Huang-Yu Star Map (epoch 1052 A.D.) of Song dynasty of China (Pan-Nai, 1989) ; secondly. the Right Ascension and the Declination correlative to each observational position were determined with the Huang-Yu Star Map and Zhou Zhong Star Catalogue (published in 1052 A.D.) (Pan-Nai. 1989); finally, the equatorial coordinates of some 363 sets of original observation records of comets for a total of 88 different comets from 146 B.C. to 1760 A.D. were translated to mean equatorial coordinates for epoch 2000.0. Figure 1 shows the apparent positions of an older comet corresponding to the original records in 1106 on the Huang-Yu Star Map (epoch 1052 A.D.). The observation dates and the numbers of ancient Chinese cometary records (from 146 B.C. to 1760 A.D.) are summarized in Table 1.

3. Determination

of orbits

From Table 1 we can show that most of the Chinese ancient observational records have been used by previous computers. For further researches, we calculated preliminary orbits using the Olber’s method for parabolic orbits for each set of original observations. But, the Olber’s method is unsatisfactory for 14 sets of original observations, and we calculated those preliminary orbits again using the Laplace method for ellipsoidal orbits. The numerical integrations of motion of every recorded comet were then performed while taking into account the perturbations of the nine planets using the method of the N-

of orbits

record on

body problem. The coordinates of the Sun and Planets are derived with the formulas of Celestial Mechanics (Taff, 1985). Finally, improvements of the comet’s orbits were also carried out using a least-squares method. Looking at Table 1, it is seen that orbits were determined for a selection of the data and that there were comets without a corresponding orbit, i.e. there are 30 sets of original records for which orbits have not been computed. For these observation sets, we have computed new orbits and the results are presented in Table 2. The method of Laplace was used to compute orbits for the comets of 1021. 1430 and 1496.

4. Concluding remarks

(1) The cometary records among A Compilation of’chiwse ,4ncient Records qf Celestial Phenomena provided a wealth of cometary observation data. In this work, we reduced only 363 sets of original cometary records (from 146 B.C. to 1760 A.D.). Additional Chinese ancient and medieval observation reductions are in process. (II) Reduction results show that the Chinese ancient cometary records are available. They are an important source and basis for the research of the evolution and orbital motion of comets. However. there are some differences between our computed orbits and the orbits already published in the Catulogue of’cometary Orbits 1996 (Marsden et al.. 1996) for many recorded comets. In Table 3 both sets of the orbits for four older comets (including comet Halley) are listed. These circumstances are understood easily, in fact, there are two separate determinations of orbits based on the different data. For example, Hasegawa (1979) used the ancient cometary records of Japan. China and Korea to

H. Zhou et al. : Reductions of orbits Table 1. The summary of observation

Year -146 39 71 85 126 141 182 238 240 390 400 418 423 442 451 565 568 574 634 676 681 770 821 838 839 893 905 962 975 989 1003 1005 1018 1021 1049 1080 1092 1097 1106 1123 1132 1161 1222 1240 1264 1273 1315 1337 1351 1368 1376 1378 1385 1430 1433 1439 1449 1456 1457 1458 1462 1468 1472 1490 1496 1499 1500 1502

Number of observations 3 3 3 3 6 8 3 3 3 5 6 3 3 4 6 4 9 6 3 3 3 3 3 3 4 3 4 4 3 4 3 3 5 3 3 3 4 4 5 5 3 3 3 3 5 6 3 11 4 3 4 6 5 3 4 3 3 5 7 4 4 7 9 4 3 7 6 3

1553 data in Chinese Ancient Cometary Records (146 B.C.-1760 A.D.)

