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 Nov 22 02:37:10 2009
# Orbit generated from Bernstein formalism
# Fitting 24 observations of 24
# Arc: 3.20y
# First observation: 1998/11/19
# Last observation: 2002/01/31
Preliminary a, adot, b, bdot, g, gdot:
0.000308 0.035075 0.000062 0.009052 0.031255 0.000000
# Chi-squared of fit: 141.77 DOF: 42 RMS: 0.43
# Min/Max residuals: -1.32 0.70
# Exact a, adot, b, bdot, g, gdot:
1.750067E-05 3.564842E-02 3.818670E-06 9.232814E-03 3.121405E-02 1.269447E-03
# Covariance matrix:
3.4289E-13 -1.4152E-13 1.7088E-14 -4.4706E-14 4.2758E-13 -1.9108E-12
-1.4152E-13 4.7104E-13 -4.1768E-14 1.2438E-13 1.7791E-13 4.7746E-12
1.7088E-14 -4.1768E-14 1.2691E-13 -8.5960E-14 1.7187E-15 -5.6478E-13
-4.4706E-14 1.2438E-13 -8.5960E-14 1.2786E-13 8.5253E-15 1.6508E-12
4.2758E-13 1.7791E-13 1.7187E-15 8.5253E-15 1.0978E-12 -1.0254E-13
-1.9108E-12 4.7746E-12 -5.6478E-13 1.6508E-12 -1.0254E-13 6.4348E-11
# lat0 lon0 xBary yBary zBary JD0
1.631275 56.633880 -0.011665 0.027795 -0.983922 2451136.911951
# Heliocentric elements and errors
Epoch: 2451130.5000 = 1998/11/13
Mean Anomaly: 9.89886 +/- 0.054
Argument of Peri: 352.03641 +/- 0.079
Long of Asc Node: 50.54351 +/- 0.000
Inclination: 14.57770 +/- 0.000
Eccentricity: 0.17348951 +/- 0.0001
Semi-Major Axis: 39.77482046 +/- 0.0070
Time of Perihelion: 2448611.1225 +/- 13.7
Perihelion: 32.87430633 +/- 0.0082
Aphelion: 46.67533459 +/- 0.0101
Period (y) 250.8537 +/- 0.07
# Ecliptic coordinates at JD0 (AU and AU/d)
Ecliptic X 18.15224367 +/- 0.0006
Ecliptic Y 27.57358874 +/- 0.0009
Ecliptic Z 0.91212962 +/- 0.0000
Ecliptic XDOT -0.00256349 +/- 0.0000
Ecliptic YDOT 0.00180251 +/- 0.0000
Ecliptic ZDOT 0.00081264 +/- 0.0000
# Distances at JD0 (AU)
Heliocenter to KBO 33.02481985 +/- 0.0008
Geocenter to KBO 32.03685444 +/- 0.0011
# Hcoef: 8.08
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
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 0.12 0.00 0.18 2 0.0002 -6.50 0.02 0.54 0.37 3 0.0785 -2486.49 0.29 124.63 -0.26 4 0.0786 -2490.28 -0.23 125.05 0.01 5 0.0787 -2493.11 0.06 124.72 -0.45 6 0.0810 -2556.08 0.40 127.53 -0.61 7 0.0812 -2561.61 0.10 127.96 -0.43 8 0.0814 -2568.24 -0.84 127.43 -1.20 9 0.1529 -4098.94 0.22 205.23 0.21 10 0.1554 -4133.45 0.31 207.74 0.57 11 1.0289 6396.19 0.09 1952.78 0.40 12 1.0290 6395.33 -0.12 1952.77 0.36 13 1.0294 6382.91 0.37 1953.46 0.41 14 1.0294 6381.81 -0.09 1953.61 0.53 15 1.1139 3924.15 -0.40 2053.94 0.19 16 1.1139 3923.29 -0.20 2053.93 0.14 17 1.1142 3916.46 -0.09 2054.71 0.70 18 1.1142 3914.72 -1.32 2053.99 -0.04 19 1.1221 3740.16 0.63 2060.28 -0.01 20 1.1222 3736.45 0.47 2060.33 -0.08 21 1.1272 3629.87 -0.28 2063.56 -0.54 22 1.1274 3626.39 0.28 2064.58 0.32 23 3.1996 17106.00 0.17 5829.41 -0.29 24 3.1996 17105.40 0.05 5829.22 -0.46
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 39.878 39.899 39.857 ecceobj 0.175 0.176 0.175 incobj 14.568 14.568 14.568 qmin 32.881 32.826 32.872 qmax 46.339 46.437 46.341 amean 39.456 39.456 39.456 amin 39.297 39.277 39.314 amax 39.623 39.640 39.606 emean 0.154 0.155 0.153 emin 0.135 0.137 0.132 emax 0.170 0.172 0.170 imean 13.660 13.606 13.673 imin 13.039 13.045 12.990 imax 14.347 14.178 14.400 excite_mean 0.282 0.282 0.282 fracstop 1.000 1.000 1.000 cjmean 2.961 2.961 2.962 libcent 0 179.9 179.5 178.8 libamp 0 86.9 94.3 77.4 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 184.0 185.1 181.3 kozaiamp 180.0 179.9 180.0