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: 10KZ39 # Created Sat Jul 26 01:38:15 2014 # Orbit generated from Bernstein formalism # Fitting 28 observations of 28 # Arc: 1.83y # First observation: 2010/05/21 # Last observation: 2012/03/20 Preliminary a, adot, b, bdot, g, gdot: -0.000004 0.017980 -0.000021 -0.008399 0.021730 0.000000 # Chi-squared of fit: 44.34 DOF: 50 RMS: 0.22 # Min/Max residuals: -0.57 0.58 # Exact a, adot, b, bdot, g, gdot: 1.529771E-05 1.813923E-02 -7.746774E-06 -8.498688E-03 2.202071E-02 -8.733344E-04 # Covariance matrix: 2.8984E-13 -4.8498E-13 6.2440E-15 -3.5928E-14 7.7861E-13 -1.8229E-13 -4.8498E-13 1.6677E-12 1.2937E-14 -1.8137E-13 -1.3070E-12 1.8228E-11 6.2440E-15 1.2937E-14 1.0936E-13 -8.1398E-14 4.7284E-14 7.6433E-13 -3.5928E-14 -1.8137E-13 -8.1398E-14 2.0332E-13 -3.5279E-13 -7.4244E-12 7.7861E-13 -1.3070E-12 4.7284E-14 -3.5279E-13 3.6920E-12 1.2663E-11 -1.8229E-13 1.8228E-11 7.6433E-13 -7.4244E-12 1.2663E-11 5.0426E-10 # lat0 lon0 xBary yBary zBary JD0 -7.416964 -111.554313 0.156312 -0.129135 -0.991794 2455337.615016 # Heliocentric elements and errors Epoch: 2455330.5000 = 2010/05/14 Mean Anomaly: 245.94158 +/- 0.640 Argument of Peri: 316.42643 +/- 0.609 Long of Asc Node: 53.19648 +/- 0.001 Inclination: 26.10994 +/- 0.002 Eccentricity: 0.05620407 +/- 0.0010 Semi-Major Axis: 45.25347004 +/- 0.0187 Time of Perihelion: 2490559.5648 +/- 196.5 Perihelion: 42.71004063 +/- 0.0472 Aphelion: 47.79689946 +/- 0.0481 Period (y) 304.4290 +/- 0.19 # Ecliptic coordinates at JD0 (AU and AU/d) Ecliptic X -17.05202421 +/- 0.0015 Ecliptic Y -42.75787160 +/- 0.0036 Ecliptic Z -5.86250878 +/- 0.0005 Ecliptic XDOT 0.00218887 +/- 0.0000 Ecliptic YDOT -0.00059554 +/- 0.0000 Ecliptic ZDOT -0.00103383 +/- 0.0000 # Distances at JD0 (AU) Heliocenter to KBO 46.40448386 +/- 0.0034 Geocenter to KBO 45.41179782 +/- 0.0040 # Hcoef: 3.94
The following table shows the complete astrometric record for 10KZ39. 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 (10KZ39) followed by the observatory code and reference code for the source of the astrometry.
