Nakano Note (Nakano wa Kangaeru noda) NK 3997 13P/Olbers

The following improved orbital elements, by S. Nakano, are from 44 observations 1815 to 1956, including planetary perturbations by Mercury to Neptune and three minor planets, Ceres, Pallas, Vesta, and non-gravitational effect of style II. The weighting mean residual is +/- 1.57 arc seconds. Epoch = 1956 June 16.0 TT T = 1956 June 19.13750 +/- 0.00160 (m.e.) TT Peri. = 64.64225 +/- 0.00183 Node = 86.10516 +/- 0.00028 (2000.0) Inc. = 44.60854 +/- 0.00031 q = 1.1784735 +/- 0.0000126 AU e = 0.9303163 +/- 0.0000007 a = 16.9117511 +/- 0.0000152 AU n' = 0.01417168 +/- 0.00000002 P = 69.548 +/- 0.0000936 years A1 = +0.916 +/- 0.629 A2 = +0.06568 +/- 0.00086 T = 1815 Apr. 26.48769 TT Epoch = 1815 Apr. 17.0 TT Peri. = 65.59157 e = 0.9317009 Node = 86.03353 (2000.0) a = 17.7590448 AU Inc. = 44.49588 n'= 0.01316966 q = 1.2129275 AU P = 74.839 years T = 1887 Oct. 8.97290 TT Epoch = 1887 Oct. 16.0 TT Peri. = 65.35523 e = 0.9309572 Node = 86.05832 (2000.0) a = 17.3674609 AU Inc. = 44.56957 n'= 0.01361757 q = 1.1990989 AU P = 72.378 years The predicted orbit for the 2024 return is as follows: T = 2024 June 30.53173 TT Epoch = 2024 June 19.0 TT Peri. = 64.41184 e = 0.9302962 Node = 85.84834 (2000.0) a = 16.8643328 AU Inc. = 44.66468 n'= 0.01423149 q = 1.1755085 AU P = 69.255 years The following residuals in seconds of arc are from the above orbital elements: Date Code Residual(") Date Code Residual(") Date Code Residual(") 1815/ 870913 058 1.0- 3.2+ 880616 662 10.7+ 7.0- 150317 500 0.3+ 3.6- 870913 582 0.1+ 6.9+ 880618 662 12.9- 8.5+ 150331 500 5.1- 5.4+ 870915 526 8.0- 2.8+ 880702 662(63.6+ 4.7+) 150410 500 6.1- 4.9+ 870915 522 4.1- 0.3- 880703 662 (0.7+ 19.2+) 150422 500 8.7- 3.2+ 870915 526 4.5- 0.5- 880705 662 10.8+ 10.4- 150505 500 7.7- 2.5- 870916 526 1.2- 0.5+ 880706 662(22.1+ 22.8+) 150516 500 6.8- 12.3+ 870916 526 2.6+ 0.7+ 880706 662(32.6+ 36.2+) 150529 500 5.4- 4.2+ 870917 787 9.0- 8.9- 1955/ 150610 500 8.8- 7.9+ 870919 526 0.1+ 0.2- 551112 711 3.1+ 0.2- 150624 500 0.7+ 10.7+ 870920 787(26.2+ 56.7+) 551112 711 (4.2+ 0.0 ) 150706 500 0.5+ 11.6+ 870926 084(19.0+ 2.9-) 1956/ 150730 500 11.9+ 15.4- 871011 084 1.5- 0.8- 560102 388 3.9- 0.1+ 150825 500 18.6+ 1.1- 871011 582 0.3+ 2.7+ 560104 059(0.28+ 0.36+)X 1887/ 871013 582 6.3+ 6.3+ 560109 059(0.03+ 0.01-)X 870827 296(16.6- 0.5-) 871014 582 3.9+ 1.2+ 560113 754 (4.5- 0.2-) 870828 058 5.7- 1.2+ 871016 084 1.1+ 6.2+ 560113 754 0.1+ 1.7+ 870828 296 4.2+ 2.6+ 871018 582 3.7+ 14.9- 560114 754(11.2+ 2.0-) 870828 759 3.0- 4.0- 871020 582 1.1+ 0.4+ 560114 388 0.0 0.9- 870829 058 10.8- 0.6+ 871022 582 1.3- 7.5+ 560115 388 2.0- 0.3- 870829 296 1.1+ 3.2- 871022 084 8.6+ 0.4- 560117 388 2.2- 3.4- 870829 759 6.9- 5.7+ 871026 582 4.7+ 2.8+ 560117 377 (6.8+ 6.8-) 870830 058 0.4- 1.3+ 871029 582 2.8+ 0.3- 560131 754 (0.7+ 19.0-) 870830 475 9.6+ 9.8+ 871105 582 1.5+ 0.3+ 560204 662 1.9+ 0.7+ 870830 008 7.8- 2.7- 871107 582 5.0- 3.7+ 560204 662 2.5+ 1.1+ 870830 016(52.2+ 3.3-) 871113 084 5.5+ 1.4+ 560205 754 0.1- 0.5+ 870830 008 6.3- 2.4- 871115 582 1.4+ 2.4+ 560205 754 0.3+ 1.2+ 870830 296 3.3- 2.4- 871115 084 0.5+ 1.9+ 560312 662 1.3- 0.1- 870830 787 8.0- 1.3+ 871116 582 (1.4- 29.1-) 560312 662 1.7- 0.0 870830 787 (0.8- 18.0+) 871117 582(11.8+ 24.0-) 560330 377 (2.7- 4.7-) 870831 016 2.0- 0.2+ 871207 582 11.5+ 3.0- 560408 045 2.0+ 0.2+ 870831 296 1.1- 5.2- 871211 582 8.5+ 2.5- 560420 662 1.6+ 0.7- 870831 787 8.3+ 5.7+ 871214 582 10.4+ 6.7+ 560420 662 0.9+ 0.9- 870831 787 2.4- 3.3+ 871217 582 11.4+ 3.0- 560519 662 0.2+ 1.1+ 870901 475(13.1+ 24.1-) 871219 582 9.8+ 1.4+ 560519 662 0.5- 1.5+ 870901 008 0.6- 0.7+ 1888/ 560807 754 (2.2+ 10.6-) 870901 008 0.5+ 0.9- 880221 008 0.4+ 9.2+ 560816 035 1.9- 0.4+ 870901 787(15.9- 11.0-) 880221 008 0.8+ 11.0+ 560816 035 2.6- 1.3- 870902 016 4.7- 7.4- 880323 008 8.1+ 0.8- 560816 035 3.1- 0.8- 870903 008(28.2+ 4.5+) 880323 008 2.4+ 10.8+ 560902 754 2.7+ 0.1+ 870907 558 8.4+ 3.5+ 880324 008 3.4+ 7.0- 560903 754 2.3+ 1.0+ 870907 558 8.4+ 4.0+ 880325 008 3.7+ 9.5+ 560912 754 1.4+ 0.1- 870911 058 2.3+ 0.1+ 880325 008 (1.6+ 31.8+) 560912 754 (5.6- 0.1+) ( ) -------- Rejected Obs.

Associate of the CBAT Late edition Syuichi Nakano 2015 May 15

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