Nakano Note (Nakano wa Kangaeru noda) NK 2469 98P/Takamizawa

The following improved orbital elements, by S. Nakano, are from 122 observations 1991 to 2013, 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 +/- 0.84 arc second. The 2013 observations show the residuals of -58" for R. A. and +22" for Decl. off from the prediction in NK 1922 (= HICQ 2012) with the delta-T correction = +0.03 day. See the previous orbits in NK 506, NK 628, NK 931 and NK 1922. Epoch = 2013 Aug. 16.0 TT T = 2013 Aug. 5.38414 +/- 0.00068 (m.e.) TT Peri. = 157.88951 +/- 0.00027 Node = 114.74090 +/- 0.00016 (2000.0) Inc. = 10.54397 +/- 0.00002 q = 1.6735449 +/- 0.0000014 AU e = 0.5606754 +/- 0.0000002 a = 3.8093584 +/- 0.0000010 AU n' = 0.13256422 +/- 0.00000005 P = 7.435 +/- 0.0000028 years A1 = +0.607 +/- 0.028 A2 = +0.04918 +/- 0.00028 T = 1991 Aug. 17.91242 TT Epoch = 1991 Aug. 12.0 TT Peri. = 147.67716 e = 0.5745901 Node = 124.92015 (2000.0) a = 3.7370084 AU Inc. = 9.47942 n'= 0.13643254 q = 1.5897606 AU P = 7.224 years T = 1998 Nov. 7.99269 TT Epoch = 1998 Nov. 3.0 TT Peri. = 147.80198 e = 0.5751754 Node = 124.84692 (2000.0) a = 3.7314078 AU Inc. = 9.48969 n'= 0.13673982 q = 1.5851937 AU P = 7.208 years T = 2006 Mar. 6.46924 TT Epoch = 2006 Mar. 6.0 TT Peri. = 157.88093 e = 0.5621223 Node = 114.76536 (2000.0) a = 3.7973050 AU Inc. = 10.55696 n'= 0.13319590 q = 1.6627552 AU P = 7.400 years The predicted orbit for the 2021 return is as follows: T = 2021 Jan. 4.94351 TT Epoch = 2020 Dec. 17.0 TT Peri. = 157.92353 e = 0.5622555 Node = 114.71115 (2000.0) a = 3.7990791 AU Inc. = 10.56140 n'= 0.13310261 q = 1.6630260 AU P = 7.405 years The following residuals in seconds of arc are from the above orbital elements: Date Code Residual(") Date Code Residual(") Date Code Residual(") 1991/ 910912 801 (5.1- 0.1+) 060630 204 0.7+ 0.3- 910212 372 (2.4- 2.5+) 910912 801 (4.7- 0.0 ) 060630 204 0.4- 0.2+ 910217 691 0.2- 1.8+ 910913 801 (5.6- 2.0+) 060708 213 0.1+ 0.1- 910217 691 0.2- 0.6+ 910913 801 (5.9- 0.5-) 060708 213 0.2+ 0.0 910217 691 0.2+ 1.4+ 1998/ 060708 213 0.2+ 0.0 910219 691 0.6+ 0.9+ 980302 867 (2.0- 2.2+) 060720 704 0.2+ 0.8+ 910219 691 0.9+ 0.2+ 980302 867 (3.3- 3.6+) 060720 704 1.4+ 0.8+ 910219 691 0.4+ 0.4+ 980302 867 (1.5- 2.8+) 060720 704 0.3+ 0.5+ 910222 372 1.4+ 0.5+ 980516 118 0.3- 0.3+ 060721 170 0.4+ 0.3+ 910317 801 1.3- 1.5+ 980516 118 0.3- 0.1+ 060721 170 0.4+ 0.1+ 910317 801 0.6- 1.5+ 980519 867 0.5+ 0.2+ 060721 170 0.8+ 0.3- 910320 801 1.2- 1.0+ 980519 867 0.8- 0.3- 060721 585 0.4+ 1.0- 910320 801 