2023MNRAS.518.2068G

Query : 2023MNRAS.518.2068G

2023MNRAS.518.2068G - Mon. Not. R. Astron. Soc., 518, 2068-2075 (2023/January-2)

Chaos in multiplanetary extrasolar systems.

GAJDOS P. and VANKO M.

Abstract (from CDS):

Here, we present an initial look at the dynamics and stability of 178 multiplanetary systems that are already confirmed and listed in the NASA Exoplanet Archive. To distinguish between the chaotic and regular nature of a system, the value of the Mean Exponential Growth factor of Nearby Orbits (MEGNO) indicator for each system was determined. Almost three-quarters of them could be labelled as long-term stable. Only 45 studied systems show chaotic behaviour. We consequently investigated the effects of the number of planets and their parameters on the system stability. A comparison of results obtained using the MEGNO indicator and machine-learning algorithm SPOCK (Stability of Planetary Orbital Configuration Klassifier) suggests that the SPOCK could be used as an effective tool for reviewing the stability of multiplanetary systems. A similar study was already published by Laskar and Petit. We compared their analysis based on the AMD (Angular Momentum Deficit) criterion with our results. The possible discrepancies are discussed.

Abstract Copyright: © 2022 The Author(s) Published by Oxford University Press on behalf of Royal Astronomical Society

Journal keyword(s): methods: numerical - planets and satellites: dynamical evolution and stability - planetary systems