Time interval of observations

Computer (year) and reference

- 146 Aug. 06- 146 Aug. 18 39 Mar. 13-39 Apr. 30 71 Mar. 06-71 May 05 85May21-85June30 126 Mar. 24-126 Mar. 30 141 Mar. 27-141 May 30 182 Sep. 01-182 Sep. 23 238 Sep. 30-238 Oct. 11 240 Nov. lo-240 Dec. 19 390 Aug. 07-390 Sep. 17 400 Mar. 19400 Apr. 20 418 Sep. 15418 Nov. 12 423 Feb. 13423 Mar. 13 442 Nov. 01443 Feb. 10 451 June lo-451 Aug. 14 565 July 22-565 Nov. 02 568 July 20-568 Nov. 05 574 Apr. 04-574 June 09 634 Sep. 20-634 Oct. 11 676 Sep. 04-676 Nov. 01 68 1 Oct. 17-68 1 Nov. 03 770 May 26770 July 09 821 Feb. 26821 Mar. 07 838 Nov. 1l-838 Nov. 21 839 Feb. 07-839 Mar. 12 893 May06893June 12 905May22-905June 12 962 Jan. 28-962 Apr. 02 975 Aug. 03-975 Oct. 25 989 Aug. 12-989 Sep. 10 1003 Dec. 24-1004 Jan. 24 1005 Oct. 04-1005 Oct. 15 1018 Aug. 04-1018 Sep. 09 1021 May 25-1021 Aug. 08 1049 Mar. 10-1049 July 02 1080 Aug. lo-1080 Aug. 18 1092 Jan. 08-1092 Jan. 30 1097 Oct. 061097 Oct. 17 1106 Feb. l&l 106 Apr. 09 1123 Feb. 02-l 123 Feb. 27 1132 Oct. 04-1132 Oct. 13 1161 July 13-1161 July 22 1222 Sep. l&l222 Oct. 23 1240 Jan. 31-1240 Feb. 23 1264 July 261264 Sep. 15 1273 Apr. 09-1273 Apr. 30 1315 Oct. 29-1316 Mar. 11 1337 June 26-1337 Aug. 19 1351 Nov. 24-1351 Nov. 30 1368 Apr. 08-1368 Apr. 26 1376June22-1376July 15 1378 Sep. 261378 Oct. 11 1385 Oct. 23-1385 Nov. 04 1430 Nov. 14-1430 Nov. 21 1433 Sep. 15-1433 Oct. 12 1439 Mar. 25-1439 Apr. 05 1449 Dec. 20-1450 Jan. 19 1456 Jan. 19-1456 July 06 1457 June 15-1457 Aug. 19 1458 Dec. 241459 Jan. 12 1462June29-1462July 16 1468 Sep. 18-1468 Nov. 12 1472 Jan. 16-1472 Feb. 17 1490 Dec. 31-1491 Jan. 22 1496 Jan. 08-1496 Feb. 21 1499 Aug. 161499 Sep. 04 1500May08-1500June30 1502 Nov. 29-l 502 Dec. 03

Hasegawa (1979) Publ. Astron. Sot. Japen 31,257

Yeomans and Kiang (1981) M.N.R.A.S.

197,643

Burckhardt (1804) Monad Corresp. 10, 167 Hasegawa (1979) Pub!. Astron. Sot. Japen 31,257 Hasegawa (1979) Publ. Astron. Sot. Japen 31,257 Hasegawa (1979) Publ. Astron. Sot. Japen 31,257 Yeomans and Kiang (1981) M.N.R.A.S. 197,643 Burckhardt (1804) Monatl Corresp. 10, 163 Hasegawa (1979) Publ. Astron. Sot. Japen 31,257 Hasegawa (1979) Publ. Astron. Sot. Japen 31,257

Hasegawa (1979) Publ. Astron. Sot. Japen 31, 257

Hasegawa (1979) Publ. Astron. Sot. Japen 31, 257 Hasegawa (1979) Publ. Astron. Sot. Japen 31, 257 Yeomans and Kiang (1981) M.N.R.A.S.

