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: 04HZ78
# Created Sun Oct 19 01:08:53 2025
# Orbit generated by ELGB
# -->Covariance matrix from a Bernstein fit
# Fitting 30 observations of 30
# Arc: 17.20y
# First observation: 2004/04/26
# Last observation: 2021/07/08
# Chi-squared of fit: 56.41 DOF: 54 RMS: 0.24
# Min/Max residuals: -0.73 0.52
# Exact a, adot, b, bdot, g, gdot:
1.553458E-05 3.232787E-02 -4.052831E-06 -7.647477E-03 2.957704E-02 -3.236750E-03
# Covariance matrix:
2.1967E-13 -7.6804E-14 -2.5758E-14 1.7569E-14 1.1652E-13 -1.1852E-13
-7.6804E-14 4.1804E-14 1.4972E-14 -1.0183E-14 -5.1788E-14 6.8011E-14
-2.5758E-14 1.4972E-14 9.8861E-14 -1.0312E-14 -1.9232E-14 2.4910E-14
1.7569E-14 -1.0183E-14 -1.0312E-14 3.4323E-15 1.3319E-14 -1.6958E-14
1.1652E-13 -5.1788E-14 -1.9232E-14 1.3319E-14 1.9800E-13 -9.4642E-14
-1.1852E-13 6.8011E-14 2.4910E-14 -1.6958E-14 -9.4642E-14 1.1362E-13
# lat0 lon0 xBary yBary zBary JD0
0.375539 -156.150105 -0.221567 0.006484 -0.979826 2453121.828513
# Heliocentric elements and errors
Epoch: 2453122.5000 = 2004/04/27
Mean Anomaly: 329.97920 +/- 0.001
Argument of Peri: 218.91288 +/- 0.002
Long of Asc Node: 25.75475 +/- 0.000
Inclination: 13.28615 +/- 0.000
Eccentricity: 0.15348815 +/- 0.0001
Semi-Major Axis: 39.79146481 +/- 0.1128
Time of Perihelion: 2460767.9492 +/- 357.3
Perihelion: 33.68394637 +/- 0.0956
Aphelion: 45.89898324 +/- 0.1302
Period (y) 251.0112 +/- 1.07
# Ecliptic coordinates at JD0 (AU and AU/d)
Ecliptic X -31.73246248 +/- 0.0006
Ecliptic Y -14.26776840 +/- 0.0003
Ecliptic Z 0.22148144 +/- 0.0000
Ecliptic XDOT 0.00147678 +/- 0.0000
Ecliptic YDOT -0.00262462 +/- 0.0000
Ecliptic ZDOT -0.00070972 +/- 0.0000
# Distances at JD0 (AU)
Heliocenter to KBO 34.79326326 +/- 0.0006
Geocenter to KBO 33.81010594 +/- 0.0007
# Hcoef: 7.28
The following table shows the complete astrometric record for 04HZ78. 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 (04HZ78) followed by the observatory code and reference code for the source of the astrometry.
2004 04 26.32777 13 28 52.37 -08 54 23.1 22.8g 04HZ78 568 C~0Uqw 2004 04 26.34900 13 28 52.25 -08 54 22.6 22.6g 04HZ78 568 C~0Uqw 2004 04 26.37536 13 28 52.10 -08 54 21.8 22.7g 04HZ78 568 C~0Uqw 2004 04 27.32206 13 28 47.03 -08 53 56.6 22.8g 04HZ78 568 C~0Uqw 2004 06 20.26453 13 25 22.41 -08 38 21.2 22.4i 04HZ78 568 C~0Uqw 2004 06 20.31329 13 25 22.32 -08 38 21.0 22.7i 04HZ78 568 C~0Uqw 2004 06 20.36533 13 25 22.24 -08 38 20.6 22.9i 04HZ78 568 C~0Uqw 2006 05 01.38069 13 41 17.19 -11 03 12.2 22.7r 04HZ78 568 C~0Uqw 2006 05 01.38265 13 41 17.18 -11 03 12.4 22.5r 04HZ78 568 C~0Uqw 2006 05 01.41109 13 41 17.02 -11 03 11.4 22.5r 04HZ78 568 C~0Uqw 2006 05 01.41297 13 41 17.02 -11 03 11.5 22.7r 04HZ78 568 C~0Uqw 2006 05 01.44239 13 41 16.84 -11 03 10.5 04HZ78 568 C~0Uqw 2006 05 