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: 13RN158 # Created Sun Oct 19 01:09:55 2025 # Orbit generated by ELGB # -->Covariance matrix from a Bernstein fit # Fitting 25 observations of 25 # Arc: 11.89y # First observation: 2013/09/08 # Last observation: 2025/07/29 # Chi-squared of fit: 7.86 DOF: 44 RMS: 0.10 # Min/Max residuals: -0.20 0.25 # Exact a, adot, b, bdot, g, gdot: 1.883727E-05 4.049386E-02 -2.540347E-06 -5.321271E-03 3.232351E-02 5.741940E-03 # Covariance matrix: 1.8766E-13 -3.9838E-14 3.4098E-15 1.5369E-15 1.5199E-13 -3.0415E-14 -3.9838E-14 3.7891E-14 8.6080E-15 -4.9417E-15 7.8144E-14 8.1815E-14 3.4098E-15 8.6080E-15 1.2119E-13 -1.7497E-14 5.7438E-14 2.6076E-14 1.5369E-15 -4.9417E-15 -1.7497E-14 5.1941E-15 -1.9331E-14 -1.3124E-14 1.5199E-13 7.8144E-14 5.7438E-14 -1.9331E-14 9.9399E-13 3.0065E-13 -3.0415E-14 8.1815E-14 2.6076E-14 -1.3124E-14 3.0065E-13 2.1466E-13 # lat0 lon0 xBary yBary zBary JD0 12.630485 -35.951538 -0.365778 0.205569 -0.917005 2456543.626993 # Heliocentric elements and errors Epoch: 2456544.5000 = 2013/09/09 Mean Anomaly: 16.58180 +/- 0.006 Argument of Peri: 86.47189 +/- 0.010 Long of Asc Node: 202.64071 +/- 0.000 Inclination: 14.38575 +/- 0.000 Eccentricity: 0.34126143 +/- 0.0001 Semi-Major Axis: 46.15788247 +/- 0.0090 Time of Perihelion: 2451268.6027 +/- 2.6 Perihelion: 30.40597762 +/- 0.0074 Aphelion: 61.90978732 +/- 0.0128 Period (y) 313.6007 +/- 0.09 # Ecliptic coordinates at JD0 (AU and AU/d) Ecliptic X 25.41364327 +/- 0.0008 Ecliptic Y -17.97643150 +/- 0.0006 Ecliptic Z 6.76473214 +/- 0.0002 Ecliptic XDOT 0.00247147 +/- 0.0000 Ecliptic YDOT 0.00243891 +/- 0.0000 Ecliptic ZDOT -0.00033333 +/- 0.0000 # Distances at JD0 (AU) Heliocenter to KBO 31.85531366 +/- 0.0007 Geocenter to KBO 30.93719056 +/- 0.0010 # Hcoef: 8.12
The following table shows the complete astrometric record for 13RN158. 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 (13RN158) followed by the observatory code and reference code for the source of the astrometry.