VizieR on-line data: <Available at CDS (J/MNRAS/518/2068): table1.dat>

Simbad objects: 179

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Number of rows : 179
N Identifier Otype ICRS (J2000)
RA 		ICRS (J2000)
DEC 		Mag U Mag B Mag V Mag R Mag I Sp type #ref
1850 - 2026 		#notes
1 HD 1605 PM* 00 20 31.5189144840 +30 58 29.302087188   8.55 7.52     G8IV 62 0
2 WT 2353 PM* 00 29 12.3029193648 -30 27 13.466857032   13.05 11.95     ~ 102 0
3 HD 3167 PM* 00 34 57.5242131960 +04 22 53.284093032       8.4   K0V 128 0
4 HD 4203 PM* 00 44 41.2002505536 +20 26 56.138079876       8.2   G6V 154 1
5 G 268-38 PM* 00 44 59.3309137511 -15 16 17.542839990     14.150 13.801 11.19 M4.5V 197 0
6 K2-106 PM* 00 52 19.1415736296 +10 47 40.906374828   12.58 12.10     ~ 61 0
7 HD 5319 * 00 55 01.3998443472 +00 47 22.401372408   9.03 8.05     K0III 115 1
8 HD 9446 PM* 01 33 20.1847092432 +29 15 54.539434692   9.03   8.0   G5V 84 1
9 TOI-125 PM* 01 34 22.7341114800 -66 40 32.951081784   11.72 11.02     ~ 38 0
10 HD 11506 PM* 01 52 50.5344163920 -19 30 25.108242192   8.11 7.51     G0V 104 1
11 V* TZ Ari PM* 02 00 12.9563198327 +13 03 07.000569241 15.406 14.100 12.298 10.943 9.195 M4.5V 325 0
12 HD 12661 PM* 02 04 34.2881404104 +25 24 51.513637932   8.16   7.0   K0V 278 1
13 HD 15337 PM* 02 27 28.3781273256 -27 38 06.736755624   9.95 9.09     K1V 122 0
14 NAME Teegarden's Star LM* 02 53 00.8917932409 +16 52 52.632190137   17.21 15.14 13.03 10.65 dM6 207 0
15 HD 20003 PM* 03 07 37.9177511616 -72 19 18.794564400   9.140 8.37 8.02 8.63 G8V 95 1
16 BD+20 518 PM* 03 11 14.2301712744 +21 05 50.493993288   9.26 8.50     G6V 127 1
17 HD 21749 PM* 03 26 59.2226447548 -63 29 56.762928961 10.446 9.302 8.143 7.43 6.865 K4.5V 133 1
18 HD 21693 PM* 03 27 12.4815289824 -58 19 25.249845108   8.715 7.94 8.00 8.61 G9IV-V 93 1
19 L 372-58 PM* 03 35 59.6991613260 -44 30 45.730830569 16.22 14.98 13.07 11.45 9.47 M5.5V 145 0
20 HD 23472 PM* 03 41 50.3987760888 -62 46 01.477226928   10.80 9.72     K3.5V 77 0
21 L 231-32 PM* 04 33 39.7200127728 -51 57 22.435373160     12.617 12.147   M3.0V 83 0
22 HD 30177 PM* 04 41 54.3737734560 -58 01 14.727688572   9.18 8.37     G8V 152 1
23 HD 31527 PM* 04 55 38.3826333744 -23 14 30.761639592   8.071 7.484 7.24 8.88 G0V 120 1
24 TOI-216 PM* 04 55 55.2548838048 -63 15 36.313162056           ~ 58 0
25 HD 33142 * 05 07 35.5413937248 -13 59 11.336809164   8.905 7.96     K0III 69 1
26 HD 33844 RG* 05 12 36.1003262136 -14 57 03.999312756   8.33 7.29     K0III 71 0
27 CD-26 2288 PM* 05 33 04.6005234792 -26 43 28.268361984   10.17 9.13     K3+Vk: 79 0
28 HD 37124 PM* 05 37 02.4866159419 +20 43 50.832948117   8.35   7.2   G4IV-V 321 2
29 HD 37605 PM* 05 40 01.7283246192 +06 03 38.072512008   9.52   8.1   K0 125 1
30 BD-06 1339 PM* 05 53 00.2846861073 -05 59 41.441196105 12.27 11.041 9.693 8.855 8.099 K7V/M0V 106 1
31 HD 45184 PM* 06 24 43.8795895848 -28 46 48.415725948   7.01 6.39 6.24 8.94 G2Va 238 1
32 HD 45364 PM* 06 25 38.4743561928 -31 28 51.430718388   8.82 8.06     G8V 145 1
33 CoRoT-20 * 06 30 52.9022402976 +00 13 36.858436428   15.41 14.66 14.60 13.69 ~ 32 2
34 HD 47186 PM* 06 36 08.7879310512 -27 37 20.268367464   8.36 7.63     G6V 165 1
