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Halley's "Astronomiae Cometiae Synopsis"

Edmond Halley, in the Philosophical Transactions (1705), investigated the orbits of 24 comets (or comet apparations) and calculated the orbital elements of their orbits (as approximated by parabola). In his paper, written in Latin, he finds that three of these comets, of 1531, 1607, and 1682, have very similar orbits, and concludes that they probably were different apparitions of the same comet, orbiting the Sun on a highly excentric elliptical orbit with a period of about 76 years, perturbed by gravitational influences of the giant planets Jupiter and Saturn, and predicts its return for 1758-1759.

All this was found to be correct, the comet returned on schedule, the first periodic comet to be identified. Consequently, it was named "Comet Halley", also "1P" for it is the first discovered periodic comet.

Comet   Ascending    Inclin.   Perihelion    Perihel   Log       Time of
of Year    Node      of Orbit  in Orbit       dist.    Per. di.  Perihelion
                                                  
          deg  '  "  deg '  "     deg  '  "                         day  h  '
1337   Gem 24 21  0  32 11  0  Tau  7 59  0  0.40666   9.609236  Jun  2  6 25
           84:21:00                37:59:00           
1472   Cap 11 46 20   5 20  0  Tau 15 33 30  0.54273   9.734584  Feb 28 22 23
          281:46:20                45:33:30           
1531   Tau 19 25  0  17 56  0  Aqr  1 39  0  0.56700   9.753583  Aug 24 21 18.5
           49:25:00               301:39:00           
1532   Gem 20 27  0  32 36  0  Cnc 21  7  0  0.5091    9.706803  Oct 19 22 12
           80:27:00               111:07:00           
                                                      
1556   Vir 25 42  0  32  6 30  Cap  8 50  0  0.46390   9.666424  Apr 21 20  3
          175:42:00               308:50.00
1577   Ari 25 52  0  74 32 45  Leo  9 22  0  0.18342   9.263447  Oct 26 18 45
           25:52:00               129:22:00
1580   Ari 18 57 20  64 40  0  Cnc 19  5 50  0.59628   9.775450  Nov 28 15 00
           18:57:20               109:05:50
1585   Tau  7 42 30   6  4  0  Ari  8 51  0  1.09538   0.038850  Sep 27 19 20
           37:42:30                 8:51:00
                                                      
1590   Vir 15 30 40  29 40 40  Sco  6 54 30  0.57661   9.760882  Jan 29  3 45
          165:30:40               246:54:30
1596   Aqr 12 12 30  55 12  0  Sco 18 16  0  0.51293   9.710058  Jul 31 19 55
          312:12:30               258:16:00
1607   Tau 20 21  0  17  2  0  Aqr  2 16  0  0.58680   9.768490  Oct 16  3 50
           50:21:00               302:16:00
1618   Gem 16  1  0  37 34  0  Ari  2 14  0  0.37975   9.579498  Oct 29 12 23
           76:01:00                 2:14:00
                                                       
1652   Gem 28 10  0  79 28  0  Ari 28 18 40  0.84750   9.928140  Nov  2 15 40
           88:10:00                28:18:40
1661   Gem 22 30 30  32 35 50  Cnc 25 58 40  0.44851   9.651772  Jan 16 23 41
           82:30:30               115:58:40
1664   Gem 21 14  0  21 18 30  Leo 10 41 25  1.025755  0.011044  Nov 24 11 52
           81:14:00               130:41:25
1665   Sco 18 02  0  76 05  0  Gem 11 54 30  0.10649   9.027309  Apr 14  5 15.5
          258:02:00                71:54:30

1672   Cap 27 30 30  83 22 10  Tau 16 59 30  0.69739   9.843476  Feb 20  8 37
          297:30:30                46:59:30
1677   Sco 26 49 10  79 03 15  Leo 17 37  5  0.28059   9.448072  Apr 26 00 37.5
          266:49:10               137:37:05
1680   Cap  2  2  0  60 56  0  Sgr 22 39 30  0.006125  7.787106  Dec  8 00  6
          272:02:00               262:39:30
1682   Tau 21 16 30  17 56  0  Aqr  2 52 45  0.58328   9.765877  Sep  4 07 39
           51:16:30               302:52:45

