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: 13RT156 # Created Mon Apr 28 01:09:38 2025 # Orbit generated by ELGB # -->Covariance matrix from a Bernstein fit # Fitting 21 observations of 21 # Arc: 5.21y # First observation: 2013/09/09 # Last observation: 2018/11/26 # Chi-squared of fit: 6.71 DOF: 36 RMS: 0.10 # Min/Max residuals: -0.21 0.17 # Exact a, adot, b, bdot, g, gdot: 1.053043E-05 1.274884E-02 -4.827287E-06 -5.298967E-03 1.789122E-02 -4.869551E-03 # Covariance matrix: 3.1664E-13 -8.6364E-14 -1.2651E-14 2.5509E-14 2.2856E-13 -1.0256E-12 -8.6364E-14 2.0867E-13 4.1208E-14 -9.5881E-14 1.2041E-13 3.7516E-12 -1.2651E-14 4.1208E-14 2.0912E-13 -7.1624E-14 1.5155E-14 8.3031E-13 2.5509E-14 -9.5881E-14 -7.1624E-14 6.8375E-14 -4.4245E-14 -1.9207E-12 2.2856E-13 1.2041E-13 1.5155E-14 -4.4245E-14 6.5175E-13 1.6682E-12 -1.0256E-12 3.7516E-12 8.3031E-13 -1.9207E-12 1.6682E-12 7.5232E-11 # lat0 lon0 xBary yBary zBary JD0 -4.194293 -1.157289 0.217774 -0.071904 -0.981692 2456544.709488 # Heliocentric elements and errors Epoch: 2456544.5000 = 2013/09/09 Mean Anomaly: 283.60333 +/- 0.092 Argument of Peri: 305.88896 +/- 0.038 Long of Asc Node: 168.83437 +/- 0.000 Inclination: 22.96582 +/- 0.001 Eccentricity: 0.34049282 +/- 0.0005 Semi-Major Axis: 54.98167612 +/- 0.0213 Time of Perihelion: 2488145.2455 +/- 78.1 Perihelion: 36.26080994 +/- 0.0309 Aphelion: 73.70254229 +/- 0.0397 Period (y) 407.6948 +/- 0.24 # Ecliptic coordinates at JD0 (AU and AU/d) Ecliptic X 56.71169972 +/- 0.0025 Ecliptic Y -1.36041100 +/- 0.0001 Ecliptic Z -4.08825495 +/- 0.0002 Ecliptic XDOT -0.00076910 +/- 0.0000 Ecliptic YDOT 0.00196558 +/- 0.0000 Ecliptic ZDOT -0.00075408 +/- 0.0000 # Distances at JD0 (AU) Heliocenter to KBO 56.87538361 +/- 0.0025 Geocenter to KBO 55.89361478 +/- 0.0025 # Hcoef: 6.21
The following table shows the complete astrometric record for 13RT156. 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 (13RT156) followed by the observatory code and reference code for the source of the astrometry.
2013 09 09.20871 00 02 26.343 -04 18 28.40 24.2g 13RT156 W84 C~52RN 2013 09 10.31452 00 02 22.725 -04 18 56.43 23.0r 13RT156 W84 C~52RN 2013 09 29.22256 00 01 19.666 -04 26 50.07 23.6r 13RT156 W84 C~52RN 2013 10 13.12737 00 00 34.358 -04 32 11.54 23.7i 13RT156 W84 C~52RN 2013 10 13.12878 00 00 34.349 -04 32 11.53 23.0z 13RT156 W84 C~52RN 2013 11 23.10292 23 58 57.394 -04 42 35.91 23.4i 13RT156 W84 C~52RN 2014 10 01.27583 00 04 24.456 -04 26 51.37 23.3i 13RT156 W84 C~52RN 2014 11 14.01786 00 02 21.484 -04 40 32.87 22.9z 13RT156 W84 C~52RN 2016 09 22.09840 00 11 20.943 -04 21 41.06 23.5r 13RT156 W84 C~52RN 2016 09 30.18001 00 10 53.418 -04 25 04.23 23.9r 13RT156 W84 C~52RN 2016 09 30.18137 00 10 53.394 -04 25 04.25 23.9i 13RT156 W84 C~52RN 2016 09 30.18274 00 10 53.405 -04 25 04.50 24.1g 13RT156 W84 C~52RN 2016 11 26.12379 00 08 23.547 -04 41 06.44 23.6r 13RT156 W84 C~52RN 2017 09 27.28723 00 14 20.547 -04 22 53.63 23.3r 13RT156 W84 C~52RN 2017 09 27.28860 00 14 20.528 -04 22 53.80 23.1i 13RT156 W84 C~52RN 2017 09 27.28997 00 14 20.528 -04 22 53.69 24.2g 13RT156 W84 C~52RN 2017 10 29.15915 00 12 37.994 -04 34 37.24 23.4i 13RT156 W84 C~52RN 2017 11 09.06841 00 12 09.865 -04 37 29.01 24.3g 13RT156 W84 C~52RN 2018 10 18.17817 00 16 29.752 -04 30 04.39 23.8i 13RT156 W84 C~52RN 2018 11 07.12755 00 15 32.287 -04 36 07.17 24.0r 13RT156 W84 C~52RN 2018 11 26.08382 00 14 54.345 -04 39 29.78 24.5g 13RT156 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 0.13 0.00 0.09
2 0.0030 0.00 -0.12 0.00 0.10
3 0.0548 0.00 0.02 0.00 0.07
4 0.0929 0.00 0.04 0.00 -0.05
5 0.0929 0.00 -0.03 0.00 -0.01
6 0.2050 0.00 -0.01 0.00 -0.05
7 1.0597 0.00 0.12 0.00 0.04
8 1.1795 0.00 -0.10 0.00 -0.21
9 3.0360 0.00 -0.19 0.00 -0.01
10 3.0581 0.00 0.17 0.00 0.02
11 3.0581 0.00 -0.12 0.00 0.04
12 3.0581 0.00 0.12 0.00 -0.18
13 3.2140 0.00 0.12 0.00 0.04
14 4.0495 0.00 0.09 0.00 0.08
15 4.0495 0.00 -0.12 0.00 -0.05
16 4.0495 0.00 -0.05 0.00 0.09
17 4.1368 0.00 -0.13 0.00 0.09
18 4.1666 0.00 -0.00 0.00 -0.09
19 5.1060 0.00 0.03 0.00 -0.12
20 5.1606 0.00 0.07 0.00 -0.04
21 5.2125 0.00 0.07 0.00 0.17
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.
13RT156 quality flag:3 Type: SCATNEAR SCATNEAR SCATNEAR axisobj 55.265 55.265 55.265 ecceobj 0.338 0.338 0.338 incobj 22.873 22.873 22.873 qmin 35.548 35.548 35.548 qmax 75.214 75.297 75.234 amean 54.967 54.967 54.967 amin 54.368 54.403 54.404 amax 55.690 55.739 55.707 emean 0.334 0.334 0.334 emin 0.316 0.316 0.316 emax 0.351 0.351 0.351 imean 22.656 22.655 22.655 imin 22.017 22.016 22.017 imax 23.444 23.436 23.435 excite_mean 0.510 0.510 0.510 fracstop 1.000 1.000 1.000 cjmean 2.899 2.899 2.899 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 179.7 179.8 179.7 kozaiamp 180.0 180.0 180.0