35 HD 47366 PM* 06 37 40.7934964800 -12 59 06.422813988   7.096 6.106     K1(III) 73 0
36 CoRoT-7 * 06 43 49.4690164104 -01 03 46.826642700   12.78 11.73 11.36 10.87 K0V 232 1
37 CoRoT-24 * 06 47 41.4118109352 -03 43 09.483840696       15.60 14.30 ~ 24 1
38 HD 50499 PM* 06 52 02.0241958872 -33 54 56.019365496   7.82 7.20     G0/2V 131 1
39 HD 51608 PM* 06 54 51.3407691144 -55 15 33.581230956   8.947 8.17 7.94 8.65 K0IV-V 117 1
40 HD 60532 PM* 07 34 03.1805638968 -22 17 45.843172440 5.02 4.94 4.39     F6IV-V 244 1
41 HD 63935 MS* 07 51 41.9964294054 +09 23 09.790475797       8.1   G5 56 0
42 CD-24 6144 PM* 07 54 10.8827214844 -25 18 11.422307648 12.286 11.107 9.715 8.845 8.029 M0 63 0
43 HD 67087 * 08 07 39.7559315184 +31 33 04.740976332   8.55 8.04     F8V 46 0
44 HD 69830 PM* 08 18 23.9469682407 -12 37 55.817187530   6.74 5.95     G8:V 587 1
45 HD 73526 PM* 08 37 16.4833548528 -41 19 08.790456324   9.69 9.00     G6V 206 2
46 HAT-P-13 * 08 39 31.8072358440 +47 21 07.273799280   11.15 10.42 10.40   G4 149 2
47 K2-146 LM* 08 40 06.4242250368 +19 05 34.430759088   17.87 16.25 15.97   M3.0V 49 0
48 L 675-81 Pe* 08 40 59.2057867166 -23 27 22.592748045   13.2 11.975 11.637 9.37 M3.5V 180 1
49 HD 74156 PM* 08 42 25.1219511432 +04 34 41.145751740       7.2   G1V 247 2
50 HD 75784 PM* 08 52 23.9418283800 +13 14 00.366273276 9.740 8.840 7.850     G5 61 0
51 HD 82943 PM* 09 34 50.7353072232 -12 07 46.369202196   7.17 6.53     F9VFe+0.5 498 2
52 TOI-561 MS* 09 52 44.5491687624 +06 12 58.920960204   10.909 10.243 10.065   ~ 65 0
53 BD-08 2823 PM* 10 00 47.7204762252 -09 31 00.044866538   10.94 9.874 9.801   K4:V 86 1
54 BD+20 2457 * 10 16 44.8671846183 +19 53 29.010025880   10.99 9.74     K2 64 1
55 BD+20 2459 * 10 17 06.6759730608 +19 33 30.435253452   11.26 10.19     G5 30 0
56 * 24 Sex PM* 10 23 28.3698081504 -00 54 08.092603368   7.400 6.441 6.41   K0IV 94 1
57 LP 62-217 PM* 10 28 35.0250921216 +65 51 16.381197180   13.351 11.973 11.649   ~ 21 0
58 HD 92788 PM* 10 42 48.5278074048 -02 11 01.525313004   8.01 7.30     G6V 260 1
59 HD 95089 PM* 10 58 47.7361917120 +01 43 45.170499324   8.897 7.95     G8/K0IV 58 1
60 * 47 UMa PM* 10 59 27.9727514012 +40 25 48.920572724   5.66   4.7   G1-VFe-0.5 824 1
61 HD 95735 PM* 11 03 20.1948195942 +35 58 11.576182057 10.030 8.960 7.520 5.99 4.79 M2+V 795 0
62 K2-36 * 11 17 47.7835701912 +03 51 59.005811016   12.57 11.73 11.48   K3 42 0
63 HD 99706 PM* 11 28 30.2135705208 +43 57 59.685949260   8.646 7.64 11.7   K0 56 1
64 K2-3 PM* 11 29 20.3917077216 -01 27 17.281697868   13.52 12.17 11.88   M1V 99 0
65 Ross 1003 PM* 11 41 44.6358403057 +42 45 07.102117090   13.36 13.795 11.524 9.18 M4.0V 172 1
66 BD+31 2290 PM* 11 44 40.9643370921 +30 57 33.448132849   10.09   8.3   K4V 93 1
67 HD 102329 * 11 46 46.6451659152 +03 28 27.457567572   8.93 7.89     K0III 42 1
68 LP 961-53 PM* 11 54 18.3921193416 -37 33 09.837719244     11.536 11.104   M1 47 0
69 HD 106315 * 12 13 53.3962381416 -00 23 36.553445304   9.402 8.951     F5V 62 0
70 HD 108874 PM* 12 30 26.8817398344 +22 52 47.377485192   9.49   8.3   G9V 182 1
71 WASP-107 PM* 12 33 32.8441110816 -10 08 46.225572324   14.62 11.47     K7V 121 0
