Nakano Note (Nakano wa Kangaeru noda) NK 2031 152P/Helin-Lawrence
The following improved orbital elements, by S. Nakano, are from 256 observations 1993 to 2011, including planetary perturbations by Mercury to Neptune and three minor planets, Ceres, Pallas, Vesta, and non-gravitational effect of sublimating molecule = CO (or N2) using Yabushita's theory (MN 283, 347). The mean residual is +/- 0.91 arc second. The delta-T correction for NK 1770 (= HICQ 2010/2011) is 0.026 day. RunOff values are -14" for R. A. and +6" for Decl.. See the previous orbits in NK 576 and NK 1260. Epoch = 2012 July 12.0 TT T = 2012 July 9.23604 +/- 0.00178 (m.e.) TT Peri. = 163.80034 +/- 0.00021 Node = 91.90975 +/- 0.00011 (2000.0) Inc. = 9.86724 +/- 0.00002 q = 3.1164617 +/- 0.0000010 AU e = 0.3073558 +/- 0.0000004 a = 4.4993686 +/- 0.0000006 AU n' = 0.10327060 +/- 0.00000002 P = 9.544 +/- 0.0000020 years Y1 = +0.001 +/- 0.017 Y2 = +0.02100 +/- 0.00079 T = 1993 June 30.34272 TT Epoch = 1993 June 22.0 TT Peri. = 163.72968 e = 0.3088448 Node = 92.03506 (2000.0) a = 4.4710110 AU Inc. = 9.88333 n'= 0.10425466 q = 3.0901624 AU P = 9.454 years T = 2002 Dec. 22.44696 TT Epoch = 2003 Jan. 1.0 TT Peri. = 163.68992 e = 0.3077394 Node = 92.01598 (2000.0) a = 4.4926809 AU Inc. = 9.87150 n'= 0.10350128 q = 3.1101060 AU P = 9.523 years The predicted orbit for the 2022 return is as follows: T = 2022 Jan. 13.70440 TT Epoch = 2022 Jan. 21.0 TT Peri. = 163.94428 e = 0.3086088 Node = 91.85776 (2000.0) a = 4.4763848 AU Inc. = 9.88042 n'= 0.10406698 q = 3.0949331 AU P = 9.471 years The following residuals in seconds of arc are from the above orbital elements: Date Code Residual(") Date Code Residual(") Date Code Residual(") 1993/ 941204 360 0.3- 1.3+ 020605 360 0.3+ 0.0 930421 675 (0.3- 4.0-) 941222 360 0.5+ 1.4+ 020609 704 1.8+ 1.1+ 930422 675 (1.8- 3.0-) 941222 360 1.0+ 1.5+ 020609 704 0.3+ 0.7+ 930517 675 1.9+ 2.1- 941222 360 0.1+ 1.4+ 020609 704 0.7+ 0.2+ 930517 675 1.6+ 1.9- 941222 413 0.3+ 0.8+ 020714 704 (2.0+ 1.9+) 930517 675 0.6+ 0.2- 941222 413 0.0 0.6+ 020714 704 (2.7+ 2.0+) 930519 675 2.3- 0.8+ 1995/ 020714 704 (4.1+ 2.1+) 930519 675 0.9+ 2.1- 950816 608 1.0- 0.5+ 020714 704 (3.1+ 1.0+) 930527 675 1.7- 1.8- 950817 608 0.8- 1.1+ 020714 704 (4.3+ 1.1+) 930527 675 1.5- 1.6- 950825 950 0.9+ 0.7- 2003/ 930527 894 1.8- 1.4- 950825 950 0.6+ 0.8- 030625 704 0.6+ 1.3+ 930527 894 2.4- 1.7- 950830 608 0.1- 0.6+ 030625 704 1.6+ 0.3- 930527 010 1.6+ 0.8- 950831 608 0.8- 0.2+ 030625 704 (1.1+ 2.4-) 930527 010 1.6+ 0.8- 950922 608 0.4- 0.1+ 030625 704 0.3+ 0.4- 930528 010 1.0+ 0.3- 950922 608 0.3- 0.1+ 030625 704 0.7- 1.2- 930529 010 (3.1+ 0.5+) 951017 608 0.0 1.6+ 