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: 15GR50 # Created Sat Apr 20 01:17:11 2024 # Orbit generated from Bernstein formalism # Fitting 12 observations of 13 # Arc: 1.06y # First observation: 2015/04/13 # Last observation: 2016/05/03 Preliminary a, adot, b, bdot, g, gdot: -0.000002 0.009563 -0.000002 -0.000753 0.014833 0.000000 # Chi-squared of fit: 15.25 DOF: 18 RMS: 0.20 # Min/Max residuals: -0.34 0.41 # Exact a, adot, b, bdot, g, gdot: 1.181572E-05 9.591564E-03 -2.771964E-06 -7.555194E-04 1.489338E-02 1.299256E-03 # Covariance matrix: 2.7551E-13 3.7574E-13 1.0883E-15 -5.4351E-14 8.4318E-13 7.1022E-11 3.7574E-13 5.7365E-12 9.3549E-15 -4.6442E-13 5.8418E-12 6.0738E-10 1.0883E-15 9.3549E-15 1.9095E-13 -2.0170E-13 1.0999E-14 1.1103E-12 -5.4351E-14 -4.6442E-13 -2.0170E-13 6.3358E-13 -5.4909E-13 -5.5166E-11 8.4318E-13 5.8418E-12 1.0999E-14 -5.4909E-13 8.4141E-12 7.1755E-10 7.1022E-11 6.0738E-10 1.1103E-12 -5.5166E-11 7.1755E-10 7.2139E-08 # lat0 lon0 xBary yBary zBary JD0 -0.113657 -156.254569 0.017380 -0.001828 -0.999571 2457125.623078 # Heliocentric elements and errors Epoch: 2457120.5000 = 2015/04/08 Mean Anomaly: 145.86880 +/- 3.796 Argument of Peri: 21.24340 +/- 3.694 Long of Asc Node: 22.30242 +/- 0.002 Inclination: 4.49172 +/- 0.005 Eccentricity: 0.29354332 +/- 0.0069 Semi-Major Axis: 53.97749362 +/- 0.2259 Time of Perihelion: 2398428.7027 +/- 1482.2 Perihelion: 38.13276107 +/- 0.4032 Aphelion: 69.82222617 +/- 0.4717 Period (y) 396.5768 +/- 2.49 # Ecliptic coordinates at JD0 (AU and AU/d) Ecliptic X -62.38449338 +/- 0.0120 Ecliptic Y -27.42407899 +/- 0.0052 Ecliptic Z -0.13338611 +/- 0.0000 Ecliptic XDOT 0.00048844 +/- 0.0000 Ecliptic YDOT -0.00171595 +/- 0.0000 Ecliptic ZDOT -0.00013928 +/- 0.0000 # Distances at JD0 (AU) Heliocenter to KBO 68.14633457 +/- 0.0112 Geocenter to KBO 67.14393892 +/- 0.0131 # Hcoef: 6.60
The following table shows the complete astrometric record for 15GR50. 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 (15GR50) followed by the observatory code and reference code for the source of the astrometry.
2015 04 13.12230 13 27 44.935 -09 19 21.57 24.8r 15GR50 807 C~1x8u 2015 04 13.21164 13 27 44.701 -09 19 20.69 15GR50 807 C~1x8u 2015 04 13.30360 13 27 44.399 -09 19 19.34 15GR50 807 C~1x8u 2015 04 18.11853 13 27 30.078 -09 17 56.90 15GR50 304 C~1x8u 2015 04 18.28707 13 27 29.549 -09 17 54.09 15GR50 304 C~1x8u 2015 04 19.18541 13 27 26.899 -09 17 38.79 15GR50 304 C~1x8u 2015 04 19.28954 13 27 26.644 -09 17 36.50 24.8r 15GR50 304 C~1x8u 2015 04 20.26896 13 27 23.684 -09 17 20.31 15GR50 304 C~1x8u 2015 05 22.15568 13 25 57.608 -09 09 06.92 15GR50 304 C~1x8u 2016 03 09.35707 13 31 19.373 -09 42 47.02 15GR50 304 C~1x8u 2016 03 10.23738 13 31 17.306 -09 42 35.22 15GR50 304 C~1x8u 2016 05 03.05166 13 28 45.232 -09 28 12.11 24.8r 15GR50 304 C~2AE2 2016 05 03.17184 13 28 44.853 -09 28 10.05 15GR50 304 C~2AE2
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 -0.34 0.00 0.41
2 0.0002 -3.54 0.40 -0.46 0.01
3 0.0005 -8.20 0.15 -0.85 -0.33
4 0.0137 -235.64 0.06 -2.47 0.08
5 0.0141 -243.96 -0.20 -2.75 -0.08
6 0.0166 -286.06 -0.04 -3.01 0.01
7 0.0169 -290.42 ( 0.57) -2.28 ( 0.82)
8 0.0196 -337.12 -0.07 -3.41 0.09
9 0.1069 -1703.72 0.05 -16.10 -0.17
10 0.9069 3467.17 -0.05 -140.23 -0.26
11 0.9093 3434.40 0.05 -140.46 -0.06
12 1.0566 1025.06 0.28 -164.23 0.18
13 1.0569 1019.09 -0.29 -164.38 0.11
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.
15GR50 quality flag:3 Type: SCATNEAR SCATNEAR SCATNEAR axisobj 53.520 54.367 53.083 ecceobj 0.303 0.325 0.290 incobj 4.524 4.524 4.524 qmin 37.007 36.325 37.505 qmax 71.483 73.958 70.105 amean 53.842 54.671 53.426 amin 53.256 54.045 52.860 amax 54.532 55.501 54.089 emean 0.299 0.322 0.285 emin 0.287 0.312 0.274 emax 0.311 0.334 0.296 imean 4.346 4.347 4.286 imin 3.879 3.938 3.893 imax 4.764 4.767 4.669 excite_mean 0.308 0.331 0.295 fracstop 1.000 1.000 1.000 cjmean 3.104 3.094 3.109 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 174.5 177.6 170.8 kozaiamp 180.0 180.0 180.0