72 HD 109271 PM* 12 33 35.5545820056 -11 37 18.728871528   8.71 8.05     G3/5V 87 1
73 CD-39 7945 PM* 12 57 52.4466594744 -39 45 27.707568552   10.85 10.28 10.14   ~ 19 0
74 PSR B1257+12 Psr 13 00 03.1075 +12 40 55.155           ~ 546 1
75 HD 113538 PM* 13 04 57.4765361506 -52 26 34.525896996 11.733 10.433 9.057 8.202 7.418 K9Vk: 95 1
76 PM J13119+6550 PM* 13 11 59.5600372848 +65 50 01.703045580   14.590 12.951 12.582   M3 47 0
77 HD 114783 PM* 13 12 43.7855575272 -02 15 54.130663296 9.137 8.469 7.550 7.053 6.627 K1V 214 1
78 BD+49 2212 Em* 13 24 21.0388711032 +48 53 06.363428244   10.20 9.42     G8 38 0
79 HD 121056 RG* 13 53 52.0613118474 -35 18 51.691786471   7.21 6.19     K0III 96 0
80 HAT-P-44 * 14 12 34.5714083256 +47 00 53.044781616   13.2 13.21 12.83 12.31 ~ 43 1
81 HD 128311 BY* 14 36 00.5602765558 +09 44 47.454573266 9.232 8.441 7.446 6.895 6.425 K3V 338 1
82 HD 134060 PM* 15 10 44.7430146168 -61 25 20.360681976   6.91 6.285 6.16 8.68 G0VFe+0.4 153 1
83 K2-314 * 15 12 59.5618336872 -16 43 28.198547940   12.355 11.577     ~ 30 0
84 * 23 Lib PM* 15 13 28.6669233518 -25 18 33.653388418   7.168 6.46 6.43   G6IV-V 332 1
85 BD-07 4003 BY* 15 19 26.8269387505 -07 43 20.189497466 13.403 11.76 10.560 9.461 8.911 M3V 717 2
86 * nu.02 Lup PM* 15 21 48.1499105161 -48 19 03.469906910 6.35 6.30 5.65     G2-V 354 1
87 BD-19 4086 * 15 21 55.1983073496 -20 13 53.990924232   11.81 10.88     K3 38 0
88 * gam Lib ** 15 35 31.5780958333 -14 47 22.327914429 5.67 4.93 3.91 3.20 2.65 G8.5III 171 0
89 HD 141399 PM* 15 46 53.8131805104 +46 59 10.543183404   7.93 7.20     K0 69 0
90 HD 141399e Pl 15 46 53.8131805104 +46 59 10.543183404           ~ 14 0
91 K2-38 PM* 16 00 08.0580517944 -23 11 21.329133720   12.34 11.34     ~ 45 0
92 CD-24 12581 PM* 16 10 17.6976776832 -24 59 25.260709632   12.22 11.28     ~ 58 0
93 HD 147018 PM* 16 23 00.1478804220 -61 41 19.559913914   9.07 8.30     G8/K0V 79 1
94 HD 148164 PM* 16 25 44.5337348424 +11 55 08.637568320   8.78 8.21     F8 49 0
95 HD 152843 * 16 55 08.3561051472 +20 29 28.794494940   9.38 8.85     G0 16 0
96 WASP-148 * 16 56 31.3396591416 +44 18 09.548648496   13.30 12.04     ~ 33 0
97 HD 155358 PM* 17 09 34.6176428924 +33 21 21.085565784       7.0   G0 175 1
98 HD 154857 PM* 17 11 15.7220463696 -56 40 50.871194796   7.93 7.24     G5V 110 1
99 HD 156279 PM* 17 12 23.2048155528 +63 21 07.531228764       7.6   K0 73 1
100 BD+68 946 PM* 17 36 25.8993094605 +68 20 20.909627174 11.73 10.65   8.3   M3.0V 345 0
101 HD 159868 PM* 17 38 59.5268792544 -43 08 43.842381468   7.96 7.24     G5V 159 1
102 * mu. Ara PM* 17 44 08.7031414872 -51 50 02.591603160   5.85 5.15     G3IV-V 578 2
103 HD 163607 PM* 17 53 40.4946041184 +56 23 31.040169720   8.762 7.979 7.80   G5IV 88 1
104 * nu. Oph PM* 17 59 01.5922136612 -09 46 25.080976810 5.20 4.33 3.34 2.64 2.16 G9IIIa 226 1
105 HD 168443 PM* 18 20 03.9332862096 -09 35 44.614653900   7.62 6.92     G6V 334 1
106 HD 169830 * 18 27 49.4849984976 -29 49 00.700831380   6.406 5.902 7.01   F7V 298 1
107 Kepler-102 PM* 18 45 55.8559851072 +47 12 28.845259020   12.58 12.07 11.510   K3V 137 0
108 Kepler-128 Er* 18 49 58.1342142288 +43 58 48.694489320   11.984 11.380 11.280   F2 105 0
