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: 13RL157 # Created Wed Dec 25 02:09:31 2024 # Orbit generated by ELGB # -->Covariance matrix from a Bernstein fit # Fitting 15 observations of 15 # Arc: 8.22y # First observation: 2013/09/10 # Last observation: 2021/12/01 # Chi-squared of fit: 7.74 DOF: 24 RMS: 0.13 # Min/Max residuals: -0.24 0.38 # Exact a, adot, b, bdot, g, gdot: 1.663251E-05 2.730874E-02 5.549443E-06 1.007447E-02 2.585122E-02 3.082438E-03 # Covariance matrix: 6.1827E-13 -1.2876E-14 1.3466E-14 -2.0656E-14 6.5705E-13 -2.3232E-13 -1.2876E-14 5.8631E-13 -1.1699E-13 2.3213E-13 4.6291E-13 2.7037E-12 1.3466E-14 -1.1699E-13 1.6984E-13 -7.0211E-14 -7.2918E-14 -5.5828E-13 -2.0656E-14 2.3213E-13 -7.0211E-14 1.0534E-13 1.5302E-13 1.1042E-12 6.5705E-13 4.6291E-13 -7.2918E-14 1.5302E-13 1.2649E-12 1.7936E-12 -2.3232E-13 2.7037E-12 -5.5828E-13 1.1042E-12 1.7936E-12 1.2856E-11 # lat0 lon0 xBary yBary zBary JD0 -5.723037 19.736549 0.537628 -0.084896 -0.848132 2456545.869028 # Heliocentric elements and errors Epoch: 2456546.5000 = 2013/09/11 Mean Anomaly: 12.13061 +/- 0.014 Argument of Peri: 320.93545 +/- 0.028 Long of Asc Node: 33.87071 +/- 0.000 Inclination: 20.85377 +/- 0.000 Eccentricity: 0.29724202 +/- 0.0001 Semi-Major Axis: 55.21866760 +/- 0.0131 Time of Perihelion: 2451496.3146 +/- 6.2 Perihelion: 38.80535940 +/- 0.0123 Aphelion: 71.63197579 +/- 0.0189 Period (y) 410.3336 +/- 0.15 # Ecliptic coordinates at JD0 (AU and AU/d) Ecliptic X 37.21235574 +/- 0.0016 Ecliptic Y 12.78281625 +/- 0.0005 Ecliptic Z -3.85726337 +/- 0.0002 Ecliptic XDOT -0.00057697 +/- 0.0000 Ecliptic YDOT 0.00286677 +/- 0.0000 Ecliptic ZDOT 0.00102923 +/- 0.0000 # Distances at JD0 (AU) Heliocenter to KBO 39.53521598 +/- 0.0015 Geocenter to KBO 38.68284637 +/- 0.0017 # Hcoef: 7.56
The following table shows the complete astrometric record for 13RL157. 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 (13RL157) followed by the observatory code and reference code for the source of the astrometry.
2013 09 10.36825 01 21 31.444 +02 25 00.14 23.6r 13RL157 W84 C~52RO 2013 09 10.36963 01 21 31.437 +02 24 59.91 22.9i 13RL157 W84 C~52RO 2013 10 13.20007 01 19 02.472 +02 11 55.73 23.2i 13RL157 W84 C~52RO 2013 11 08.18830 01 16 59.844 +02 03 12.13 23.9g 13RL157 W84 C~52RO 2013 11 08.19978 01 16 59.786 +02 03 11.98 23.4r 13RL157 W84 C~52RO 2013 11 08.20115 01 16 59.779 +02 03 12.15 24.0i 13RL157 W84 C~52RO 2014 10 21.25802 01 23 21.442 +03 16 19.40 23.9r 13RL157 W84 C~52RO 2014 10 28.23025 01 22 47.831 +03 13 51.41 24.0g 13RL157 W84 C~52RO 2014 10 29.22886 01 22 43.062 +03 13 31.33 23.4r 13RL157 W84 C~52RO 2014 11 14.13577 01 21 31.887 +03 08 55.47 23.3i 13RL157 W84 C~52RO 2014 11 15.17156 01 21 27.644 +03 08 41.17 23.0i 13RL157 W84 C~52RO 2014 11 16.05778 01 21 24.031 +03 08 29.10 22.6z 13RL157 W84 C~52RO 2021 12 01.108940 01 54 29.355 +10 38 53.52 23.7G 13RL157 G37 C~5J5Q 2021 12 01.160540 01 54 29.151 +10 38 52.70 13RL157 G37 C~5J5Q 2021 12 01.212500 01 54 28.953 +10 38 51.89 13RL157 G37 C~5J5Q
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 0.12
2 0.0000 0.00 -0.06 0.00 -0.08
3 0.0899 0.00 -0.02 0.00 -0.05
4 0.1610 0.00 0.10 0.00 -0.08
5 0.1611 0.00 -0.01 0.00 -0.05
6 0.1611 0.00 -0.02 0.00 0.14
7 1.1113 0.00 -0.13 0.00 0.22
8 1.1304 0.00 0.38 0.00 -0.03
9 1.1331 0.00 0.01 0.00 0.02
10 1.1766 0.00 -0.19 0.00 -0.24
11 1.1795 0.00 0.14 0.00 0.01
12 1.1819 0.00 -0.16 0.00 0.02
13 8.2238 0.00 0.10 0.00 0.13
14 8.2239 0.00 -0.05 0.00 -0.01
15 8.2241 0.00 -0.08 0.00 -0.13
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.
13RL157 quality flag:3 Type: SCATNEAR SCATNEAR SCATNEAR axisobj 55.668 55.668 55.668 ecceobj 0.303 0.303 0.303 incobj 20.821 20.821 20.821 qmin 37.511 37.516 37.506 qmax 73.641 73.653 73.618 amean 55.180 55.180 55.180 amin 54.613 54.612 54.596 amax 55.919 55.919 55.933 emean 0.300 0.300 0.300 emin 0.282 0.282 0.282 emax 0.318 0.318 0.318 imean 20.227 20.227 20.227 imin 19.548 19.548 19.549 imax 20.824 20.824 20.824 excite_mean 0.458 0.458 0.458 fracstop 1.000 1.000 1.000 cjmean 2.969 2.969 2.969 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 170.4 170.5 170.5 kozaiamp 180.0 180.0 179.9