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: 13RU157 # Created Fri Nov 22 02:09:34 2024 # Orbit generated from Bernstein formalism # Fitting 21 observations of 21 # Arc: 4.04y # First observation: 2013/09/11 # Last observation: 2017/09/24 Preliminary a, adot, b, bdot, g, gdot: -0.000054 0.016729 0.000048 -0.010318 0.022095 0.000000 # Chi-squared of fit: 5.88 DOF: 36 RMS: 0.09 # Min/Max residuals: -0.25 0.23 # Exact a, adot, b, bdot, g, gdot: 1.221516E-05 1.650325E-02 -6.062625E-06 -1.017247E-02 2.204306E-02 -3.156562E-03 # Covariance matrix: 3.5593E-13 -7.6758E-14 3.3806E-15 -1.1963E-14 3.1960E-13 2.7574E-13 -7.6758E-14 2.6930E-13 4.8999E-14 -1.6205E-13 1.6686E-13 3.9439E-12 3.3806E-15 4.8999E-14 2.2067E-13 -9.4224E-14 4.8803E-14 8.1863E-13 -1.1963E-14 -1.6205E-13 -9.4224E-14 1.3734E-13 -1.6319E-13 -2.7103E-12 3.1960E-13 1.6686E-13 4.8803E-14 -1.6319E-13 8.7198E-13 3.9364E-12 2.7574E-13 3.9439E-12 8.1863E-13 -2.7103E-12 3.9364E-12 6.5903E-11 # lat0 lon0 xBary yBary zBary JD0 -9.944178 9.470897 0.362831 -0.162216 -0.925802 2456546.763018 # Heliocentric elements and errors Epoch: 2456540.5000 = 2013/09/05 Mean Anomaly: 258.15095 +/- 0.091 Argument of Peri: 319.23759 +/- 0.069 Long of Asc Node: 173.72849 +/- 0.000 Inclination: 33.06921 +/- 0.000 Eccentricity: 0.18406138 +/- 0.0003 Semi-Major Axis: 43.35193288 +/- 0.0086 Time of Perihelion: 2486036.6675 +/- 24.9 Perihelion: 35.37251646 +/- 0.0160 Aphelion: 51.33134930 +/- 0.0176 Period (y) 285.4440 +/- 0.09 # Ecliptic coordinates at JD0 (AU and AU/d) Ecliptic X 45.06147732 +/- 0.0019 Ecliptic Y 7.15241327 +/- 0.0003 Ecliptic Z -7.83443795 +/- 0.0003 Ecliptic XDOT -0.00093958 +/- 0.0000 Ecliptic YDOT 0.00192123 +/- 0.0000 Ecliptic ZDOT -0.00117664 +/- 0.0000 # Distances at JD0 (AU) Heliocenter to KBO 46.29332751 +/- 0.0018 Geocenter to KBO 45.36574702 +/- 0.0019 # Hcoef: 6.53
The following table shows the complete astrometric record for 13RU157. 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 (13RU157) followed by the observatory code and reference code for the source of the astrometry.
2013 09 11.26224 00 50 27.030 -05 23 31.17 23.0g 13RU157 W84 C~52RP 2013 09 29.21656 00 49 17.120 -05 33 41.83 24.3g 13RU157 W84 C~52RP 2013 09 29.21795 00 49 17.121 -05 33 41.92 23.3r 13RU157 W84 C~52RP 2013 09 29.21933 00 49 17.113 -05 33 42.03 22.9i 13RU157 W84 C~52RP 2013 11 08.08585 00 46 42.023 -05 51 29.15 22.9i 13RU157 W84 C~52RP 2013 11 08.08722 00 46 42.017 -05 51 29.28 22.8z 13RU157 W84 C~52RP 2014 10 03.30184 00 53 27.288 -05 45 40.17 22.7r 13RU157 W84 C~52RP 2014 10 03.30321 00 53 27.266 -05 45 40.33 22.7i 13RU157 W84 C~52RP 2016 08 16.42600 01 05 03.236 -05 38 03.71 22.4i 13RU157 W84 C~52RP 2016 08 26.36153 01 04 38.820 -05 43 35.95 23.4r 13RU157 W84 C~52RP 2016 09 30.20197 01 02 34.840 -06 03 53.77 23.3r 13RU157 W84 C~52RP 2016 09 30.20335 01 02 34.831 -06 03 53.82 23.2i 13RU157 W84 C~52RP 2016 09 30.20472 01 02 34.821 -06 03 53.89 23.9g 13RU157 W84 C~52RP 2016 11 07.20759 01 00 02.516 -06 21 07.28 21.6z 13RU157 W84 C~52RP 2017 08 28.32246 01 09 04.262 -05 54 07.68 23.5r 13RU157 W84 C~52RP 2017 08 28.32384 01 09 04.255 -05 54 07.86 23.2i 13RU157 W84 C~52RP 2017 08 28.32522 01 09 04.264 -05 54 08.04 24.1g 13RU157 W84 C~52RP 2017 08 28.40635 01 09 04.018 -05 54 10.70 22.3z 13RU157 W84 C~52RP 2017 09 24.24497 01 07 31.129 -06 10 03.69 23.2r 13RU157 W84 C~52RP 2017 09 24.24634 01 07 31.139 -06 10 03.79 23.1i 13RU157 W84 C~52RP 2017 09 24.32878 01 07 30.810 -06 10 06.65 22.9z 13RU157 W84 C~52RP
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 -0.08 0.00 -0.25
2 0.0492 -1200.02 -0.04 -150.14 0.10
3 0.0492 -1200.04 0.03 -150.23 0.02
4 0.0492 -1200.19 -0.02 -150.29 -0.03
5 0.1583 -3748.54 0.05 -221.45 0.02
6 0.1583 -3748.67 -0.01 -221.53 -0.07
7 1.0597 1948.22 0.15 -2283.38 0.15
8 1.0597 1947.85 -0.12 -2283.39 0.14
9 2.9299 11677.19 0.23 -6001.18 0.02
10 2.9572 11208.83 -0.06 -6160.08 0.03
11 3.0525 9020.55 0.07 -6537.16 -0.02
12 3.0525 9020.41 0.02 -6537.15 -0.00
13 3.0525 9020.25 -0.04 -6537.16 0.00
14 3.1566 6520.59 -0.06 -6578.48 -0.06
15 3.9618 14603.15 -0.01 -8336.13 0.10
16 3.9618 14602.98 -0.11 -8336.26 -0.00
17 3.9618 14603.03 0.02 -8336.48 -0.20
18 3.9621 14598.58 -0.09 -8337.44 0.03
19 4.0355 12938.70 -0.12 -8653.41 0.11
20 4.0355 12938.79 0.07 -8653.56 -0.03
21 4.0358 12933.12 0.12 -8654.21 -0.05
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.
13RU157 quality flag:3 Type: SCATEXTD SCATEXTD SCATEXTD axisobj 43.518 43.542 43.494 ecceobj 0.180 0.181 0.180 incobj 32.957 32.956 32.957 qmin 34.237 34.190 34.251 qmax 52.921 52.731 52.697 amean 43.334 43.335 43.298 amin 42.965 42.956 42.950 amax 43.764 43.773 43.707 emean 0.187 0.186 0.186 emin 0.167 0.168 0.167 emax 0.209 0.207 0.207 imean 32.473 32.481 32.485 imin 31.983 31.998 31.982 imax 32.860 32.878 32.876 excite_mean 0.569 0.569 0.568 fracstop 1.000 1.000 1.000 cjmean 2.683 2.683 2.683 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 171.4 174.0 173.3 kozaiamp 180.0 180.0 180.0