197,643

Hasegawa (1979) Publ. Astron. Sot. Japen 31,257 Landraf (1978) Mitt. Astron. Virein 17, 67 Hasegawa (1979) Publ. Astron. Sot. Japen 31,257 Hasegawa (1979) Publ. Astron. Sot. Japen 31,257 Ogura (1917) Ann. Obs. Tokyo 5(3), 17 Yeomans and Kiang (1981) M.N.R.A.S. Ogura (1917) Ann. Obs. Tokyo 513). 20 Hoek (1857) Dissert. Leiden Hasegawa Hasegawa Hasegawa Hasegawa Yeomans Hasegawa

197,643

(1979) Publ. Astron. Sot. Japen 31,257 (1979) Publ. Astron. Sot. Japen 31,257 (1979) Publ. Astron. Sot. Japen 31,257 (1979) Publ. Astron. Sot. Japen 31,257 and Kiang (198 1) M.N. R. A.S. 197,643 (1979) Publ. Astron. Sot. Japen 31,257

Celoria (1921) Pubbl. Obs. Brera 55, 8 Hasegawa (1979) Publ. Astron. Sot. Japen 31,257 Celoria (1921) Pubbl. Obs. Brera 55, 8 Yeomans and Kiang (198 1) M. N. R. A.S. 197,643 Celoria (1921) Pubbl. Obs. Brera 55, 45 Hasegawa (1979) Publ. Astron. Sot. Japen 31, 257 Hasegawa (1979) Publ. Astron. Sot. Japen 31,257 Hasegawa (1979) Pub/. Astron. Sot. Japen 31,257 Celoria (1921) Pubbl. Oss. Brera 55, 56 Hasegawa (1979) Publ. Astron. Sot. Japen 31,257 Hasegawa (1979) Publ. Astron. Sot. Japen 31,257 Hasegawa (1979) Publ. Astron. Sot. Japen 31,257

H. Zhou et al. : Reductions

1554

of orbits

Table 1. Continued

Year

Number of observations

1506 1531 1532 1533 1534 1536 1556 1577 1591 1593 1607 1618 1664 1665 1680 1686 1142 1743 1748 1760

5 5 4 3 3 3 3 4 3 3 3 6 3 9 4 3 3 5 4 3

Time interval of observations

Computer (year) and reference

1506 July 31-1506 Aug. 14 1531 Aug. 0551531 Sep. 05 1532 Sep. 02-l 532 Dec. 26 1533 July 01-I 533 Aug. 03 l534June 12~1534JulyO5 1536 Mar. 24-l 536 Apr. 27 1556 Mar. OlIl556 May IO 1577 Oct. 14-1577 Nov. 14 1591 Apr. 13.-1591 Apr. 30 1593 July 12-1593 Aug. 19 1607 Sep. 20-1607 Oct. I? 1618 Nov. 261619 Jan. 04 1664 Nov. IX-1664 Dec. 79 1665 Jan. OlI1665 Apr. 17 1680 Nov. 2331680 Dec. 30 1686 Aug. 261686 Sep. 07 I742 Mar. 02-l 742 Mar. 07 1743 Dec.22-1744Jan.05 1748 Apr. 261748 May OX 1760 Jan. 0991760 Jan. 14

Hasegawa (1979) Publ. Astron. Sot. Japen 31, 257 Yeomans and Kiang (1981) M.N.R.A.S. 197,643 Olbers (1787) Leipzig. Mag. Reine Angewandte Met. 4,444 Kokott (1981) J. Hist. Astron. 12, 127 Woldstedt (1844) Astron. Nechr. 23. 122

Table 2. The results of orbital determinations Year

7

39 71 85 I36 182 238 418 423 634 676 681 821 838 839 893 975 1003 1005 1021 1049 1106 1133 1161 1373 1315 1430 1496 I502 1536 1760

