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: 13RB157 # Created Fri Nov 22 02:09:33 2024 # Orbit generated from Bernstein formalism # Fitting 10 observations of 10 # Arc: 4.02y # First observation: 2013/09/10 # Last observation: 2017/09/18 Preliminary a, adot, b, bdot, g, gdot: 0.000007 0.030525 0.000010 0.001612 0.028454 0.000000 # Chi-squared of fit: 5.29 DOF: 14 RMS: 0.13 # Min/Max residuals: -0.20 0.30 # Exact a, adot, b, bdot, g, gdot: 1.695677E-05 3.121352E-02 4.296790E-07 1.660554E-03 2.890688E-02 6.852145E-03 # Covariance matrix: 6.7273E-13 1.7059E-13 -2.1904E-14 2.0437E-14 7.0042E-13 2.7044E-12 1.7059E-13 1.2921E-12 -4.5906E-14 7.9069E-14 1.1524E-12 1.1131E-11 -2.1904E-14 -4.5906E-14 3.1566E-13 -9.5059E-14 -6.0972E-14 -4.2598E-13 2.0437E-14 7.9069E-14 -9.5059E-14 5.7131E-14 7.9029E-14 7.1392E-13 7.0042E-13 1.1524E-12 -6.0972E-14 7.9029E-14 1.7569E-12 1.0866E-11 2.7044E-12 1.1131E-11 -4.2598E-13 7.1392E-13 1.0866E-11 1.0030E-10 # lat0 lon0 xBary yBary zBary JD0 -8.436682 7.133320 0.339541 -0.139116 -0.938610 2456545.816908 # Heliocentric elements and errors Epoch: 2456540.5000 = 2013/09/05 Mean Anomaly: 51.66607 +/- 0.016 Argument of Peri: 213.71664 +/- 0.036 Long of Asc Node: 77.07291 +/- 0.003 Inclination: 8.70473 +/- 0.000 Eccentricity: 0.22628141 +/- 0.0003 Semi-Major Axis: 39.56133387 +/- 0.0058 Time of Perihelion: 2443496.5904 +/- 2.8 Perihelion: 30.60933954 +/- 0.0129 Aphelion: 48.51332819 +/- 0.0140 Period (y) 248.8368 +/- 0.06 # Ecliptic coordinates at JD0 (AU and AU/d) Ecliptic X 34.93794281 +/- 0.0016 Ecliptic Y 4.03329343 +/- 0.0002 Ecliptic Z -5.07548961 +/- 0.0002 Ecliptic XDOT 0.00028660 +/- 0.0000 Ecliptic YDOT 0.00301486 +/- 0.0000 Ecliptic ZDOT 0.00006050 +/- 0.0000 # Distances at JD0 (AU) Heliocenter to KBO 35.53432001 +/- 0.0015 Geocenter to KBO 34.59384003 +/- 0.0016 # Hcoef: 8.23
The following table shows the complete astrometric record for 13RB157. 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 (13RB157) followed by the observatory code and reference code for the source of the astrometry.
2013 09 10.31613 00 39 32.683 -04 55 08.70 24.4g 13RB157 W84 C~52RN 2013 09 10.31750 00 39 32.678 -04 55 08.77 24.7r 13RB157 W84 C~52RN 2013 11 08.08168 00 34 43.011 -05 22 27.62 22.9r 13RB157 W84 C~52RN 2013 11 23.13356 00 33 51.301 -05 24 46.25 23.9i 13RB157 W84 C~52RN 2014 11 14.05768 00 40 44.037 -04 36 32.68 23.9r 13RB157 W84 C~52RN 2014 11 15.12462 00 40 40.124 -04 36 44.32 24.0r 13RB157 W84 C~52RN 2016 11 25.10179 00 52 32.031 -03 05 27.21 23.5r 13RB157 W84 C~52RN 2017 08 28.36267 01 05 21.219 -01 41 24.98 23.7r 13RB157 W84 C~52RN 2017 09 18.25801 01 03 53.934 -01 52 32.12 23.0i 13RB157 W84 C~52RN 2017 09 18.25938 01 03 53.940 -01 52 32.30 23.5r 13RB157 W84 C~52RN
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 0.02 0.00 0.10
2 0.0000 -0.10 0.04 -0.03 0.07
3 0.1609 -4623.72 0.12 205.29 -0.06
4 0.2021 -5388.50 -0.07 382.42 -0.19
5 1.1766 1421.62 -0.20 601.87 -0.15
6 1.1795 1363.29 0.01 614.38 0.17
7 3.2082 13336.13 0.14 1396.93 0.30
8 3.9645 26036.87 -0.05 1396.73 -0.09
9 4.0217 24548.31 -0.06 1310.76 0.03
10 4.0217 24548.32 0.06 1310.56 -0.17
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.
13RB157 quality flag:3 Type: 3:2E 3:2E 3:2E axisobj 39.789 39.807 39.770 ecceobj 0.230 0.230 0.230 incobj 8.710 8.710 8.710 qmin 29.846 29.861 29.839 qmax 49.850 50.012 49.876 amean 39.457 39.457 39.456 amin 38.875 38.871 38.892 amax 40.092 40.113 40.122 emean 0.227 0.226 0.228 emin 0.210 0.209 0.213 emax 0.244 0.247 0.245 imean 7.001 7.012 6.938 imin 6.298 6.523 6.357 imax 7.761 7.600 7.583 excite_mean 0.258 0.257 0.258 fracstop 1.000 1.000 1.000 cjmean 2.976 2.977 2.976 libcent 0 180.5 179.7 180.5 libamp 0 130.8 133.5 127.6 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 199.2 174.4 258.5 kozaiamp 180.0 180.0 180.0