OAA computing section circular NK 1044 96P/Machholz 1

The following improved orbital elements, by S. Nakano, are from 137 observations 1986 to 2002, including planetary perturbations by Mercury to Neptune and three minor planets, Ceres, Pallas, Vesta, and non-gravitational effect of style II. The mean residual is +/- 0.86 arc second. See a previous orbit in NK 690 and also in MPC 44505. Epoch = 2002 Jan. 6.0 TT T = 2002 Jan. 8.62534 +/- 0.00013 (m.e.) TT Peri. = 14.58066 +/- 0.00006 Node = 94.60848 +/- 0.00002 (2000.0) Inc. = 60.18672 +/- 0.00007 q = 0.1241058 +/- 0.0000003 AU e = 0.9588109 +/- 0.0000001 a = 3.0130717 +/- 0.0000030 AU n' = 0.18844728 +/- 0.00000028 P = 5.230 +/- 0.0000077 years A1 = +0.008 +/- 0.006 A2 = -0.00015 +/- 0.00000 T = 1986 Apr. 23.51656 TT Epoch = 1986 May 10.0 TT Peri. = 14.53371 e = 0.9580119 Node = 94.50060 (2000.0) a = 3.0192802 AU Inc. = 59.98836 n'= 0.18786632 q = 0.1267740 AU P = 5.246 years T = 1991 July 21.98256 TT Epoch = 1991 July 3.0 TT Peri. = 14.53639 e = 0.9583688 Node = 94.51757 (2000.0) a = 3.0157066 AU Inc. = 60.14623 n'= 0.18820035 q = 0.1255475 AU P = 5.237 years T = 1996 Oct. 15.06690 TT Epoch = 1996 Oct. 4.0 TT Peri. = 14.58612 e = 0.9586361 Node = 94.53204 (2000.0) a = 3.0151635 AU Inc. = 60.07431 n'= 0.18825121 q = 0.1247191 AU P = 5.236 years The predicted orbit for the 2007 return is as follows: T = 2007 Apr. 4.61930 TT Epoch = 2007 Apr. 10.0 TT Peri. = 14.61811 e = 0.9586847 Node = 94.55066 (2000.0) a = 3.0162725 AU Inc. = 59.95525 n'= 0.18814740 q = 0.1246183 AU P = 5.238 years The following residuals in seconds of arc are from the above orbital elements: Date Code Residual(") Date Code Residual(") Date Code Residual(") 1986/ 860615 494 1.5+ 0.9- 910705 474 0.4- 0.0 860513 688 1.3+ 0.4+ 860625 657 2.0- 0.3- 910802 372 0.6- 1.8- 860513 688 0.6- 0.3- 860626 657 1.4- 0.4- 910802 372 (0.8+ 2.7-) 860513 392 (7.5+ 0.5+) 860626 657 1.1+ 0.7+ 910802 372 0.1- 1.5- 860513 392 (3.4+ 0.1-) 860630 323 (3.2- 4.0+) 910803 587 0.6- 0.6+ 860514 372 1.7+ 0.9+ 860704 293 2.3- 0.1+ 910814 675 (2.4+ 4.7-) 860514 372 (3.0+ 1.5+) 860704 293 (2.5- 5.4-) 910814 675 (1.8+ 3.0-) 860515 801 1.6- 1.9- 860704 801 0.1+ 0.1+ 1997/ 860515 657 (3.8+ 0.7+) 860705 691 0.5+ 0.4+ 970415 568 0.8+ 0.1- 860515 657 1.7+ 1.9+ 860705 691 0.6+ 1.1+ 970415 568 0.5+ 0.2- 860516 657 2.0+ 0.9- 860705 691 1.0+ 0.9+ 970415 568 0.6+ 0.1- 860516 688 1.9- 2.2+ 860705 691 0.5+ 1.9+ 970415 568 0.6+ 0.2- 860516 688 (9.2- 3.6+) 860707 323 1.1- 0.1- 970415 568 0.6+ 0.1- 860517 688 1.9- 0.7- 860708 801 0.2- 1.1- 970417 568 0.7+ 0.0 860517 688 0.1+ 1.0- 860710 691 0.3+ 0.8- 970417 568 0.3+ 0.4- 860517 392 (2.8+ 4.3+) 860710 691 0.1- 0.6- 970712 696 0.2+ 1.0- 860517 392 (2.0- 2.6-) 860710 691 0.1- 0.8- 970712 696 0.0 0.9- 860517 372 1.0- 0.4+ 860712 707 0.6- 1.0- 970712 696 0.1- 1.2- 860517 372 (3.2+ 2.0-) 860727 691 0.6+ 0.1- 2001/ 860517 372 (3.9+ 0.3+) 860727 691 0.3+ 0.1- 011217 