39 Mar. 04.1 71 Mar. 15.0 85 May 28.4 126 Mar. 14.2 182 Sep. 04.4 238 Sep. 17.4 418 Oct. 01.3 423 Feb. 03.2 634 Sep. 24.4 676 Sep. 20.2 681 Nov. 27.1 821 Feb. 28.1 838 Oct. 20.8 839 Feb. 15.3 893 May 15.0 975 Aug. 30.6 1002 Dec. 13.4 1005 Sep. 30.2 1021 May0l.l 1049 May I I.5 1106 Feb. 24.3 1123 Feb. 10.1 1161 July 04.5 1273 Mar. 15.6 1316 Jan. 02.6 1430 May 11.5 1495 Dec. 21.1 1502 Nov. 25.5 1536 Mar. 28.1 1759 Dec. 19.5

on 30 sets original records.’

4

0.97047 0.9665 1 0.95445 0.95716 0.9608 I 0.94185 0.97106 1.10537 I .06010 1.23194 0.89392 0.95206 0.96039 0.98927 0.87919 1.11517 0.98173 1.0253 I 1.10194 0.81723 0.82215 1.04513 I .0029 1 0.87302 2.19572 0.98299 0.98518 I .79026 I .35499 1.21291

Hoek (1861) Astron. Nechr. 55, 216 Landgraf (1977) Mitt. Astron. Verein. 16, 68 Hind (1846) .4stron. Nechr. 25, 13 I Lacaille (1747) Mem. Acud. Paris 1747, 562 Yeomans and Kiang (1981) M.N.R.A.S. 197,643 Pingre (1618) Cometegruphie 2, 100 Lindelof (I 854) Dissest. Hilsingfers Halley (I 705) Phil. Tram 24, 1883 Encke (1818) Z. Astron. 6, 157 Hind ( 1876) Neture 14, 257 Cohn (1906) Astron. Nechr. 172, 105 Olbers (1823) Astron. Nechr. 2, 379 Maraldi (1748) Mem. Acad. Paris 1748, 232

(1,

1.0 I.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 I.0 1.0 1.0 1.0 1.0 1.0 I.0 1.0 0.95389 I.0 1.0 1.0 1.0 1.0 1.0 0.98342 0.9783 I 1.0 1.0 1.0

‘IThe successive columns signify : Year = year of observation records of comets. T = perihelion time (in UT). y = perihelion distance (in AU). e = eccentricity. (11= argument of perihelion (in degree), equinox 2000.0. R = longitude of the ascending node (in degree). equinox 2000.0 i = inclination (in degree), equinox 2000.0. Epoch = osculation date of orbital determination (in UT).

73.15016 200.99389 189.33618 279.87001 309.64818 145.49463 287.97138 264.00365 224.45522 336.49780 174.13082 66.63825 303.17433 104.79360 135.14780 45.14933 44.10382 333.23628 338.91832 186.88233 317.60586 267.44689 75.59339 323.75785 43.33308 58.08891 88.31003 3 11.29699 231.46102 14.96925

R

i

125.73482 242.32116 50.09766 305.72993 348.95279 24.44275 142.54390 3 10.60075 180.66002 234.51405 225.09224 150.00794 103.68069 302.94965 125.51019 156.12226 113.91537 208.51179 6.98715 227.93567 154.27661 313.11234 306.80994 138.57153

114.46857 132.94326 73.84587 167.55195 11.53679 23.87222 145.93030 42.94797 33.04784 85.10105 80.11148 26.41450 69.27089 138.06960 102.79676 65.05589 84.61190 156.05122 12.39542 64.28947 60.22988 42.37681 69.67842 59.21884 89.46979 14.90297 5.99337 100.80413 144.65806 42.32839

