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: 13XM40 # Created Sun Dec 22 02:09:53 2024 # Orbit generated from Bernstein formalism # Fitting 7 observations of 7 # Arc: 5.00y # First observation: 2013/12/02 # Last observation: 2018/12/01 Preliminary a, adot, b, bdot, g, gdot: 0.000055 0.026917 -0.000093 0.001741 0.026782 0.000000 # Chi-squared of fit: 1.81 DOF: 8 RMS: 0.09 # Min/Max residuals: -0.11 0.16 # Exact a, adot, b, bdot, g, gdot: 1.688010E-05 2.689253E-02 1.564320E-06 1.674291E-03 2.584662E-02 1.464831E-03 # Covariance matrix: 5.0696E-13 -3.0975E-13 1.2918E-14 -9.0074E-15 -7.0664E-14 -1.5546E-12 -3.0975E-13 1.8813E-12 -2.8949E-14 -3.5668E-14 -8.2471E-13 1.3688E-11 1.2918E-14 -2.8949E-14 4.7824E-13 -1.1738E-13 -9.9012E-14 -2.5595E-13 -9.0074E-15 -3.5668E-14 -1.1738E-13 5.7822E-14 1.6429E-13 -2.1278E-13 -7.0664E-14 -8.2471E-13 -9.9012E-14 1.6429E-13 2.2181E-12 -5.4862E-12 -1.5546E-12 1.3688E-11 -2.5595E-13 -2.1278E-13 -5.4862E-12 1.0228E-10 # lat0 lon0 xBary yBary zBary JD0 -47.078380 -7.329664 -0.959561 -0.159669 -0.148693 2456628.679478 # Heliocentric elements and errors Epoch: 2456620.5000 = 2013/11/24 Mean Anomaly: 43.38378 +/- 0.075 Argument of Peri: 222.18032 +/- 0.101 Long of Asc Node: 77.91945 +/- 0.001 Inclination: 47.02840 +/- 0.000 Eccentricity: 0.10471349 +/- 0.0004 Semi-Major Axis: 41.78548201 +/- 0.0147 Time of Perihelion: 2444731.0578 +/- 19.5 Perihelion: 37.40997848 +/- 0.0224 Aphelion: 46.16098553 +/- 0.0244 Period (y) 270.1135 +/- 0.14 # Ecliptic coordinates at JD0 (AU and AU/d) Ecliptic X 26.47047597 +/- 0.0015 Ecliptic Y -2.43451251 +/- 0.0002 Ecliptic Z -28.33200448 +/- 0.0016 Ecliptic XDOT 0.00059090 +/- 0.0000 Ecliptic YDOT 0.00279333 +/- 0.0000 Ecliptic ZDOT 0.00000729 +/- 0.0000 # Distances at JD0 (AU) Heliocenter to KBO 38.84990897 +/- 0.0016 Geocenter to KBO 38.68977884 +/- 0.0022 # Hcoef: 7.88
The following table shows the complete astrometric record for 13XM40. 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 (13XM40) followed by the observatory code and reference code for the source of the astrometry.
2013 12 02.17870 01 09 34.290 -44 56 39.26 24.2r 13XM40 W84 C~52S3 2013 12 06.17764 01 09 19.647 -44 52 56.31 24.5g 13XM40 W84 C~52S3 2013 12 29.11479 01 08 34.737 -44 27 02.51 23.4r 13XM40 W84 C~52S3 2016 10 06.07523 01 34 59.934 -42 13 30.39 23.9r 13XM40 W84 C~52S3 2017 10 17.32598 01 39 52.524 -41 14 56.61 23.2r 13XM40 W84 C~52S3 2018 11 08.25100 01 43 25.728 -40 12 24.12 24.1r 13XM40 W84 C~52S3 2018 12 01.21567 01 41 19.441 -40 01 42.02 24.4g 13XM40 W84 C~52S3
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 -0.09 0.00 -0.11
2 0.0109 -4.97 0.16 271.80 0.12
3 0.0737 460.40 -0.08 1829.83 -0.04
4 2.8443 19208.74 0.04 -1861.36 0.14
5 3.8745 24013.28 -0.03 -1161.60 -0.11
6 4.9338 28334.76 0.01 214.81 -0.08
7 4.9967 27611.02 -0.01 1643.62 0.08
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.
13XM40 quality flag:3 Type: SCATEXTD SCATEXTD SCATEXTD axisobj 42.048 42.094 42.001 ecceobj 0.110 0.111 0.108 incobj 47.056 47.056 47.056 qmin 36.598 36.508 36.619 qmax 47.476 47.629 47.341 amean 41.898 41.945 41.849 amin 41.570 41.621 41.507 amax 42.248 42.308 42.201 emean 0.109 0.110 0.107 emin 0.094 0.095 0.094 emax 0.124 0.126 0.122 imean 45.607 45.605 45.607 imin 45.370 45.343 45.356 imax 45.834 45.839 45.839 excite_mean 0.723 0.723 0.723 fracstop 1.000 1.000 1.000 cjmean 2.359 2.359 2.359 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 181.1 181.9 181.4 kozaiamp 180.0 179.9 180.0