109 Kepler-297 Er* 18 52 50.1951598032 +48 46 39.435391848   15.031 14.351 14.299   ~ 73 0
110 Kepler-62 Er* 18 52 51.0518497680 +45 20 59.399622996   14.702 13.982 13.807   G5 158 1
111 Kepler-101 Er* 18 53 01.3205511624 +48 21 18.784380528   14.474 13.729 13.574   G4 63 0
112 Kepler-30 Er* 19 01 08.0746104528 +38 56 50.218268856   16.50   15.767 14.55 ~ 180 1
113 Kepler-129 Er* 19 01 14.7043468776 +47 50 54.901789800   12.67 11.81 11.603   G4V 106 0
114 Kepler-10 Em* 19 02 43.0613892904 +50 14 28.701617339       11.00   G2V 238 1
115 HD 176986 PM* 19 03 05.8729653768 -11 02 38.130757620   9.39 8.45     K2.5V 81 0
116 Kepler-177 Er* 19 04 11.3086186360 +45 03 11.548856286   15.885 15.078 15.110   ~ 74 0
117 Kepler-277 Er* 19 06 19.9577165304 +39 04 37.861617108       13.491   ~ 66 0
118 Kepler-105 Er* 19 11 32.9514004104 +46 16 34.384220652   13.59 12.92 12.89   F6IV 92 0
119 Kepler-113 Er* 19 11 59.4990081336 +50 56 39.668230356   14.990 13.718 13.477   K4 74 0
120 Kepler-50 Er* 19 12 24.2128368312 +50 02 01.374741852   11.02 10.54 10.387   F5 131 1
121 Kepler-131 Er* 19 14 07.4053097208 +40 56 32.328971700   12.379 11.677 11.516   G2V 95 0
122 BD+40 3638 Er* 19 14 45.2915908224 +41 09 04.210237980   11.643 11.115 11.009   F6IV 159 1
123 Kepler-117 Er* 19 15 10.3301577216 +48 02 24.785162160   15.056 14.476 14.266 13.69 F2 94 1
124 Kepler-60 Er* 19 15 50.6983640712 +42 15 54.050260968   14.477 14.083 13.934   G2 132 1
125 Kepler-103 Er* 19 15 56.2939334304 +40 03 52.285818168   13.136 12.360 12.254   G5Ib 114 0
126 Kepler-1662 Em* 19 17 21.9470227680 +46 59 17.635271604           K5 60 1
127 Kepler-138 Er* 19 21 31.5679755816 +43 17 34.680970608   14.621 13.168 12.680   M1V 145 0
128 Kepler-109 Er* 19 21 34.2534438336 +40 17 05.498443284   13.162 12.388 12.320   G4V 94 0
129 Kepler-161 Er* 19 22 03.9577627968 +43 05 01.745967912       14.344   ~ 55 0
130 Kepler-88 Er* 19 24 35.5430965488 +40 40 09.809893020   14.192 13.257 13.084   G8IV 101 1
131 Kepler-36 Er* 19 25 00.0428079600 +49 13 54.630900876   12.795 12.174 12.094   F2 251 1
132 HD 181433 PM* 19 25 09.5666936172 -66 28 07.676956827   9.42 8.38     K3III-IV 144 1
133 Kepler-323 Ro* 19 25 31.7357525064 +38 07 38.897081760           G0 64 0
134 Kepler-100 Er* 19 25 32.6432787456 +41 59 24.945100548   12.009 11.278 11.128   G8IV 142 0
135 Kepler-145 Er* 19 25 33.0613997040 +44 31 44.752299852   12.737 12.035 11.903   G1V 88 0
136 Kepler-406 Er* 19 27 23.5375431360 +44 58 05.726111052   13.401 12.672 12.482   G5IV 88 0
137 HD 183263 * 19 28 24.5713671072 +08 21 29.004515424   8.51 7.86     G6IV 149 1
138 Kepler-28 Er* 19 28 32.8904682216 +42 25 45.959315016       14.991   M0V 85 1
139 Kepler-27 Er* 19 28 56.8196229816 +41 05 09.140476848   16.865 15.992 16.010   ~ 95 1
140 Kepler-1703 Ro* 19 32 36.1974184536 +41 43 45.257065068           ~ 36 0
141 Kepler-57 Er* 19 34 33.9093923088 +44 39 25.358372136   16.019 15.035 14.860   ~ 78 1
142 Kepler-231 Er* 19 35 53.6056683624 +50 31 54.842378196   17.018 15.893 15.626   M1V 64 0
143 Kepler-114 PM* 19 36 29.1357624552 +48 20 58.291722816   14.972 13.803 13.746   M0V 86 0
144 Kepler-23 Er* 19 36 52.5355328952 +49 28 45.252600204   14.190 13.547 13.71   G2V 98 1
