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: 13RL158 # Created Fri Nov 22 02:09:35 2024 # Orbit generated by ELGB # -->Covariance matrix from a Bernstein fit # Fitting 14 observations of 14 # Arc: 10.01y # First observation: 2013/09/03 # Last observation: 2023/09/06 # Chi-squared of fit: 4.92 DOF: 22 RMS: 0.10 # Min/Max residuals: -0.19 0.21 # Exact a, adot, b, bdot, g, gdot: 1.635362E-05 2.733690E-02 2.114099E-06 3.645410E-03 2.663844E-02 -1.107675E-03 # Covariance matrix: 5.3469E-13 -2.8742E-13 4.6920E-14 -3.5420E-14 1.3289E-12 -8.4879E-13 -2.8742E-13 2.6567E-13 -3.4048E-14 3.4441E-14 -7.7403E-13 8.5747E-13 4.6920E-14 -3.4048E-14 1.6476E-13 -2.3366E-14 1.6457E-13 -1.0791E-13 -3.5420E-14 3.4441E-14 -2.3366E-14 1.0928E-14 -1.0147E-13 1.1398E-13 1.3289E-12 -7.7403E-13 1.6457E-13 -1.0147E-13 5.1565E-12 -2.3479E-12 -8.4879E-13 8.5747E-13 -1.0791E-13 1.1398E-13 -2.3479E-12 2.8511E-12 # lat0 lon0 xBary yBary zBary JD0 12.883760 -32.908375 -0.234931 0.219066 -0.957382 2456538.703405 # Heliocentric elements and errors Epoch: 2456538.5000 = 2013/09/03 Mean Anomaly: 322.54309 +/- 0.197 Argument of Peri: 101.18378 +/- 0.222 Long of Asc Node: 268.77201 +/- 0.001 Inclination: 14.61470 +/- 0.000 Eccentricity: 0.05712175 +/- 0.0002 Semi-Major Axis: 40.27096704 +/- 0.0155 Time of Perihelion: 2466250.6617 +/- 70.2 Perihelion: 37.97061875 +/- 0.0167 Aphelion: 42.57131534 +/- 0.0182 Period (y) 255.5620 +/- 0.15 # Ecliptic coordinates at JD0 (AU and AU/d) Ecliptic X 31.67493434 +/- 0.0026 Ecliptic Y -20.21512098 +/- 0.0017 Ecliptic Z 8.37045264 +/- 0.0007 Ecliptic XDOT 0.00135698 +/- 0.0000 Ecliptic YDOT 0.00246339 +/- 0.0000 Ecliptic ZDOT 0.00033999 +/- 0.0000 # Distances at JD0 (AU) Heliocenter to KBO 38.49699695 +/- 0.0023 Geocenter to KBO 37.53980242 +/- 0.0032 # Hcoef: 7.33
The following table shows the complete astrometric record for 13RL158. 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 (13RL158) followed by the observatory code and reference code for the source of the astrometry.
2013 09 03.202627 21 39 42.46 -00 20 57.4 23.2g 13RL158 W84 C~55Nc 2013 09 05.05071 21 39 33.908 -00 21 49.79 23.8g 13RL158 W84 C~55Nc 2013 09 08.086377 21 39 20.10 -00 23 16.8 23.1g 13RL158 W84 C~55Nc 2013 09 23.04418 21 38 18.435 -00 30 39.05 23.9g 13RL158 W84 C~55Nc 2013 09 24.037581 21 38 14.80 -00 31 08.9 23.8g 13RL158 W84 C~55Nc 2013 09 29.111389 21 37 57.22 -00 33 39.1 22.9r 13RL158 W84 C~55Nc 2013 09 29.129641 21 37 57.15 -00 33 39.5 23.0i 13RL158 W84 C~55Nc 2013 10 10.080162 21 37 25.77 -00 38 54.0 23.0r 13RL158 W84 C~55Nc 2016 08 25.22950 21 57 18.679 +01 52 50.71 23.5z 13RL158 W84 C~55Nc 2016 08 30.21362 21 56 54.274 +01 50 36.19 22.9i 13RL158 W84 C~55Nc 2016 08 30.21500 21 56 54.264 +01 50 36.37 22.9r 13RL158 W84 C~55Nc 2023 09 06.256410 22 36 31.957 +06 50 26.58 23.1G 13RL158 G37 C~7Ax8 2023 09 06.292450 22 36 31.780 +06 50 25.26 13RL158 G37 C~7Ax8 2023 09 06.329040 22 36 31.599 +06 50 24.39 13RL158 G37 C~7Ax8
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 -0.03 0.00 0.00
2 0.0051 0.00 0.04 0.00 -0.10
3 0.0134 0.00 0.06 0.00 0.05
4 0.0543 0.00 -0.19 0.00 0.15
5 0.0570 0.00 -0.06 0.00 -0.11
6 0.0709 0.00 0.10 0.00 0.02
7 0.0710 0.00 -0.03 0.00 0.16
8 0.1010 0.00 0.10 0.00 -0.07
9 2.9761 0.00 0.21 0.00 -0.18
10 2.9898 0.00 -0.04 0.00 -0.08
11 2.9898 0.00 -0.09 0.00 0.14
12 10.0070 0.00 -0.04 0.00 0.11
13 10.0071 0.00 -0.01 0.00 -0.15
14 10.0072 0.00 0.01 0.00 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.
13RL158 quality flag:3 Type: SCATEXTD SCATEXTD SCATEXTD axisobj 40.423 40.423 40.423 ecceobj 0.061 0.061 0.061 incobj 14.624 14.624 14.624 qmin 37.072 37.202 37.155 qmax 43.944 43.854 43.888 amean 40.424 40.420 40.422 amin 40.095 40.089 40.098 amax 40.754 40.754 40.766 emean 0.063 0.060 0.061 emin 0.043 0.044 0.047 emax 0.079 0.076 0.078 imean 16.631 16.633 16.618 imin 15.516 15.531 15.498 imax 17.461 17.443 17.433 excite_mean 0.293 0.292 0.293 fracstop 1.000 1.000 1.000 cjmean 2.959 2.960 2.960 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 178.6 179.4 179.3 kozaiamp 180.0 179.9 180.0