The following information shows the result of the orbit fit based on Gary Bernstein's method. Most of the information should be self-explanatory. Take special note that while the original Bernstein software works with barycentric coordinates, we convert these results into a heliocentric coordinate system.
# Object: 13RA156 # Created Fri Nov 22 02:09:32 2024 # Orbit generated from Bernstein formalism # Fitting 15 observations of 15 # Arc: 3.18y # First observation: 2013/09/02 # Last observation: 2016/11/06 Preliminary a, adot, b, bdot, g, gdot: -0.000140 0.031129 -0.000013 0.006751 0.030486 0.000000 # Chi-squared of fit: 2.72 DOF: 24 RMS: 0.08 # Min/Max residuals: -0.19 0.12 # Exact a, adot, b, bdot, g, gdot: 1.612573E-05 3.103218E-02 3.582679E-06 6.733404E-03 3.055918E-02 6.776009E-04 # Covariance matrix: 7.1933E-13 2.5129E-13 -2.2366E-14 9.4641E-14 7.6474E-13 4.4920E-12 2.5129E-13 1.0182E-12 -6.3710E-14 2.4793E-13 1.1217E-12 1.1710E-11 -2.2366E-14 -6.3710E-14 3.4310E-13 -1.4168E-13 -7.1095E-14 -7.8411E-13 9.4641E-14 2.4793E-13 -1.4168E-13 1.2931E-13 2.8722E-13 3.0471E-12 7.6474E-13 1.1217E-12 -7.1095E-14 2.8722E-13 1.7666E-12 1.3596E-11 4.4920E-12 1.1710E-11 -7.8411E-13 3.0471E-12 1.3596E-11 1.4391E-10 # lat0 lon0 xBary yBary zBary JD0 -4.996410 15.401053 0.588988 -0.071371 -0.817428 2456537.860308 # Heliocentric elements and errors Epoch: 2456530.5000 = 2013/08/26 Mean Anomaly: 178.05733 +/- 0.242 Argument of Peri: 159.55251 +/- 0.241 Long of Asc Node: 35.94390 +/- 0.001 Inclination: 13.06968 +/- 0.000 Eccentricity: 0.08184891 +/- 0.0001 Semi-Major Axis: 31.00952382 +/- 0.0032 Time of Perihelion: 2488407.1830 +/- 42.1 Perihelion: 28.47142812 +/- 0.0037 Aphelion: 33.54761952 +/- 0.0041 Period (y) 172.6835 +/- 0.03 # Ecliptic coordinates at JD0 (AU and AU/d) Ecliptic X 32.37554831 +/- 0.0014 Ecliptic Y 8.31051942 +/- 0.0004 Ecliptic Z -2.84988823 +/- 0.0001 Ecliptic XDOT -0.00063558 +/- 0.0000 Ecliptic YDOT 0.00270931 +/- 0.0000 Ecliptic ZDOT 0.00059582 +/- 0.0000 # Distances at JD0 (AU) Heliocenter to KBO 33.54642640 +/- 0.0013 Geocenter to KBO 32.72338798 +/- 0.0014 # Hcoef: 7.85
The following table shows the complete astrometric record for 13RA156. The first three columns show the date of observation. The next six columns are RA and DEC. The next column (when provided) is the observed magnitude and filter. The next column is the object name (13RA156) followed by the observatory code and reference code for the source of the astrometry.
