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: 98WZ31
# Created Sun Dec 22 02:07:59 2024
# Orbit generated by ELGB
# -->Covariance matrix from a Bernstein fit
# Fitting 29 observations of 29
# Arc: 23.03y
# First observation: 1998/11/19
# Last observation: 2021/12/01
# Chi-squared of fit: 178.19 DOF: 52 RMS: 0.44
# Min/Max residuals: -1.49 0.75
# Exact a, adot, b, bdot, g, gdot:
1.707804E-05 3.564981E-02 4.563606E-06 9.232031E-03 3.121476E-02 1.278699E-03
# Covariance matrix:
2.5188E-13 -4.8969E-14 1.3696E-14 -1.0564E-14 2.9036E-13 -4.1292E-14
-4.8969E-14 2.2686E-14 -6.1873E-15 5.5143E-15 -4.6493E-14 2.1555E-14
1.3696E-14 -6.1873E-15 6.6746E-14 -5.1533E-15 1.4985E-14 -6.0520E-15
-1.0564E-14 5.5143E-15 -5.1533E-15 2.1588E-15 -9.9268E-15 5.4522E-15
2.9036E-13 -4.6493E-14 1.4985E-14 -9.9268E-15 5.0385E-13 -3.8800E-14
-4.1292E-14 2.1555E-14 -6.0520E-15 5.4522E-15 -3.8800E-14 2.1313E-14
# lat0 lon0 xBary yBary zBary JD0
1.631275 56.633880 -0.011665 0.027794 -0.983922 2451136.911951
# Heliocentric elements and errors
Epoch: 2451136.5000 = 1998/11/19
Mean Anomaly: 9.98654 +/- 16.563
Argument of Peri: 351.94361 +/- 0.000
Long of Asc Node: 50.54259 +/- 0.000
Inclination: 14.57601 +/- 0.000
Eccentricity: 0.17355567 +/- 0.0004
Semi-Major Axis: 39.77467632 +/- 0.0036
Time of Perihelion: 2448594.8203 +/- 4215.5
Perihelion: 32.87155592 +/- 0.0180
Aphelion: 46.67779672 +/- 0.0183
Period (y) 250.8524 +/- 0.03
# Ecliptic coordinates at JD0 (AU and AU/d)
Ecliptic X 18.15185267 +/- 0.0009
Ecliptic Y 27.57297035 +/- 0.0014
Ecliptic Z 0.91213267 +/- 0.0000
Ecliptic XDOT -0.00256309 +/- 0.0000
Ecliptic YDOT 0.00180321 +/- 0.0000
Ecliptic ZDOT 0.00081258 +/- 0.0000
# Distances at JD0 (AU)
Heliocenter to KBO 33.02406675 +/- 0.0012
Geocenter to KBO 32.03613516 +/- 0.0017
# Hcoef: 8.12
The following table shows the complete astrometric record for 98WZ31. 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 (98WZ31) followed by the observatory code and reference code for the source of the astrometry.
1998 11 19.41122 03 35 42.14 +20 59 22.1 22.7R 98WZ31 695 Ca3608 1998 11 19.48013 03 35 41.68 +20 59 21.1 98WZ31 695 Ca3608 1998 12 18.08809 03 32 47.61 +20 51 35.1 98WZ31 950 Ca3608 1998 12 18.13019 03 32 47.34 +20 51 34.6 98WZ31 950 Ca3608 1998 12 18.17053 03 32 47.15 +20 51 33.6 98WZ31 950 Ca3608 1998 12 19.00361 03 32 42.74 +20 51 21.3 98WZ31 950 Ca3608 1998 12 19.07132 03 32 42.35 +20 51 20.4 98WZ31 950 Ca3608 1998 12 19.14566 03 32 41.90 +20 51 18.3 98WZ31 950 Ca3608 1999 01 14.26103 03 30 54.62 +20 46 26.2 23.1R 98WZ31 695 Ca3608 1999 01 15.16859 03 30 52.19 +20 46 20.3 98WZ31 695 Ca3608 1999 11 30.23471 03 42 35.96 +21 55 26.6 22.8R 98WZ31 695 Ca9916 1999 11 30.24182 03 42 35.90 +21 55 26.4 