844 0.6- 0.6- 860518 026 (3.1+ 1.4-) 860727 691 0.1+ 0.6- 011217 844 (2.1- 0.7-) 860518 688 (3.7- 1.5-) 860730 691 0.7- 0.7- 011217 844 (5.0+ 2.2-) 860518 688 (4.6- 1.6-) 860730 691 0.9- 0.7- 011219 844 0.0 1.4- 860519 688 (5.8+ 1.7-) 860730 691 0.8- 1.1- 011219 844 1.0+ 0.4- 860526 657 (0.8+ 13.8-) 860815 675 0.2+ 0.3- 011219 844 (1.1+ 3.3-) 860526 372 (1.1+ 3.8+) 860815 675 0.3+ 0.2+ 011219 844 1.5+ 1.0- 860526 372 (5.3+ 7.5+) 860816 675 0.2+ 0.2+ 011219 844 (0.2- 2.3-) 860529 984 (2.8+ 9.1+) 860816 675 0.2+ 0.1- 2002/ 860529 372 (4.7- 0.2-) 860905 691 1.9- 1.0+ 020113 349 (7.7+ 2.3-) 860529 372 (0.6+ 4.3-) 860905 691 0.2+ 0.1- 020113 349 (7.2+ 1.2-) 860529 372 0.4+ 0.4+ 860905 691 0.2+ 0.8+ 020113 349 (5.4+ 4.6-) 860530 657 0.7- 1.7+ 860905 691 0.8+ 0.1+ 020121 349 1.3+ 0.2- 860531 372 0.5- 1.0+ 1988/ 020121 349 1.1+ 0.7- 860531 372 1.5- 0.7- 880515 809 0.1- 0.1- 020121 349 0.2+ 0.0 860602 657 1.2- 0.6+ 880515 809 0.2- 0.1- 020121 349 0.8+ 0.3- 860603 801 1.0- 0.6- 880515 809 0.2- 0.1- 020125 349 0.6- 0.5+ 860603 552 (7.2- 5.0-) 880516 809 0.3- 0.0 020125 349 0.9- 0.6+ 860603 552 (4.8- 0.8-) 880516 809 0.3- 0.0 020125 349 0.1+ 0.3+ 860604 801 (2.9+ 2.1+) 880516 809 0.3- 0.1- 020125 349 0.8- 0.8+ 860605 801 1.5+ 0.3+ 880517 809 0.0 0.4- 020125 349 0.4- 0.1- 860605 691 0.3- 0.2+ 880517 809 0.2- 0.3- 020125 349 0.2+ 0.6- 860605 691 1.7+ 0.5- 1989/ 020127 349 0.3+ 0.7- 860605 691 0.7- 0.3+ 890406 807 0.4+ 0.4+ 020127 349 0.0 0.2- 860605 691 0.8+ 1.0- 890406 807 0.2+ 0.6+ 020127 349 0.8- 1.6+ 860606 707 0.1- 0.5- 890406 807 0.3- 0.2+ 020127 349 0.0 0.9+ 860606 691 1.1+ 0.2- 890406 807 0.4+ 0.4+ 020130 349 0.8- 0.1+ 860606 691 1.5+ 0.9+ 890406 807 0.2+ 0.3+ 020130 349 0.9- 0.7- 860607 707 0.0 0.6- 890406 807 0.1- 1.0+ 020130 349 0.3+ 0.4- 860607 372 (8.2- 2.4-) 890602 568(0.13- 0.07-) 020130 349 0.1+ 0.4+ 860609 801 0.0 0.3+ 890603 568 1.3- 0.1- 020130 349 0.9- 1.8+ 860609 399 (7.5- 1.8+) 890603 568 1.4- 0.5- 020207 349 0.9- 0.2- 860610 801 0.8- 0.7- 890801 568 0.2+ 0.3- 020207 349 1.0- 0.2+ 860611 046 1.5+ 0.1+ 1990/ 020207 349 1.7- 0.5+ 860611 046 0.1+ 0.2- 900429 807 1.8- 0.0 020207 372 1.1- 1.1+ 860611 691 1.1+ 1.0- 900429 807 1.1- 0.1+ 020214 349 1.2- 0.4- 860611 691 0.7+ 0.4+ 900429 807 1.3- 0.3+ 020214 349 (0.6- 2.0+) 860611 691 (7.1+ 4.4+) 900429 807 1.5- 0.6+ 020214 349 1.8- 0.7+ 860612 707 0.2- 0.8+ 900429 807 1.2- 0.5+ 020214 349 (2.1- 2.1+) 860612 657 (2.4- 4.0-) 1991/ 020521 704 0.5+ 0.1- 860612 392(11.4- 10.2-) 910703 474 0.5+ 0.2- 020521 704 0.0 0.2- 860612 392 (6.7- 9.4-) 910703 474 0.2- 2.1- 020521 704 0.2+ 0.3+ 860613 657 (1.0- 3.0-) 910704 474 1.3- 2.1+ 020616 468 0.3+ 1.4+ 860613 707 (3.1- 1.4-) 910704 474 (3.3- 0.4+) 020616 468 0.9+ 1.0+ 860614 392(11.0- 1.3-) 910704 474 0.9- 1.8+ 860614 392 (8.0- 0.3+) 910705 474 0.7- 1.3+ ( ) -------- Rejected Obs.

Director, Computing Section Syuichi Nakano 2004 Apr. 6

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