2013 09 02.35953 01 04 26.168 +01 27 05.50 24.2g 13RA156 W84 C~52RL 2013 10 03.12129 01 01 47.746 +01 11 00.90 23.2g 13RA156 W84 C~52RL 2013 10 13.20726 01 00 50.005 +01 05 43.64 22.9i 13RA156 W84 C~52RL 2013 11 08.19267 00 58 30.119 +00 54 20.77 22.9i 13RA156 W84 C~52RL 2014 11 18.15582 01 03 44.046 +01 53 35.48 22.6z 13RA156 W84 C~52RL 2015 11 07.11042 01 10 35.722 +02 59 32.23 22.9r 13RA156 W84 C~52RL 2015 11 07.11179 01 10 35.725 +02 59 32.11 22.7i 13RA156 W84 C~52RL 2015 11 07.11317 01 10 35.717 +02 59 32.22 23.7g 13RA156 W84 C~52RL 2015 11 20.13788 01 09 34.263 +02 55 10.31 22.8z 13RA156 W84 C~52RL 2016 08 26.33786 01 22 47.647 +04 35 45.33 22.8i 13RA156 W84 C~52RL 2016 08 26.33924 01 22 47.651 +04 35 45.31 22.9r 13RA156 W84 C~52RL 2016 10 23.21972 01 17 52.966 +04 07 58.80 23.9g 13RA156 W84 C~52RL 2016 10 29.16012 01 17 19.531 +04 05 12.60 22.9r 13RA156 W84 C~52RL 2016 10 29.16150 01 17 19.531 +04 05 12.61 22.8i 13RA156 W84 C~52RL 2016 11 06.13866 01 16 36.486 +04 01 47.39 23.0z 13RA156 W84 C~52RL
The following table shows the residuals to the orbit fit. The first coumn is the point number. The second column is the time, in years, measured from the first observation. The third and fifth columns are the regularized positions used in the orbit fit. The fourth and sixth columns are the residuals, in arc seconds, for RA and Dec respectively.
1 0.0000 0.00 -0.01 0.00 -0.02
2 0.0842 -2564.11 0.06 20.91 -0.03
3 0.1118 -3485.69 -0.08 60.40 0.11
4 0.1830 -5686.14 0.08 235.63 -0.09
5 1.2096 26.78 -0.13 1710.65 0.04
6 2.1786 7245.12 -0.06 3002.31 0.05
7 2.1787 7245.12 0.05 3002.18 -0.09
8 2.1787 7245.05 0.09 3002.32 0.04
9 2.2143 6293.22 0.05 3112.56 -0.02
10 2.9815 19631.77 -0.06 4172.52 0.09
11 2.9815 19631.82 0.07 4172.48 0.05
12 3.1399 14887.72 -0.08 4304.09 -0.19
13 3.1562 14359.16 -0.00 4340.76 -0.00
14 3.1562 14359.16 0.12 4340.77 -0.00
15 3.1780 13682.28 -0.08 4396.21 0.06
The following table comes from a 10My integration of the orbit of the object. Three columns are shown. The first column is the result of integrating the nominal orbit. The other two columns are based on clones of the nominal orbit that are +/- 3 sigma from the nominal orbit. If all three types agree then the classificiation is deemed secure. The basis for these calculations is described in more detail in AJ, 129, 1117 (2005). Any use made of these calculations should refer to and credit this publication and the Deep Ecliptic Survey Team.
13RA156 quality flag:3 Type: CENTAURR CENTAURR CENTAURR axisobj 31.126 31.135 31.118 ecceobj 0.078 0.078 0.078 incobj 13.050 13.050 13.050 qmin 24.243 24.394 24.613 qmax 38.816 41.987 38.235 amean 31.405 32.117 31.242 amin 30.700 30.655 30.424 amax 32.787 34.959 32.220 emean 0.159 0.156 0.153 emin 0.077 0.069 0.064 emax 0.220 0.223 0.214 imean 10.567 10.826 11.183 imin 7.169 7.609 8.666 imax 13.931 13.888 14.178 excite_mean 0.248 0.248 0.252 fracstop 0.085 0.296 0.050 cjmean 2.938 2.940 2.937 libcent 0 -180.0 -180.0 -180.0 libamp 0 -180.0 -180.0 -180.0 libcent 1 -180.0 -180.0 -180.0 libamp 1 -180.0 -180.0 -180.0 libcent 2 -180.0 -180.0 -180.0 libamp 2 -180.0 -180.0 -180.0 libcent 3 -180.0 -180.0 -180.0 libamp 3 -180.0 -180.0 -180.0 libcent 4 -180.0 -180.0 -180.0 libamp 4 -180.0 -180.0 -180.0 kozaimean 183.8 181.2 173.5 kozaiamp 63.6 56.4 73.9