22.9R 98WZ31 695 Ca9916 1999 11 30.38241 03 42 35.02 +21 55 24.3 98WZ31 695 Ca9916 1999 11 30.38950 03 42 34.94 +21 55 24.2 98WZ31 695 Ca9916 1999 12 31.25007 03 39 41.45 +21 47 47.4 22.8R 98WZ31 695 Ca9916 1999 12 31.26647 03 39 41.39 +21 47 47.2 22.7R 98WZ31 695 Ca9916 1999 12 31.37380 03 39 40.90 +21 47 46.4 23.3R 98WZ31 695 Ca9916 1999 12 31.38181 03 39 40.79 +21 47 45.3 22.6R 98WZ31 695 Ca9916 2000 01 03.24931 03 39 28.49 +21 47 11.6 23.3R 98WZ31 697 Ca9916 2000 01 03.30771 03 39 28.23 +21 47 10.8 23.6R 98WZ31 697 Ca9916 2000 01 05.12975 03 39 20.73 +21 46 49.6 23.5R 98WZ31 697 Ca9916 2000 01 05.19913 03 39 20.47 +21 46 49.8 23.4R 98WZ31 697 Ca9916 2002 01 31.05815 03 54 09.62 +23 36 24.4 23.2 98WZ31 304 Cf1458 2002 01 31.08125 03 54 09.58 +23 36 24.1 98WZ31 304 Cf1458 2008 10 22.33053 05 02 08.06 +29 20 19.3 23.2r 98WZ31 695 C~0gLs 2008 10 22.41787 05 02 07.68 +29 20 19.8 23.8r 98WZ31 695 C~0gLs 2021 12 01.423300 06 54 24.206 +34 27 41.84 23.7G 98WZ31 G37 C~5J0s 2021 12 01.462810 06 54 23.992 +34 27 42.75 98WZ31 G37 C~5J0s 2021 12 01.502390 06 54 23.773 +34 27 43.15 98WZ31 G37 C~5J0s
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 0.20 0.00 0.07
2 0.0002 0.00 0.05 0.00 0.24
3 0.0785 0.00 0.55 0.00 -0.29
4 0.0786 0.00 -0.07 0.00 -0.15
5 0.0787 0.00 0.35 0.00 -0.53
6 0.0810 0.00 0.75 0.00 -0.60
7 0.0812 0.00 0.38 0.00 -0.49
8 0.0814 0.00 -0.39 0.00 -1.47
9 0.1529 0.00 0.37 0.00 0.18
10 0.1554 0.00 0.37 0.00 0.54
11 1.0289 0.00 -0.15 0.00 0.41
12 1.0290 0.00 -0.35 0.00 0.32
13 1.0294 0.00 0.14 0.00 0.48
14 1.0294 0.00 -0.37 0.00 0.50
15 1.1139 0.00 -0.59 0.00 0.11
16 1.1139 0.00 -0.36 0.00 0.12
17 1.1142 0.00 -0.38 0.00 0.68
18 1.1142 0.00 -1.49 0.00 -0.31
19 1.1221 0.00 0.54 0.00 0.16
20 1.1222 0.00 0.39 0.00 0.05
21 1.1272 0.00 -0.27 0.00 -0.57
22 1.1274 0.00 0.10 0.00 0.40
23 3.1996 0.00 -0.09 0.00 0.22
24 3.1996 0.00 -0.18 0.00 0.04
25 9.9245 0.00 0.17 0.00 0.09
26 9.9247 0.00 0.13 0.00 -0.12
27 23.0336 0.00 -0.16 0.00 0.01
28 23.0337 0.00 0.02 0.00 0.11
29 23.0338 0.00 0.12 0.00 -0.29
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.
98WZ31 quality flag:3 Type: 3:2E 3:2E 3:2E axisobj 39.875 39.875 39.875 ecceobj 0.175 0.175 0.175 incobj 14.567 14.567 14.567 qmin 32.556 32.562 32.550 qmax 46.874 46.866 46.877 amean 39.457 39.457 39.457 amin 39.039 39.036 39.035 amax 39.927 39.934 39.921 emean 0.154 0.154 0.154 emin 0.128 0.128 0.127 emax 0.175 0.175 0.175 imean 13.669 13.667 13.671 imin 13.043 13.043 13.043 imax 14.422 14.422 14.424 excite_mean 0.282 0.282 0.282 fracstop 1.000 1.000 1.000 cjmean 2.961 2.961 2.961 libcent 0 180.3 179.7 179.7 libamp 0 85.5 85.3 85.3 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 183.1 182.9 183.1 kozaiamp 180.0 179.9 180.0