145 Kepler-326 Er* 19 37 18.1337949432 +46 00 08.063097696   14.811 13.863 13.584   K1V 79 0
146 Kepler-595 Ro* 19 38 16.8883496904 +50 40 22.860462864           K0 46 0
147 Kepler-345 Er* 19 40 54.9106057152 +45 58 15.668282640       14.104   ~ 52 0
148 Kepler-450 Er* 19 41 56.7727769064 +51 00 48.582305136   11.99 11.692 11.685   ~ 86 0
149 Kepler-328 Ro* 19 43 14.2300387272 +40 00 30.634558164     15.79   15.00 ~ 36 0
150 Kepler-396 Er* 19 44 31.8711622728 +48 58 38.563365252   12.832 12.032 11.828   G4 83 0
151 Kepler-51 Er* 19 45 55.1428629456 +49 56 15.650520684       14.829   G4 165 1
152 HD 187123 PM* 19 46 58.1122487784 +34 25 10.281404460       7.4   G2V 264 1
153 Kepler-107 Er* 19 48 06.7734610824 +48 12 30.964175676   13.330 12.639 12.448   ~ 116 0
154 Kepler-11 Er* 19 48 27.6226218768 +41 54 32.903163504   14.635 13.838 13.742   G2V 377 1
155 Kepler-289 Er* 19 49 51.6736237968 +42 52 58.268872164   14.724 14.175 14.019   G2 94 0
156 BD+47 2936 EB* 19 50 50.2472976936 +48 04 51.101390496       8.8   K4V 359 1
157 Kepler-307 EB* 19 51 10.8252284400 +40 25 03.669502080   15.092 14.299 14.082   ~ 75 0
158 Kepler-87 Ro* 19 51 40.0490199888 +46 57 54.425250252           F9 71 2
159 Kepler-414 Er* 19 51 50.7704135328 +48 14 39.740146656   14.364 13.540 13.209   K0IV 66 0
160 Kepler-18 Er* 19 52 19.0688312520 +44 44 46.807928916   14.750 13.767 13.93   ~ 146 1
161 Kepler-223 Er* 19 53 16.4202435936 +47 16 46.308434088   16.209 15.570 15.78   ~ 192 1
162 Kepler-29 Er* 19 53 23.6017612992 +47 29 28.436776467   16.014 15.456 15.540   G7 80 1
163 Kepler-1659 Er* 19 53 29.7223329192 +40 37 06.379732380   15.866 14.991 14.869   ~ 50 0
164 Kepler-462 Er* 19 59 17.0778691680 +43 48 51.412412124   12.074 11.738 11.616   A9V 61 0
165 Kepler-79 Er* 20 02 04.1057010912 +44 22 53.646047436   14.55 13.98 14.00   F5 136 1
166 Kepler-106 Er* 20 03 27.3499329384 +44 20 15.191981988   13.592 12.963 12.817   G1 94 0
167 HD 197481 BY* 20 45 09.5324974119 -31 20 27.237889841   10.05 8.627 9.078 6.593 M1VeBa1 1344 0
168 HD 200964 PM* 21 06 39.8422794792 +03 48 11.226709188   7.379 6.487     G8IV 101 1
169 HAT-P-17 PM* 21 38 08.7310010424 +30 29 19.446386748   11.33 10.38 10.24   G0 85 1
170 G 264-12 PM* 21 46 40.2407357179 +66 48 10.646948698   14.66   12.740   M4.0V 70 0
171 HD 215497 PM* 22 46 36.7539769920 -56 35 58.326725148   9.92 8.95     K3V 74 1
172 BD-15 6290 BY* 22 53 16.7325836486 -14 15 49.304052185 12.928 11.749 10.192 9.013 7.462 M3.5V 1106 1
173 HD 217107 ** 22 58 15.5408995872 -02 23 43.383234768   6.919 6.163     G8IV-V 398 1
174 TRAPPIST-1 LM* 23 06 29.3684948589 -05 02 29.037301866     18.798 16.466 14.024 M7.5e 1306 0
175 HD 219134 PM* 23 13 16.9749603608 +57 10 06.083823619 7.460 6.560 5.570 4.76 4.23 K3V 677 1
176 K2-138 * 23 15 47.7686067840 -10 50 58.895461284   13.01 12.21 12.12 11.40 ~ 75 0
177 K2-285 * 23 17 32.2274265744 +01 18 01.074749508   12.87 11.75 11.88   G9 20 0
178 StKM 1-2122 PM* 23 23 39.9709098120 -01 11 21.448681332   12.14 11.45     K7V 61 0
179 BD-02 5958 PM* 23 27 04.8376907739 -01 17 10.582653030   11.57 10.10 10.09 8.89 K6V 110 0

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