1.89333 34.65841 13.07164 130.89488 42.87735 58.32222

Epoch 39 Apr. 10.6 71 Apr. 05.6 85 June 10.9 126 Mar. 27.6 182 Sep. 15.6 238 Sep. 05.6 418 Oct. 21.6 423 Feb. 18.5 634 Sep. 26.6 676 Sep. 24.6 681 Nov. 03.6 821 Mar. 02.5 838 Nov. Il.5 839 Feb. 29.5 893 May 28.6 975 Aug. 13.9 1003 Dec. 29.6 1005 Oct. 09.6 1021 May 25.6 1049 May 16.6 11.06 Mar. 10.5 1123 Feb. 13.5 1161 July 17.6 1273 Apr. 09.6 1315 Nov. 11.6 1043 Nov. 17.5 1496 Jan. 07.9 1502 Nov. 29.6 1536 Apr. 07.5 1769 Jan. 09.5

H. Zhou et al. : Reductions

Table 3. The comparison

of orbits of orbital elements

Comet

T

141 (Halley) 1378 (Halley) 240

141 Mar. 23.50 141 Mar. 22.43 1378 Nov. 11.50 1378 Nov. 10.69 240 Nov. 02.5 240 Nov. 10.0 1468 Oct. 06.6 1468 Oct. 07.3 1742 Feb. 28.5 1742 Feb. OS.696

1468 1742

1555 for four comets”

9

e

0

n

0.5907 0.583 1 0.5818 0.5762 1.03341 0.37 0.89622 0.85 1.00099 0.76577

0.9503 0.9678 0.9691 0.9684 1.0 1.0 1.0 1.0 1.0 1.0

97.827 93.694 98.713 105.295 263.11864 82.0 72.446 16 91.0 353.90175 328.043

35.954 37.219 57.943 51.020 159.55499 214.0 150.75073 106.7 106.91658 189.201

i

62.876 63.437 63.7658 63.113 11.66188 44.0 151.03910 138.0 132.89254 112.948

Computer This work Yeomans ( 198 1) This work Y eomans ( 198 1) This work Burckhardt (1804) This work Hasegawa (1979) This work Cohn (1906)

a The successive columns signify : Year = year of observation records of comets. T = perihelion time (in UT). q = perihelion distance (in AU). e = eccentricity. Q = argument of perihelion (in degree), equinox 2000.0. R = longitude of the ascending node (in degree), equinox 2000.0. i = inclination (in degree), equinox 2000.0. Epoch = osculation date of orbital determination (in UT).

calculate the orbital elements of older comets 1468, but in this work we only used Chinese ancient cometary obser-

vation data (see Table 3). (III) In our determination errors :

of orbits,

Purple Mountain comments.

Observatory

of China

for

his

valuable

there are several References

(i) Many

older comets, especially, some of long-period comets only three Chinese ancient observation records, so that, it could not provide their positions accurately enough for computing reliable orbits. (ii) The reduction of observation data could cause error with Huang-Yu Star Map and Zhou Zhong Star the recorded position error Catalogue. Usually, zz f 5’ .o A’ f lO’.O, and the recorded time errors z +1.0 - + 5.0 days. (%) There is the integral error of numerical method, in this work the calculated precision z 10P5. (iv) The new orbits derived from original records, which are given in Section 3, have not been included in the Catalogue qf Cometary Orbits 1996. Acknolr,ledgemc,nts.

The authors

wish to thank Dr Pinxin Xu of

Beijing Observatory. (1988) A Compilation of’ Chinese Ancient Records of Celestial Phenomena. Jiangsu Sciences and Technology Press. Chang, Y. C. (1978) Acta Astron. Sinica 19, 108. Hasegawa, I. (1979) PASf 31,257-279. Hasegawa, I. (1995) 47, 6999710. Ho, Y. P. (1962) Vistas Astron. 5, 127. Kiang. T. (1972) MNRAS 76,27. Marsden, B. G. and Williams, G. V. (1996) Catalogue sf Cometary Orbits, 1 lth ed. IAU Center Bureau for Astronomical Telegrams of Minor Planet Center. Pan-Nai. (1989) History on Stellar Obserzrations in China. Xue Lin Press. Taff, L. G. (1985) Celestial Mechanics. Wiley-Interscience Publication. Yeomans, D. K. (1977) AJ 82,435.