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: 13RE158 # Created Sun Dec 22 02:09:36 2024 # Orbit generated from Bernstein formalism # Fitting 7 observations of 7 # Arc: 4.10y # First observation: 2013/09/13 # Last observation: 2017/10/21 Preliminary a, adot, b, bdot, g, gdot: 0.000290 0.029301 -0.000018 -0.013635 0.029893 0.000000 # Chi-squared of fit: 3.77 DOF: 8 RMS: 0.13 # Min/Max residuals: -0.13 0.31 # Exact a, adot, b, bdot, g, gdot: 1.672571E-05 3.046777E-02 -7.186117E-06 -1.426612E-02 2.933014E-02 1.014851E-02 # Covariance matrix: 9.8138E-13 -6.4070E-13 8.1784E-14 3.6439E-13 2.5699E-12 -6.5910E-12 -6.4070E-13 3.9438E-12 1.1585E-13 -2.1134E-12 -1.0620E-12 3.9049E-11 8.1784E-14 1.1585E-13 3.2307E-13 -1.3991E-13 3.6575E-13 1.0111E-12 3.6439E-13 -2.1134E-12 -1.3991E-13 1.2495E-12 8.2734E-13 -2.1490E-11 2.5699E-12 -1.0620E-12 3.6575E-13 8.2734E-13 1.0058E-11 -1.4714E-11 -6.5910E-12 3.9049E-11 1.0111E-12 -2.1490E-11 -1.4714E-11 3.9683E-10 # lat0 lon0 xBary yBary zBary JD0 13.586536 -32.648282 -0.390541 0.218112 -0.902127 2456548.625778 # Heliocentric elements and errors Epoch: 2456540.5000 = 2013/09/05 Mean Anomaly: 30.55665 +/- 0.055 Argument of Peri: 84.10958 +/- 0.043 Long of Asc Node: 173.90407 +/- 0.001 Inclination: 28.29592 +/- 0.000 Eccentricity: 0.39445230 +/- 0.0008 Semi-Major Axis: 47.82853993 +/- 0.0540 Time of Perihelion: 2446285.5782 +/- 5.8 Perihelion: 28.96246238 +/- 0.0504 Aphelion: 66.69461748 +/- 0.0845 Period (y) 330.7797 +/- 0.56 # Ecliptic coordinates at JD0 (AU and AU/d) Ecliptic X 28.89646507 +/- 0.0030 Ecliptic Y -18.04761699 +/- 0.0020 Ecliptic Z 8.00904555 +/- 0.0009 Ecliptic XDOT 0.00256686 +/- 0.0000 Ecliptic YDOT 0.00172797 +/- 0.0000 Ecliptic ZDOT -0.00107174 +/- 0.0000 # Distances at JD0 (AU) Heliocenter to KBO 34.99809971 +/- 0.0027 Geocenter to KBO 34.09461678 +/- 0.0037 # Hcoef: 7.81
The following table shows the complete astrometric record for 13RE158. 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 (13RE158) followed by the observatory code and reference code for the source of the astrometry.
2013 09 13.12500 21 39 43.316 +00 23 51.74 23.7i 13RE158 W84 C~52RQ 2013 09 24.03811 21 38 58.191 +00 16 01.75 23.7g 13RE158 W84 C~52RQ 2013 10 10.06601 21 38 07.915 +00 04 41.87 24.0r 13RE158 W84 C~52RQ 2013 10 11.07033 21 38 05.511 +00 04 00.66 22.9z 13RE158 W84 C~52RQ 2013 10 12.01338 21 38 03.358 +00 03 22.40 22.9z 13RE158 W84 C~52RQ 2016 09 26.03934 22 01 04.066 -00 17 49.48 24.9g 13RE158 W84 C~52RQ 2017 10 21.05167 22 06 54.787 -00 44 04.70 21.2i 13RE158 W84 C~52RQ
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 -0.06 0.00 -0.10
2 0.0299 -795.19 -0.10 -216.13 0.31
3 0.0738 -1733.54 0.04 -604.15 -0.04
4 0.0765 -1781.32 -0.03 -630.90 -0.13
5 0.0791 -1824.57 0.14 -656.13 -0.08
6 3.0360 17315.90 0.11 -8814.85 0.18
7 4.1038 21798.23 -0.08 -12095.32 -0.13
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.
13RE158 quality flag:2 Type: CENTAURS CENTAURR CENTAURR axisobj 47.923 48.095 47.755 ecceobj 0.395 0.397 0.393 incobj 28.251 28.252 28.251 qmin 28.435 28.129 27.935 qmax 70.323 72.938 68.978 amean 49.143 49.330 47.805 amin 46.950 46.793 46.947 amax 50.869 51.782 48.737 emean 0.359 0.401 0.398 emin 0.311 0.341 0.383 emax 0.405 0.437 0.418 imean 30.113 28.176 27.482 imin 27.511 27.060 27.035 imax 31.674 29.826 27.799 excite_mean 0.618 0.620 0.609 fracstop 1.000 0.298 0.086 cjmean 2.674 2.677 2.690 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 176.4 227.4 117.1 kozaiamp 179.9 130.5 31.4