1683   Vir 23 23  0  83 11  0  Gem 25 29 30  0.56020   9.748343  Jul  3  2 50
          173:23:00                85:29;30
1684   Sgr 28 15  0  65 48 40  Sco 28 52  0  0.96015   9.982339  May 29 10 16
          268:15:00               238:52:00
1686   Psc 20 34 40  31 21 40  Gem 17 00 30  0.32500   9.511883  Sep  6 14 33
          350:34:40                77:00:30
1698   Sgr 27 44 15  11 46  0  Cap 00 51 15  0.69129   9.839660  Oct  8 16 57
          267:44:15               270:51:15

Modern astronomical data of Halley's comets:

                   Perihelion Date  Peri.Dist Excent.  Asc.Node Len.Peri Inclinat  m_max Exp  Observations from-to                                                                                       
                                                                                                                                                                                                         
Anonymus  1337     1337-06-14.85    0.749     1.0       79.6     96.9    143.6     2.9   4.0  1337-06-26 1337-08-19
Anonymus  1472     1472-03-01.439   0.48589   1.0      245.764  292.210  170.863   2.0   4.0  1472-01-10 1472-01-22
P/Halley  1531     1531-08-26.239   0.58120   0.96775  106.957   52.340  162.914   4.0   4.0                       
                   1531-08-14.0 
Anonymus  1532     1532-10-18.832   0.51922   1.0       24.52    93.12    32.59    1.8   4.0  1532-10-02 1532-11-08
                                                                                                                                                                                        
Anonymus  1556     1556-04-22.685   0.49082   1.0      100.868  180.736   32.377   3.0   4.0  1556-02-27 1556-04-19
Anonymus  1577I    1577-10-27.448   0.1775    1.0      255.669   30.538  104.878  -0.5   5.5  1577-11-13 1578-01-26
Anonymus  1580     1580-11-28.993   0.60237   1.0       89.363   24.251   64.606   4.0   4.0  1580-10-11 1580-11-12
                   1580-10-26.0
Anonymus  1585     1585-10-08.5262  1.094846  1.0      331.7326  42.4901   6.1302  6.0   4.0  1585-10-28 1585-11-22
                                                                                                                                                                 
Anonymus  1590     1590-02-08.5271  0.567726  1.0      307.670  170.642  150.457   6.0   4.0  1590-03-05 1590-03-16
Anonymus  1596     1596-07-25.7143  0.567156  1.0       59.417  335.266  128.074   5.7   4.0  1596-07-27 1596-08-03
P/Halley  1607     1607-10-27.5406  0.583615  0.967490 107.5314  53.0535 162.9020  3.5   4.0  
                   1607-10-24.0
Anonymus  1618II   1618-11-08.8507  0.389544  1.0      287.4248  80.3114  37.1956  4.6   4.0  1618-11-30 1619-01-22
                                                                                                                   
Anonymus  1652     1652-11-13.153   0.84750   1.0      300.18    92.30    79.46    5.5   4.0  1652-12-20 1653-01-07
Anonymus  1661     1661-01-27.381   0.442722  1.0       33.438   85.873   33.015   4.6   4.0  1661-02-03 1661-03-10
Anonymus  1664     1664-12-04.9834  1.025531  1.0      310.6569  85.3373 158.6966  2.4   4.0  1664-12-14 1665-02-13
Anonymus  1665     1665-04-24.719   0.10649   1.0      156.09   232.00   103.90    4.9   4.0  1665-04-06 1665-04-20
                                                                                                                   
Anonymus  1672     1672-03-01.9467  0.695458  1.0      109.5297 301.9913  82.9677  3.4   4.0  1672-03-06 1672-03-30
Anonymus  1677     1677-05-06.526   0.28059   1.0       99.168  240.619  100.931   4.4   4.0  1677-04-29 1677-05-08
Anonymus  1680     1680-12-18.4876  0.006222  0.999986 350.6202 275.9317  60.6771  4.4   2.1  1680-11-14 1681-03-19
                   1680-11-29.0
P/Halley  1682     1682-09-15.2794  0.582621  0.967933 109.2028  54.8507 162.2617  4.0   4.0  
                   1682-08-31.0
                                                                                                                                                                 