01.44432 13 41 16.87 -11 03 10.5 04HZ78 568 C~0Uqw 2006 05 02.31707 13 41 12.16 -11 02 48.0 04HZ78 568 C~0Uqw 2006 06 29.28370 13 37 43.95 -10 46 51.8 22.7r 04HZ78 568 C~0Uqw 2006 06 29.29672 13 37 43.95 -10 46 51.6 23.0r 04HZ78 568 C~0Uqw 2006 06 30.26416 13 37 42.96 -10 46 49.4 22.9r 04HZ78 568 C~0Uqw 2008 06 08.98378 13 51 23.41 -12 59 02.1 04HZ78 807 C~0Uqw 2008 06 09.10509 13 51 22.98 -12 58 59.6 04HZ78 807 C~0Uqw 2016 03 08.298530 14 55 18.099 -21 44 09.59 22.8V 04HZ78 W84 C~98JD 2016 03 08.300594 14 55 18.095 -21 44 09.54 22.9V 04HZ78 W84 C~98JD 2016 03 13.40962 14 55 03.70 -21 44 12.5 22.4R 04HZ78 G37 C~1pPj 2016 03 13.50022 14 55 03.42 -21 44 12.3 04HZ78 G37 C~1pPj 2021 07 08.96952 15 24 08.098 -25 54 41.65 22.7r 04HZ78 269 C~8iQT 2021 07 08.97204 15 24 08.089 -25 54 41.63 23.3g 04HZ78 269 C~8iQT 2021 07 08.97526 15 24 08.078 -25 54 41.56 22.2z 04HZ78 269 C~8iQT 2021 07 08.97801 15 24 08.071 -25 54 41.48 22.4z 04HZ78 269 C~8iQT 2021 07 08.98077 15 24 08.062 -25 54 41.46 22.2z 04HZ78 269 C~8iQT 2021 07 08.98388 15 24 08.050 -25 54 41.39 23.1g 04HZ78 269 C~8iQT 2021 07 08.98644 15 24 08.044 -25 54 41.36 22.7r 04HZ78 269 C~8iQT
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 -0.14
2 0.0001 0.00 0.28 0.00 -0.21
3 0.0001 0.00 0.19 0.00 -0.11
4 0.0027 0.00 0.14 0.00 -0.14
5 0.1504 0.00 0.02 0.00 -0.21
6 0.1505 0.00 -0.11 0.00 -0.22
7 0.1507 0.00 -0.01 0.00 -0.05
8 2.0125 0.00 -0.30 0.00 0.44
9 2.0125 0.00 -0.29 0.00 0.19
10 2.0125 0.00 -0.33 0.00 0.44
11 2.0126 0.00 -0.18 0.00 0.29
12 2.0126 0.00 -0.44 0.00 0.52
13 2.0126 0.00 0.17 0.00 0.46
14 2.0150 0.00 0.01 0.00 0.12
15 2.1737 0.00 0.12 0.00 -0.18
16 2.1738 0.00 0.35 0.00 -0.01
17 2.1764 0.00 0.21 0.00 0.02
18 4.1195 0.00 -0.24 0.00 -0.73
19 4.1199 0.00 -0.42 0.00 -0.14
20 11.8658 0.00 -0.03 0.00 -0.28
21 11.8658 0.00 -0.01 0.00 -0.23
22 11.8798 0.00 0.27 0.00 -0.22
23 11.8800 0.00 0.41 0.00 -0.10
24 17.2009 0.00 -0.04 0.00 0.08
25 17.2009 0.00 -0.05 0.00 0.06
26 17.2010 0.00 -0.06 0.00 0.07
27 17.2010 0.00 -0.03 0.00 0.10
28 17.2010 0.00 -0.02 0.00 0.08
29 17.2010 0.00 -0.05 0.00 0.09
30 17.2010 0.00 -0.01 0.00 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.
04HZ78 quality flag:3 Type: 3:2E 3:2E 3:2E axisobj 39.339 39.339 39.339 ecceobj 0.147 0.147 0.147 incobj 13.347 13.347 13.347 qmin 32.825 32.825 32.831 qmax 46.698 46.737 46.701 amean 39.457 39.457 39.457 amin 38.974 38.975 38.981 amax 39.990 39.989 39.979 emean 0.151 0.151 0.151 emin 0.132 0.132 0.132 emax 0.169 0.169 0.169 imean 12.740 12.738 12.745 imin 12.119 12.119 12.125 imax 13.330 13.330 13.372 excite_mean 0.267 0.267 0.267 fracstop 1.000 1.000 1.000 cjmean 2.970 2.970 2.970 libcent 0 179.9 179.6 180.2 libamp 0 113.0 111.8 111.9 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 179.8 179.6 179.8 kozaiamp 180.0 180.0 179.9