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: 13RA157 # Created Tue Apr 1 01:09:38 2025 # Orbit generated by ELGB # -->Covariance matrix from a Bernstein fit # Fitting 24 observations of 24 # Arc: 5.23y # First observation: 2013/09/10 # Last observation: 2018/12/02 # Chi-squared of fit: 8.18 DOF: 42 RMS: 0.10 # Min/Max residuals: -0.21 0.37 # Exact a, adot, b, bdot, g, gdot: 1.632551E-05 3.268371E-02 -1.080528E-05 -2.285621E-02 3.094878E-02 1.116979E-03 # Covariance matrix: 1.7014E-13 -3.2464E-14 -2.6649E-15 1.9695E-14 1.3008E-13 -1.9669E-13 -3.2464E-14 2.4861E-13 5.1829E-14 -1.6276E-13 2.8473E-13 1.4814E-12 -2.6649E-15 5.1829E-14 1.4925E-13 -7.0806E-14 5.1858E-14 3.4488E-13 1.9695E-14 -1.6276E-13 -7.0806E-14 1.3973E-13 -1.1791E-13 -1.1528E-12 1.3008E-13 2.8473E-13 5.1858E-14 -1.1791E-13 8.5915E-13 1.0041E-12 -1.9669E-13 1.4814E-12 3.4488E-13 -1.1528E-12 1.0041E-12 1.0599E-11 # lat0 lon0 xBary yBary zBary JD0 -14.644440 19.033014 0.528099 -0.216911 -0.830484 2456545.803528 # Heliocentric elements and errors Epoch: 2456546.5000 = 2013/09/11 Mean Anomaly: 0.76504 +/- 0.006 Argument of Peri: 201.87690 +/- 0.016 Long of Asc Node: 178.84248 +/- 0.000 Inclination: 37.63863 +/- 0.000 Eccentricity: 0.39670642 +/- 0.0001 Semi-Major Axis: 54.93508186 +/- 0.0113 Time of Perihelion: 2456230.4524 +/- 2.7 Perihelion: 33.14198197 +/- 0.0090 Aphelion: 76.72818175 +/- 0.0169 Period (y) 407.1767 +/- 0.13 # Ecliptic coordinates at JD0 (AU and AU/d) Ecliptic X 30.53579600 +/- 0.0009 Ecliptic Y 9.97849249 +/- 0.0003 Ecliptic Z -8.16933525 +/- 0.0002 Ecliptic XDOT -0.00134195 +/- 0.0000 Ecliptic YDOT 0.00259657 +/- 0.0000 Ecliptic ZDOT -0.00198111 +/- 0.0000 # Distances at JD0 (AU) Heliocenter to KBO 33.14728908 +/- 0.0008 Geocenter to KBO 32.31146583 +/- 0.0010 # Hcoef: 8.35
The following table shows the complete astrometric record for 13RA157. 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 (13RA157) followed by the observatory code and reference code for the source of the astrometry.
