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: 13UK15 # Created Fri Nov 22 02:09:45 2024 # Orbit generated by ELGB # -->Covariance matrix from a Bernstein fit # Fitting 24 observations of 24 # Arc: 6.94y # First observation: 2013/10/13 # Last observation: 2020/09/21 # Chi-squared of fit: 47.56 DOF: 42 RMS: 0.25 # Min/Max residuals: -0.54 0.45 # Exact a, adot, b, bdot, g, gdot: 1.161108E-05 1.428688E-02 2.179034E-06 -1.106813E-03 1.848735E-02 -1.954875E-03 # Covariance matrix: 2.0365E-13 -1.2466E-13 -8.3508E-15 6.8806E-15 8.4192E-14 -8.7471E-13 -1.2466E-13 1.3726E-13 1.0608E-14 -9.1820E-15 -9.6900E-14 1.1888E-12 -8.3508E-15 1.0608E-14 1.3660E-13 -3.4273E-14 -2.1753E-14 8.9162E-14 6.8806E-15 -9.1820E-15 -3.4273E-14 1.5726E-14 8.1434E-15 -8.8399E-14 8.4192E-14 -9.6900E-14 -2.1753E-14 8.1434E-15 4.4213E-13 -5.5861E-13 -8.7471E-13 1.1888E-12 8.9162E-14 -8.8399E-14 -5.5861E-13 1.1966E-11 # lat0 lon0 xBary yBary zBary JD0 -11.062647 7.262141 -0.214363 -0.186794 -0.956020 2456578.686138 # Heliocentric elements and errors Epoch: 2456578.5000 = 2013/10/13 Mean Anomaly: 229.85894 +/- 0.049 Argument of Peri: 33.18949 +/- 0.041 Long of Asc Node: 119.63435 +/- 0.002 Inclination: 11.71019 +/- 0.000 Eccentricity: 0.19778384 +/- 0.0002 Semi-Major Axis: 48.01683946 +/- 0.0058 Time of Perihelion: 2500512.4876 +/- 21.7 Perihelion: 38.51988446 +/- 0.0097 Aphelion: 57.51379447 +/- 0.0110 Period (y) 332.7351 +/- 0.06 # Ecliptic coordinates at JD0 (AU and AU/d) Ecliptic X 53.59871553 +/- 0.0019 Ecliptic Y 7.04938049 +/- 0.0002 Ecliptic Z -10.37903164 +/- 0.0004 Ecliptic XDOT -0.00058667 +/- 0.0000 Ecliptic YDOT 0.00205748 +/- 0.0000 Ecliptic ZDOT -0.00010518 +/- 0.0000 # Distances at JD0 (AU) Heliocenter to KBO 55.04770883 +/- 0.0018 Geocenter to KBO 54.09118419 +/- 0.0019 # Hcoef: 5.89
The following table shows the complete astrometric record for 13UK15. 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 (13UK15) followed by the observatory code and reference code for the source of the astrometry.