030627 704 0.2- 1.6+ 930529 010 1.9+ 0.1- 951017 360 0.3- 1.3+ 030627 704 0.8- 0.0 930529 010 2.0+ 0.5- 951017 360 0.9- 1.0+ 030627 704 1.1- 0.4- 930604 361 1.2+ 1.0- 951017 360 0.3+ 0.6+ 030627 704 0.9- 1.8- 930604 361 0.1+ 0.2- 951018 608 0.5+ 1.1+ 030702 704 1.2+ 0.2- 930604 413 1.0- 1.2- 951018 608 (0.4- 2.1+) 030702 704 (0.7+ 2.0-) 930608 670 1.9- 1.0+ 1996/ 030702 704 0.9+ 1.9- 930608 670 1.4- 0.1- 960119 691 0.6+ 0.5+ 030702 704 0.9+ 1.9- 930608 670 1.2- 0.4+ 960119 691 0.4+ 0.1+ 030702 704 0.3+ 1.9- 930611 361 0.9- 0.4- 960119 691 0.7+ 0.2+ 030703 428 1.0- 0.2+ 930611 361 1.7- 0.2- 960120 691 0.4- 0.3+ 030703 428 0.6- 0.0 930611 360 0.9- 0.6- 960120 691 0.6- 0.6+ 030711 204 0.7- 0.2- 930611 361 0.0 1.8- 960120 691 0.4- 1.1+ 030711 204 0.4- 0.6- 930611 361 0.9- 0.3+ 1997/ 030711 204 1.2- 0.6- 930611 360 0.7- 0.2- 971229 568 1.2+ 0.1+ 030711 204 0.6- 0.1+ 930611 361 0.7- 1.2- 971230 568 1.0+ 0.7+ 030711 204 0.5- 0.2- 930617 675 (0.3+ 3.3-) 2001/ 030711 204 0.5- 0.2+ 930618 801 0.7- 0.3+ 010123 695 0.2- 1.5+ 030719 859 (5.1- 1.9+) 930618 801 0.5- 0.2- 010123 695 0.4- 1.1+ 030719 859 (2.9- 1.5+) 930619 675 (0.7+ 2.5-) 010123 695 0.4+ 0.1+ 030719 859 (3.2- 1.4+) 930620 675 1.8- 1.8- 011224 867 0.8- 1.0+ 030729 859 1.2- 1.3+ 930621 675 0.5+ 1.3- 011224 867 0.8+ 0.5- 030729 859 0.5+ 0.5+ 930621 675 0.5+ 2.4- 011224 867 0.2- 0.5+ 030729 859 (2.0- 1.2+) 930626 675 (2.5+ 0.1-) 011224 867 0.0 0.7+ 030928 704 0.5+ 1.0- 930626 675 1.0+ 1.1- 2002/ 030928 704 1.5+ 0.9- 930627 587 0.1+ 1.1+ 020111 461 1.1- 0.6+ 030928 704 (2.4+ 0.4+) 930627 587 0.9+ 0.4+ 020111 461 (0.1- 2.2+) 030928 704 (2.5+ 0.2+) 930627 587 0.1- 1.1+ 020111 461 1.0+ 1.1+ 030928 704 (2.8+ 0.0 ) 930701 413 0.6+ 0.3- 020224 360 0.5- 1.4+ 030929 704 0.3+ 0.6+ 930701 413 0.4+ 0.2- 020224 360 0.7- 0.5+ 030929 704 1.0+ 0.8- 930715 675 0.2+ 1.0+ 020224 360 0.5- 0.9+ 030929 704 1.7+ 0.4- 930720 675 1.8+ 1.5+ 020311 360 0.9- 0.6+ 030929 704 1.3+ 0.2+ 930720 675 0.6- 0.5+ 020311 360 1.1- 0.8+ 030929 704 (2.6+ 0.0 ) 930722 372 1.3+ 0.6- 020311 360 0.7- 0.6+ 031027 704 0.5- 0.7- 930722 372 1.4- 1.2- 020313 691 0.4+ 0.6+ 031027 704 0.0 0.3+ 930731 413 0.8- 0.2- 020313 691 0.9+ 1.5+ 031027 704 1.1+ 0.1- 930731 413 0.8- 0.1- 020320 704 0.3+ 0.2+ 031027 704 0.8+ 0.4+ 930810 474 0.2+ 0.9+ 020320 704 0.5- 1.0+ 2004/ 930810 474 0.2- 1.5+ 020320 704 0.6+ 1.9+ 040624 E12 0.3- 0.6- 930815 474 0.9- 0.8- 020320 704 (1.1- 2.5+) 040624 E12 1.8- 0.5- 930815 474 0.6- 1.5- 020410 704 0.7+ 0.4+ 040624 E12 0.9- 0.2+ 930820 675 1.7+ 0.1+ 020410 704 1.2+ 1.5+ 040624 E12 (2.5- 1.0-) 930821 675 0.8+ 2.3+ 020410 704 0.2+ 1.6+ 040826 E12 0.4- 0.4+ 930822 675 0.6+ 1.2- 020410 704 0.3- 0.4+ 