2013 09 10.30275 01 32 23.110 -06 06 38.90 24.2g 13RA157 W84 C~52RN 2013 09 10.30413 01 32 23.091 -06 06 38.84 23.7r 13RA157 W84 C~52RN 2013 09 10.30552 01 32 23.092 -06 06 38.90 23.6i 13RA157 W84 C~52RN 2013 09 11.28434 01 32 19.133 -06 07 31.26 24.3g 13RA157 W84 C~52RN 2013 09 11.29219 01 32 19.117 -06 07 31.71 23.6r 13RA157 W84 C~52RN 2013 10 02.28229 01 30 40.692 -06 25 51.56 22.9i 13RA157 W84 C~52RN 2013 10 04.22956 01 30 30.555 -06 27 28.60 23.4r 13RA157 W84 C~52RN 2013 10 04.23211 01 30 30.538 -06 27 28.80 23.6r 13RA157 W84 C~52RN 2013 10 04.23349 01 30 30.533 -06 27 28.92 23.3i 13RA157 W84 C~52RN 2014 10 03.25869 01 39 37.301 -06 56 40.26 23.0i 13RA157 W84 C~52RN 2014 10 27.17465 01 37 28.903 -07 14 35.06 23.6r 13RA157 W84 C~52RN 2015 10 17.18378 01 47 24.858 -07 37 09.30 23.3i 13RA157 W84 C~52RN 2015 11 01.21126 01 46 03.063 -07 47 11.18 22.8z 13RA157 W84 C~52RN 2017 09 26.28547 02 07 05.721 -08 17 02.39 24.1g 13RA157 W84 C~52RN 2017 09 26.28686 02 07 05.711 -08 17 02.28 23.6i 13RA157 W84 C~52RN 2017 11 01.19081 02 03 57.956 -08 44 32.33 22.6z 13RA157 W84 C~52RN 2017 11 16.14009 02 02 38.740 -08 51 44.00 24.0r 13RA157 W84 C~52RN 2017 11 16.14148 02 02 38.722 -08 51 44.12 23.9i 13RA157 W84 C~52RN 2017 11 16.14286 02 02 38.739 -08 51 44.21 23.1g 13RA157 W84 C~52RN 2017 11 27.15606 02 01 46.431 -08 54 57.28 22.5i 13RA157 W84 C~52RN 2017 12 14.06902 02 00 42.929 -08 56 14.68 23.7r 13RA157 W84 C~52RN 2018 11 17.15302 02 11 30.877 -09 19 14.75 23.6i 13RA157 W84 C~52RN 2018 11 28.18958 02 10 37.417 -09 22 19.64 24.0r 13RA157 W84 C~52RN 2018 12 02.14622 02 10 20.030 -09 22 58.03 24.3g 13RA157 W84 C~52RN
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 0.14 0.00 -0.14
2 0.0000 0.00 -0.06 0.00 -0.00
3 0.0000 0.00 0.04 0.00 0.01
4 0.0027 0.00 -0.13 0.00 -0.01
5 0.0027 0.00 0.12 0.00 -0.04
6 0.0602 0.00 0.04 0.00 0.00
7 0.0655 0.00 0.03 0.00 0.11
8 0.0655 0.00 -0.03 0.00 0.04
9 0.0655 0.00 0.01 0.00 -0.01
10 1.0622 0.00 -0.21 0.00 -0.09
11 1.1276 0.00 -0.02 0.00 0.06
12 2.0996 0.00 -0.07 0.00 0.18
13 2.1407 0.00 -0.10 0.00 0.01
14 4.0438 0.00 0.06 0.00 -0.19
15 4.0438 0.00 0.01 0.00 -0.01
16 4.1421 0.00 0.09 0.00 0.10
17 4.1830 0.00 0.17 0.00 0.11
18 4.1830 0.00 0.01 0.00 0.02
19 4.1830 0.00 0.37 0.00 -0.04
20 4.2132 0.00 -0.01 0.00 -0.08
21 4.2595 0.00 -0.07 0.00 -0.01
22 5.1851 0.00 -0.08 0.00 -0.03
23 5.2153 0.00 -0.08 0.00 -0.04
24 5.2261 0.00 -0.15 0.00 0.10
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.
13RA157 quality flag:3 Type: SCATNEAR SCATNEAR SCATNEAR axisobj 55.283 55.283 55.284 ecceobj 0.401 0.401 0.401 incobj 37.553 37.553 37.553 qmin 31.373 31.546 31.668 qmax 79.523 79.181 79.490 amean 54.866 54.835 54.877 amin 54.239 54.193 54.030 amax 55.714 55.668 55.842 emean 0.402 0.399 0.399 emin 0.380 0.375 0.371 emax 0.427 0.424 0.424 imean 36.904 37.012 37.044 imin 36.149 36.262 36.319 imax 37.667 37.845 37.893 excite_mean 0.723 0.722 0.723 fracstop 1.000 1.000 1.000 cjmean 2.526 2.525 2.525 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 185.9 185.2 189.4 kozaiamp 180.0 179.9 179.9