2013 10 13.18536 00 44 12.402 -07 16 44.21 22.9z 13UK15 W84 C~4yRI 2013 10 29.04186 00 43 18.857 -07 21 20.33 23.2r 13UK15 304 C~1x8Y 2013 10 29.10905 00 43 18.643 -07 21 21.47 13UK15 304 C~1x8Y 2013 10 30.03111 00 43 15.743 -07 21 34.64 13UK15 304 C~1x8Y 2013 10 30.12393 00 43 15.450 -07 21 36.32 13UK15 304 C~1x8Y 2013 12 24.08375 00 41 34.995 -07 22 48.14 13UK15 I11 C~1x8Y 2013 12 25.07320 00 41 34.899 -07 22 36.18 13UK15 I11 C~1x8Y 2014 08 29.58357 00 49 48.574 -06 42 35.46 23.5r 13UK15 568 C~1x8Y 2014 08 29.62068 00 49 48.493 -06 42 36.48 13UK15 568 C~1x8Y 2014 10 22.20625 00 46 49.903 -07 03 24.82 13UK15 304 C~1x8Y 2014 10 23.10420 00 46 46.857 -07 03 40.37 13UK15 304 C~1x8Y 2015 09 04.29571 00 52 41.237 -06 28 39.15 22.6z 13UK15 W84 C~4yRI 2016 08 31.27584 00 55 58.740 -06 10 53.12 23.2r 13UK15 W84 C~4yRI 2016 08 31.27720 00 55 58.735 -06 10 53.32 23.2i 13UK15 W84 C~4yRJ 2016 09 30.19783 00 54 22.473 -06 23 24.24 23.3r 13UK15 W84 C~4yRJ 2016 09 30.19920 00 54 22.471 -06 23 24.26 23.0i 13UK15 W84 C~4yRJ 2016 10 01.21225 00 54 18.869 -06 23 47.90 22.9r 13UK15 W84 C~4yRJ 2016 10 01.21500 00 54 18.883 -06 23 47.93 23.5g 13UK15 W84 C~4yRJ 2016 11 06.11263 00 52 16.165 -06 34 48.66 23.3z 13UK15 W84 C~4yRJ 2017 09 24.32739 00 57 53.049 -06 04 25.59 21.7z 13UK15 W84 C~4yRJ 2017 09 25.24365 00 57 49.898 -06 04 47.69 24.5g 13UK15 W84 C~4yRJ 2017 09 27.27307 00 57 42.826 -06 05 37.53 23.5z 13UK15 W84 C~4yRJ 2020 09 21.251620 01 07 34.910 -05 12 42.89 23.2G 13UK15 G37 C~49xD 2020 09 21.313100 01 07 34.687 -05 12 44.05 13UK15 G37 C~49xD
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 0.37 0.00 -0.54
2 0.0434 0.00 -0.15 0.00 0.05
3 0.0436 0.00 -0.08 0.00 -0.11
4 0.0461 0.00 0.32 0.00 -0.07
5 0.0464 0.00 0.41 0.00 -0.43
6 0.1968 0.00 -0.34 0.00 0.45
7 0.1996 0.00 -0.45 0.00 0.31
8 0.8772 0.00 -0.54 0.00 0.24
9 0.8773 0.00 -0.22 0.00 0.15
10 1.0240 0.00 0.26 0.00 0.38
11 1.0265 0.00 0.13 0.00 0.37
12 1.8922 0.00 0.09 0.00 -0.21
13 2.8832 0.00 0.07 0.00 0.00
14 2.8832 0.00 0.06 0.00 -0.16
15 2.9651 0.00 0.05 0.00 -0.18
16 2.9651 0.00 0.10 0.00 -0.17
17 2.9679 0.00 -0.12 0.00 0.06
18 2.9679 0.00 0.24 0.00 0.09
19 3.0662 0.00 -0.08 0.00 -0.22
20 3.9484 0.00 -0.07 0.00 -0.27
21 3.9509 0.00 0.10 0.00 0.19
22 3.9564 0.00 -0.02 0.00 -0.10
23 6.9406 0.00 0.06 0.00 -0.07
24 6.9408 0.00 -0.14 0.00 0.31
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.
13UK15 quality flag:3 Type: 2:1E 2:1E 2:1E axisobj 48.266 48.266 48.266 ecceobj 0.192 0.192 0.192 incobj 11.700 11.700 11.700 qmin 37.847 37.856 37.881 qmax 58.520 58.625 58.512 amean 47.797 47.797 47.797 amin 47.195 47.178 47.204 amax 48.472 48.489 48.479 emean 0.184 0.183 0.183 emin 0.156 0.156 0.156 emax 0.208 0.210 0.209 imean 10.618 10.662 10.677 imin 9.909 9.892 9.901 imax 11.700 11.701 11.722 excite_mean 0.260 0.261 0.261 fracstop 1.000 1.000 1.000 cjmean 3.065 3.064 3.064 libcent 0 180.7 179.5 180.0 libamp 0 155.2 153.7 154.5 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 164.8 179.8 183.1 kozaiamp 179.9 179.9 180.0