2013 09 08.126215 21 28 49.41 -01 33 44.5 24.0g 13RN158 W84 C~55Nc 2013 09 11.168924 21 28 34.62 -01 35 41.9 23.3r 13RN158 W84 C~55Nc 2013 09 11.170301 21 28 34.61 -01 35 41.9 23.0i 13RN158 W84 C~55Nc 2013 09 13.117488 21 28 25.45 -01 36 57.4 22.7i 13RN158 W84 C~55Nc 2013 09 13.120289 21 28 25.44 -01 36 57.3 22.4z 13RN158 W84 C~55Nc 2013 09 24.036169 21 27 39.08 -01 44 01.8 23.5g 13RN158 W84 C~55Nc 2013 09 29.138137 21 27 20.69 -01 47 17.7 23.0r 13RN158 W84 C~55Nc 2013 09 29.139537 21 27 20.68 -01 47 17.7 22.9i 13RN158 W84 C~55Nc 2013 10 10.077211 21 26 49.63 -01 54 01.9 22.6r 13RN158 W84 C~55Nc 2016 09 08.089213 21 55 47.04 -00 12 30.9 22.9i 13RN158 W84 C~55Nc 2016 09 28.029502 21 54 15.18 -00 25 38.3 22.4z 13RN158 W84 C~55Nc 2017 08 19.21370 22 06 21.126 +00 26 02.87 22.8r 13RN158 W84 C~55Nc 2017 08 19.21508 22 06 21.137 +00 26 03.15 22.7g 13RN158 W84 C~55Nc 2017 10 11.10580 22 02 12.990 -00 07 26.41 23.2r 13RN158 W84 C~55Nc 2017 10 11.10717 22 02 12.981 -00 07 26.29 23.3i 13RN158 W84 C~55Nc 2017 10 21.05167 22 01 47.782 -00 13 22.38 23.3i 13RN158 W84 C~55Nc 2017 10 22.04361 22 01 45.836 -00 13 55.87 23.7i 13RN158 W84 C~55Nc 2017 10 22.04773 22 01 45.817 -00 13 56.09 24.9g 13RN158 W84 C~55Nc 2017 10 22.04910 22 01 45.817 -00 13 56.09 23.9r 13RN158 W84 C~55Nc 2018 09 17.20809 22 12 27.296 +00 34 29.68 23.1z 13RN158 W84 C~55Nc 2018 09 17.20946 22 12 27.291 +00 34 29.59 22.7i 13RN158 W84 C~55Nc 2018 09 17.21084 22 12 27.281 +00 34 29.55 23.4r 13RN158 W84 C~55Nc 2025 07 29.369630 23 13 18.751 +03 49 04.60 23.7G 13RN158 G37 C~93Rt 2025 07 29.414290 23 13 18.579 +03 49 04.05 13RN158 G37 C~93Rt 2025 07 29.458540 23 13 18.422 +03 49 03.21 13RN158 G37 C~93Rt
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 0.19 0.00 0.05
2 0.0083 0.00 0.07 0.00 -0.13
3 0.0083 0.00 0.02 0.00 -0.07
4 0.0137 0.00 -0.08 0.00 -0.12
5 0.0137 0.00 -0.03 0.00 0.08
6 0.0436 0.00 0.02 0.00 -0.11
7 0.0575 0.00 0.00 0.00 -0.08
8 0.0575 0.00 -0.08 0.00 -0.02
9 0.0875 0.00 0.05 0.00 0.16
10 3.0006 0.00 -0.20 0.00 -0.03
11 3.0552 0.00 -0.15 0.00 0.09
12 3.9455 0.00 -0.07 0.00 -0.08
13 3.9455 0.00 0.21 0.00 0.25
14 4.0903 0.00 0.10 0.00 -0.16
15 4.0903 0.00 0.03 0.00 0.01
16 4.1175 0.00 -0.11 0.00 0.02
17 4.1202 0.00 0.09 0.00 0.14
18 4.1203 0.00 -0.07 0.00 0.06
19 4.1203 0.00 -0.02 0.00 0.11
20 5.0242 0.00 0.02 0.00 0.01
21 5.0242 0.00 0.05 0.00 -0.02
22 5.0242 0.00 0.00 0.00 -0.01
23 11.8884 0.00 0.09 0.00 -0.11
24 11.8885 0.00 -0.07 0.00 0.05
25 11.8887 0.00 -0.01 0.00 -0.08
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.
13RN158 quality flag:3 Type: CENTAURR CENTAURR CENTAURR axisobj 46.275 46.275 46.275 ecceobj 0.343 0.343 0.343 incobj 14.386 14.386 14.386 qmin 29.119 28.308 28.795 qmax 63.806 65.091 63.494 amean 44.677 44.499 45.306 amin 40.005 38.914 42.602 amax 47.515 47.724 47.471 emean 0.307 0.305 0.323 emin 0.243 0.207 0.285 emax 0.358 0.364 0.353 imean 15.360 16.849 16.245 imin 9.420 14.391 14.330 imax 18.352 19.280 18.368 excite_mean 0.406 0.422 0.428 fracstop 0.751 0.986 0.386 cjmean 2.908 2.890 2.891 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 180.1 180.5 182.2 kozaiamp 180.0 180.0 179.6