1.3- 1.5+ 980519 867 0.1+ 1.1- 060722 585 (3.0+ 0.7+) 910408 675 0.2+ 0.6- 980525 118 (2.5+ 0.4-) 060722 585 1.0+ 1.1- 910408 675 2.1+ 0.4- 980525 118 1.5+ 0.3- 060722 585 0.8+ 0.5+ 910411 657 0.5+ 1.2+ 980619 696 0.6- 0.6+ 060722 585 (2.6+ 0.8+) 910411 657 0.5+ 0.5+ 980619 696 0.3- 0.8+ 060726 215 1.6+ 0.4- 910411 675 0.6+ 1.5- 980619 696 0.2- 0.2+ 060726 215 0.3+ 0.6- 910411 675 0.9- 1.4+ 2006/ 060726 215 0.2+ 0.6- 910412 801 0.9- 0.2+ 060324 G96 0.5+ 0.1+ 060728 130 0.5+ 0.0 910412 801 2.3- 0.6+ 060324 G96 0.8- 0.0 060728 130 1.6+ 1.0+ 910412 657 2.2- 0.9- 060324 G96 1.1- 0.2+ 060731 E12 (2.3- 0.3+) 910413 801 1.0- 0.2+ 060324 G96 0.7- 0.1+ 060731 E12 1.7- 0.1- 910413 675 0.3- 1.1- 060325 G96 0.1+ 0.8+ 060731 E12 (2.5- 0.2-) 910414 801 0.4- 0.3+ 060325 G96 0.4+ 0.8+ 060731 E12 1.2- 0.1- 910414 801 0.2- 0.1+ 060325 G96 0.6+ 0.2+ 060805 349 1.1- 0.6- 910422 691 0.1+ 0.2- 060325 G96 0.1+ 0.5+ 060805 349 1.2- 0.1+ 910422 691 0.3+ 0.1+ 060402 349 (5.3- 0.8+) 060807 213 0.5+ 1.7+ 910422 691 0.1+ 0.3+ 060402 349 (4.7- 1.3+) 060807 213 0.8- 1.2+ 910502 657 0.3- 0.1+ 060402 349 (5.2- 1.5+) 060807 349 0.9- 0.1- 910502 657 0.1+ 0.3- 060403 349 (4.7- 1.0-) 060807 349 0.6- 0.0 910511 801 0.1- 0.4- 060403 349 (4.9- 0.6+) 060828 A02 1.6- 0.6+ 910511 801 0.6+ 0.7- 060420 E12 0.6- 0.6+ 060828 A02 1.1- 0.3+ 910512 801 0.0 0.5- 060420 E12 1.1- 0.8- 060828 A02 0.8- 0.1- 910512 801 0.0 0.6- 060420 E12 1.7- 0.5- 060902 349 0.6- 0.8+ 910514 494 1.4+ 1.2+ 060420 E12 (2.3- 0.6+) 060902 349 0.4+ 0.9+ 910517 801 0.6+ 1.6- 060505 415 0.4+ 0.7+ 060914 415 0.1+ 0.1- 910517 801 0.6+ 1.2- 060505 415 0.6+ 0.0 060920 703 1.2+ 1.2+ 910611 801 1.8+ 1.2- 060507 467 0.5+ 0.2- 060920 703 (1.7- 2.8+) 910611 801 1.8+ 1.3- 060507 467 0.5+ 0.0 060920 703 0.9- 0.5+ 910614 801 1.6+ 1.5- 060507 467 0.9+ 0.1+ 060920 703 (0.3+ 2.0+) 910614 801 1.2+ 1.7- 060607 I77 0.6- 1.1+ 060925 415 0.4+ 0.4- 910710 801 (0.1- 2.8-) 060607 I77 0.8- 0.3+ 060925 415 1.1- 1.0+ 910710 801 0.7- 1.0- 060607 I77 1.1- 0.4- 2013/ 910712 801 0.5- 1.3- 060608 I77 0.3- 0.5- 130315 C10 1.2+ 0.6+ 910712 801 0.6- 1.7- 060608 I77 0.0 0.8+ 130315 C10 0.7+ 0.7+ 910806 801 (2.7- 2.4-) 060608 I77 0.6- 0.3- 130315 D90 0.5+ 0.7+ 910806 801 (3.5- 0.5-) 060608 I77 1.9+ 0.8+ 130315 D90 0.1- 1.2+ 910812 801 1.1- 0.7+ 060627 204 0.6+ 0.2- 130318 C10 0.5- 1.2+ 910812 801 2.0- 0.6+ 060627 204 0.7+ 0.0 130318 C10 0.1+ 1.0+ ( ) -------- Rejected Obs.

Associate of Central Bureau for Astronomical Telegrams Syuichi Nakano 2013 Apr. 5

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