Anonymus  1683     1683-07-13.5907  0.559584  1.0       87.8099 177.1369  96.7443  5.0   4.0  1683-07-24 1683-09-05
Anonymus  1684     1684-06-08.763   0.95827   1.0      330.307  271.896   65.423   5.3   4.0  1684-07-01 1684-07-17
Anonymus  1686     1686-09-16.3249  0.33602   1.0       81.913  357.745   34.963   5.0   4.0  1686-08-17 1686-09-15
Anonymus  1698     1698-10-17.5149  0.72865   1.0      151.35    69.55   169.09    5.6   4.0  1698-09-02 1698-09-28

Halley's orbital parameters compared to modern values:

Comet   Ascending  Inclin.   Perihel.   Perihel    Time of
of Year    Node    of Orbit  in Orbit    dist.     Perihelion
                                                  
        deg  '  "  deg '  "  deg  '  "               day  h  m
1337     84:21:00  32:11:00   37:59:00  0.40666   Jun  2  6 25
     L   79.6     -36.40
     K   97.61    -36.40                

1472    281:46:20   5:20:00   45:33:30  0.54273   Feb 28 22 23
1531     49:25:00  17:56:00  301:39:00  0.56700   Aug 24 21 18.5
1532     80:27:00  32:36:00  111:07:00  0.5091    Oct 19 22 12
                                                      
1556   Vir 25 42  0  32  6 30  Cap  8 50  0  0.46390   Apr 21 20  3
          175:42:00               308:50.00
1577   Ari 25 52  0  74 32 45  Leo  9 22  0  0.18342   Oct 26 18 45
           25:52:00               129:22:00
1580   Ari 18 57 20  64 40  0  Cnc 19  5 50  0.59628   Nov 28 15 00
           18:57:20               109:05:50
1585   Tau  7 42 30   6  4  0  Ari  8 51  0  1.09538   Sep 27 19 20
           37:42:30                 8:51:00
                                                      
1590   Vir 15 30 40  29 40 40  Sco  6 54 30  0.57661   Jan 29  3 45
          165:30:40               246:54:30
1596   Aqr 12 12 30  55 12  0  Sco 18 16  0  0.51293   Jul 31 19 55
          312:12:30               258:16:00
1607   Tau 20 21  0  17  2  0  Aqr  2 16  0  0.58680   Oct 16  3 50
           50:21:00               302:16:00
1618   Gem 16  1  0  37 34  0  Ari  2 14  0  0.37975   Oct 29 12 23
           76:01:00                 2:14:00
                                                       
1652   Gem 28 10  0  79 28  0  Ari 28 18 40  0.84750   Nov  2 15 40
           88:10:00                28:18:40
1661   Gem 22 30 30  32 35 50  Cnc 25 58 40  0.44851   Jan 16 23 41
           82:30:30               115:58:40
1664   Gem 21 14  0  21 18 30  Leo 10 41 25  1.025755  Nov 24 11 52
           81:14:00               130:41:25
1665   Sco 18 02  0  76 05  0  Gem 11 54 30  0.10649   Apr 14  5 15.5
          258:02:00                71:54:30

1672   Cap 27 30 30  83 22 10  Tau 16 59 30  0.69739   Feb 20  8 37
          297:30:30                46:59:30
1677   Sco 26 49 10  79 03 15  Leo 17 37  5  0.28059   Apr 26 00 37.5
          266:49:10               137:37:05
1680   Cap  2  2  0  60 56  0  Sgr 22 39 30  0.006125  Dec  8 00  6
          272:02:00               262:39:30
1682   Tau 21 16 30  17 56  0  Aqr  2 52 45  0.58328   Sep  4 07 39
           51:16:30               302:52:45

1683   Vir 23 23  0  83 11  0  Gem 25 29 30  0.56020   Jul  3  2 50
          173:23:00                85:29;30
1684   Sgr 28 15  0  65 48 40  Sco 28 52  0  0.96015   May 29 10 16
          268:15:00               238:52:00
1686   Psc 20 34 40  31 21 40  Gem 17 00 30  0.32500   Sep  6 14 33
          350:34:40                77:00:30
1698   Sgr 27 44 15  11 46  0  Cap 00 51 15  0.69129   Oct  8 16 57
          267:44:15               270:51:15

Comet Halley page

Reference:

Edmond Halley, 1705. Astronomiae Cometicae Synopsis. Philosophical Transactions (1705) p. 1882-1899.

Hartmut Frommert [contact]