2010 05 21.11425 16 21 30.197 -29 01 56.15 10KZ39 304 C~0I3z 2010 05 21.18206 16 21 29.894 -29 01 55.96 10KZ39 304 C~0I3z 2010 05 23.21814 16 21 19.580 -29 01 46.43 20.2R 10KZ39 304 C~0I3z 2010 05 23.27052 16 21 19.325 -29 01 46.17 10KZ39 304 C~0I3z 2010 05 23.32313 16 21 19.048 -29 01 45.87 10KZ39 304 C~0I3z 2010 06 05.08738 16 20 14.276 -29 00 24.75 10KZ39 304 C~0IRz 2010 06 05.15706 16 20 13.942 -29 00 23.98 10KZ39 304 C~0IRz 2010 06 05.21869 16 20 13.646 -29 00 23.70 10KZ39 304 C~0IRz 2010 06 08.62734 16 19 56.540 -28 59 57.28 20.2R 10KZ39 E10 C~0IRz 2010 06 08.64014 16 19 56.475 -28 59 57.12 20.3R 10KZ39 E10 C~0IRz 2010 06 08.65818 16 19 56.393 -28 59 57.02 19.7R 10KZ39 E10 C~0IRz 2010 06 15.50253 16 19 22.83 -28 58 59.8 21.0V 10KZ39 F65 C~0Jas 2010 06 16.40770 16 19 18.46 -28 58 51.6 20.4R 10KZ39 F65 C~0Jas 2011 05 03.16532 16 27 18.670 -29 41 29.72 20.0R 10KZ39 304 C~0WGM 2011 05 03.25269 16 27 18.288 -29 41 29.75 10KZ39 304 C~0WGM 2011 05 03.35027 16 27 17.845 -29 41 29.92 10KZ39 304 C~0WGM 2011 05 12.10452 16 26 36.708 -29 41 23.50 20.1R 10KZ39 304 C~0WGM 2011 05 12.17048 16 26 36.388 -29 41 23.45 10KZ39 304 C~0WGM 2011 05 12.23944 16 26 36.071 -29 41 23.42 10KZ39 304 C~0WGM 2012 03 18.21466 16 33 55.14 -30 13 57.5 20.8R 10KZ39 304 C~0ger 2012 03 18.34579 16 33 55.00 -30 13 59.3 10KZ39 304 C~0ger 2012 03 18.41737 16 33 54.92 -30 14 00.3 10KZ39 304 C~0ger 2012 03 19.21843 16 33 54.10 -30 14 11.0 10KZ39 304 C~0ger 2012 03 19.34123 16 33 53.96 -30 14 12.6 10KZ39 304 C~0ger 2012 03 19.41778 16 33 53.86 -30 14 13.6 10KZ39 304 C~0ger 2012 03 20.18933 16 33 52.99 -30 14 23.8 10KZ39 304 C~0ger 2012 03 20.30113 16 33 52.86 -30 14 25.3 10KZ39 304 C~0ger 2012 03 20.35278 16 33 52.79 -30 14 25.9 10KZ39 304 C~0ger
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 -0.47 0.00 0.34 2 0.0002 -3.95 0.12 -0.48 0.32 3 0.0058 -138.91 -0.12 -13.72 -0.23 4 0.0059 -142.25 0.07 -14.02 -0.21 5 0.0060 -145.88 -0.03 -14.33 -0.21 6 0.0410 -997.01 -0.30 -77.66 -0.19 7 0.0412 -1001.46 -0.06 -77.65 0.11 8 0.0414 -1005.34 0.23 -78.03 -0.02 9 0.0507 -1230.98 0.02 -90.17 0.04 10 0.0507 -1231.85 0.01 -90.16 0.10 11 0.0508 -1232.92 0.14 -90.24 0.07 12 0.0695 -1676.61 0.41 -109.16 -0.07 13 0.0720 -1734.51 -0.04 -110.92 0.06 14 0.9502 4879.33 0.27 -1609.30 -0.30 15 0.9504 4874.42 0.50 -1610.10 -0.23 16 0.9507 4868.74 0.58 -1611.16 -0.35 17 0.9746 4337.95 -0.57 -1688.22 0.26 18 0.9748 4333.82 -0.51 -1688.82 0.23 19 0.9750 4329.74 -0.20 -1689.44 0.19 20 1.8264 10270.92 0.04 -2776.22 -0.01 21 1.8268 10269.38 0.01 -2778.25 0.01 22 1.8270 10268.49 -0.02 -2779.39 -0.02 23 1.8292 10259.45 0.05 -2791.49 -0.02 24 1.8295 10257.88 0.06 -2793.34 0.06 25 1.8297 10256.73 -0.07 -2794.51 0.06 26 1.8318 10246.99 -0.08 -2806.21 -0.04 27 1.8321 10245.53 0.03 -2807.93 -0.01 28 1.8323 10244.71 -0.04 -2808.65 0.06
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.