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: 13RC157 # Created Wed Apr 24 01:14:56 2024 # Orbit generated by ELGB # -->Covariance matrix from a Bernstein fit # Fitting 17 observations of 17 # Arc: 5.16y # First observation: 2013/09/10 # Last observation: 2018/11/07 # Chi-squared of fit: 12.21 DOF: 28 RMS: 0.15 # Min/Max residuals: -0.32 0.33 # Exact a, adot, b, bdot, g, gdot: 1.994107E-05 4.412757E-02 -1.109733E-06 -6.242786E-03 3.471499E-02 -2.339665E-03 # Covariance matrix: 4.5661E-13 -2.4190E-13 -2.0372E-14 2.7050E-14 1.0267E-13 -8.1308E-13 -2.4190E-13 3.5231E-13 3.4494E-14 -5.0159E-14 1.5094E-13 1.4893E-12 -2.0372E-14 3.4494E-14 2.8398E-13 -7.5866E-14 1.1109E-14 1.5800E-13 2.7050E-14 -5.0159E-14 -7.5866E-14 3.3092E-14 -2.1561E-14 -2.2878E-13 1.0267E-13 1.5094E-13 1.1109E-14 -2.1561E-14 4.5163E-13 6.1929E-13 -8.1308E-13 1.4893E-12 1.5800E-13 -2.2878E-13 6.1929E-13 6.7966E-12 # lat0 lon0 xBary yBary zBary JD0 -10.227192 10.338783 0.392023 -0.164743 -0.913677 2456545.819698 # Heliocentric elements and errors Epoch: 2456546.5000 = 2013/09/11 Mean Anomaly: 348.71313 +/- 0.010 Argument of Peri: 250.24569 +/- 0.017 Long of Asc Node: 139.48101 +/- 0.001 Inclination: 12.82809 +/- 0.000 Eccentricity: 0.25333581 +/- 0.0001 Semi-Major Axis: 39.34884942 +/- 0.0041 Time of Perihelion: 2459373.1212 +/- 14.0 Perihelion: 29.38037687 +/- 0.0040 Aphelion: 49.31732198 +/- 0.0058 Period (y) 246.8347 +/- 0.04 # Ecliptic coordinates at JD0 (AU and AU/d) Ecliptic X 28.87133173 +/- 0.0005 Ecliptic Y 4.87161576 +/- 0.0001 Ecliptic Z -5.11461038 +/- 0.0001 Ecliptic XDOT -0.00089540 +/- 0.0000 Ecliptic YDOT 0.00337424 +/- 0.0000 Ecliptic ZDOT -0.00045162 +/- 0.0000 # Distances at JD0 (AU) Heliocenter to KBO 29.72285363 +/- 0.0005 Geocenter to KBO 28.80605946 +/- 0.0006 # Hcoef: 8.76
The following table shows the complete astrometric record for 13RC157. 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 (13RC157) followed by the observatory code and reference code for the source of the astrometry.
2013 09 10.31892 00 54 03.229 -05 18 57.16 23.5g 13RC157 W84 C~52RN 2013 09 29.21656 00 52 17.400 -05 33 01.72 23.7g 13RC157 W84 C~52RN 2013 10 02.26639 00 51 59.265 -05 35 11.22 23.5r 13RC157 W84 C~52RN 2014 10 03.26724 01 01 51.462 -04 55 34.17 23.1i 13RC157 W84 C~52RN 2014 11 15.09217 00 57 52.540 -05 17 32.76 23.9r 13RC157 W84 C~52RN 2014 12 06.09197 00 56 39.732 -05 19 47.21 22.9z 13RC157 W84 C~52RN 2015 11 02.11475 01 08 54.112 -04 32 26.13 23.9r 13RC157 W84 C~52RN 2016 08 26.35469 01 24 50.358 -03 05 54.44 23.7r 13RC157 W84 C~52RN 2016 10 22.16760 01 19 51.696 -03 45 55.93 23.8r 13RC157 W84 C~52RN 2016 10 28.14679 01 19 16.150 -03 49 11.93 23.2i 13RC157 W84 C~52RN 2016 10 28.25215 01 19 15.501 -03 49 15.10 23.7r 13RC157 W84 C~52RN 2017 08 22.40165 01 34 56.531 -02 21 27.12 23.7r 13RC157 W84 C~52RN 2017 08 28.38473 01 34 38.811 -02 25 26.00 23.3g 13RC157 W84 C~52RN 2018 10 10.30084 01 41 08.705 -02 13 48.50 23.1r 13RC157 W84 C~52RO 2018 11 07.20873 01 38 20.010 -02 29 46.33 23.3r 13RC157 W84 C~52RO 2018 11 07.21010 01 38 19.990 -02 29 46.14 23.1i 13RC157 W84 C~52RO 2018 11 07.21147 01 38 19.975 -02 29 46.22 23.7g 13RC157 W84 C~52RO
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 0.17 0.00 -0.32
2 0.0517 0.00 -0.15 0.00 0.04
3 0.0601 0.00 0.01 0.00 0.13
4 1.0621 0.00 0.07 0.00 0.28
5 1.1794 0.00 -0.09 0.00 0.12
6 1.2369 0.00 0.00 0.00 -0.08
7 2.1432 0.00 -0.06 0.00 -0.32
8 2.9597 0.00 -0.06 0.00 0.05
9 3.1153 0.00 -0.05 0.00 -0.03
10 3.1316 0.00 0.30 0.00 0.01
11 3.1319 0.00 -0.00 0.00 0.09
12 3.9482 0.00 -0.16 0.00 -0.17
13 3.9646 0.00 0.02 0.00 0.33
14 5.0814 0.00 0.07 0.00 0.05
15 5.1578 0.00 0.16 0.00 -0.19
16 5.1578 0.00 -0.02 0.00 0.04
17 5.1578 0.00 -0.13 0.00 -0.01
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.
13RC157 quality flag:3 Type: 3:2E 3:2E 3:2E axisobj 39.563 39.563 39.563 ecceobj 0.257 0.257 0.257 incobj 12.809 12.809 12.809 qmin 28.986 29.005 28.991 qmax 50.787 50.744 50.758 amean 39.456 39.456 39.456 amin 38.874 38.898 38.867 amax 40.118 40.142 40.105 emean 0.251 0.251 0.251 emin 0.236 0.236 0.236 emax 0.267 0.265 0.266 imean 11.717 11.716 11.724 imin 11.160 11.161 11.159 imax 12.307 12.289 12.287 excite_mean 0.323 0.323 0.323 fracstop 1.000 1.000 1.000 cjmean 2.933 2.933 2.933 libcent 0 180.7 180.3 179.9 libamp 0 132.2 132.7 132.0 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 184.1 184.3 183.8 kozaiamp 180.0 180.0 179.9