040826 E12 0.0 1.0- 930905 360 0.0 1.9+ 020410 704 0.2- 1.1+ 040826 E12 1.2- 0.3- 930905 360 0.5- 1.8+ 020411 704 1.5+ 0.8+ 040826 E12 0.0 0.3+ 930913 675 0.9+ 0.8+ 020411 704 0.7+ 1.2+ 040906 644 0.4- 0.4+ 930913 675 0.9- 0.2+ 020411 704 0.6+ 1.3+ 040906 644 0.6- 0.4+ 930923 413 0.6+ 0.3- 020411 704 0.2+ 1.0+ 040906 644 0.3- 0.6+ 930923 413 0.6+ 0.3- 020411 704 (1.1- 2.0+) 040907 704 0.5- 0.2+ 931010 360 1.4+ 0.7+ 020416 704 0.5+ 1.2+ 040907 704 1.0- 0.5+ 931010 360 0.5+ 0.3+ 020416 704 0.9+ 1.2+ 040907 704 0.2+ 0.2- 931010 360 (1.1+ 2.5+) 020416 704 0.1+ 1.3+ 040907 704 0.2- 0.2+ 1994/ 020416 704 0.3+ 1.8+ 040907 704 0.6- 0.4- 940502 413 0.7- 0.7- 020416 704 0.4+ 1.7+ 040915 699 1.8- 0.2- 940502 413 0.8- 0.7- 020507 704 0.0 1.1+ 040915 699 (2.7- 0.5+) 940502 413 0.9- 0.8- 020507 704 0.1+ 0.1+ 040915 699 1.6- 1.2+ 940503 413 1.2- 0.7- 020507 704 0.0 1.3+ 040915 699 1.4- 1.8+ 940503 413 1.7- 0.2- 020507 704 0.3- 1.6+ 040918 204 0.1- 0.2+ 940504 413 0.8- 0.7- 020507 644 0.3+ 1.3+ 040919 204 0.7+ 1.3+ 940504 413 0.9- 0.6- 020507 704 0.7- 1.3+ 040921 704 0.9- 0.0 940803 360 0.4- 0.5+ 020507 644 0.4+ 1.1+ 040921 704 0.2- 0.8+ 940803 360 0.7- 0.7+ 020507 644 0.4+ 1.5+ 040921 704 0.3- 0.6+ 940815 360 0.9- 0.4+ 020512 644 0.6+ 0.8+ 040921 704 0.7+ 0.5+ 940815 360 1.0- 0.7+ 020512 644 0.6+ 0.7+ 040921 704 0.4+ 0.2+ 940906 691 0.8- 0.1- 020512 644 0.5+ 0.9+ 041005 704 1.1+ 0.1+ 940906 691 0.7- 0.0 020512 367 0.0 0.1- 041005 704 0.3+ 1.4+ 940906 691 0.7- 0.4+ 020512 367 0.3+ 0.3+ 041005 704 0.1- 1.3+ 940908 360 0.4- 0.9+ 020512 367 0.4+ 0.1+ 041006 704 0.7+ 1.5+ 940908 360 0.7- 0.7+ 020513 704 (2.4+ 0.8+) 041006 704 0.4+ 0.1+ 940917 413 0.1+ 0.9+ 020513 704 (2.7+ 0.8+) 041006 704 0.0 0.2- 940917 413 0.3- 1.6+ 020513 704 (2.5+ 1.2+) 041006 360 0.4+ 0.3+ 940918 413 0.7- 1.8+ 020513 704 (2.6+ 0.5+) 041006 360 0.4+ 0.3+ 940918 413 0.3- 1.9+ 020513 704 1.7+ 1.4+ 041107 644 0.8+ 0.8+ 940925 360 0.2- 0.5+ 020518 608 1.1+ 1.0- 041107 644 0.5+ 1.3+ 940925 360 0.1- 0.8+ 020518 608 0.7+ 0.0 041107 644 0.5+ 0.8+ 941024 360 0.4- 0.8+ 020518 608 1.1+ 0.3+ 041201 360 0.0 0.2- 941024 360 0.0 1.2+ 020519 360 0.3+ 0.2+ 041201 360 0.4+ 0.5+ 941025 360 0.4+ 0.2+ 020519 360 0.9+ 0.6+ 041201 360 0.5+ 0.1+ 941025 360 0.0 0.5+ 020601 170 0.7+ 0.4- 2011/ 941106 360 0.1+ 1.1+ 020601 170 0.3- 0.1+ 110201 G68 0.9- 1.0+ 941106 360 0.3+ 1.3+ 020603 118 (2.3+ 0.5+) 110201 G68 0.3+ 0.7+ 941123 360 0.1+ 1.2+ 020603 118 1.7+ 0.5+ 110204 G68 1.5+ 0.9+ 941123 360 0.1+ 1.1+ 020603 118 1.5+ 0.6+ 110204 G68 0.5+ 0.9+ 941204 360 0.3+ 1.6+ 020605 360 0.5+ 0.3+ ( ) -------- Rejected Obs.
Associate of Central Bureau for Astronomical Telegrams Syuichi Nakano 2011 Feb. 6