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: 13HR156
# Created Fri Apr 26 01:14:34 2024
# Orbit generated from Bernstein formalism
# Fitting 33 observations of 34
# Arc: 4.11y
# First observation: 2013/04/17
# Last observation: 2017/05/26
Preliminary a, adot, b, bdot, g, gdot:
-0.000123 0.027419 -0.000024 0.010205 0.026372 0.000000
# Chi-squared of fit: 13.93 DOF: 60 RMS: 0.11
# Min/Max residuals: -0.33 0.27
# Exact a, adot, b, bdot, g, gdot:
1.625448E-05 2.774052E-02 6.652508E-06 1.030812E-02 2.698279E-02 2.721709E-03
# Covariance matrix:
1.4467E-13 -1.5886E-13 2.4864E-14 -5.2731E-14 1.1684E-14 -1.3354E-12
-1.5886E-13 3.1335E-13 -5.6658E-14 1.2129E-13 2.8098E-14 3.0712E-12
2.4864E-14 -5.6658E-14 1.0042E-13 -6.6548E-14 -3.5387E-15 -6.3754E-13
-5.2731E-14 1.2129E-13 -6.6548E-14 9.3562E-14 9.6804E-15 1.3633E-12
1.1684E-14 2.8098E-14 -3.5387E-15 9.6804E-15 1.0380E-13 2.4419E-13
-1.3354E-12 3.0712E-12 -6.3754E-13 1.3633E-12 2.4419E-13 3.4522E-11
# lat0 lon0 xBary yBary zBary JD0
1.124042 -142.627681 0.171911 0.019454 -0.990697 2456399.964708
# Heliocentric elements and errors
Epoch: 2456390.5000 = 2013/04/08
Mean Anomaly: 22.68698 +/- 0.032
Argument of Peri: 329.87220 +/- 0.052
Long of Asc Node: 214.17138 +/- 0.000
Inclination: 20.43968 +/- 0.000
Eccentricity: 0.18828545 +/- 0.0002
Semi-Major Axis: 45.65865788 +/- 0.0053
Time of Perihelion: 2449288.8830 +/- 10.1
Perihelion: 37.06179706 +/- 0.0087
Aphelion: 54.25551870 +/- 0.0098
Period (y) 308.5268 +/- 0.05
# Ecliptic coordinates at JD0 (AU and AU/d)
Ecliptic X -30.33756175 +/- 0.0004
Ecliptic Y -22.95397386 +/- 0.0003
Ecliptic Z 0.72730530 +/- 0.0000
Ecliptic XDOT 0.00149909 +/- 0.0000
Ecliptic YDOT -0.00239176 +/- 0.0000
Ecliptic ZDOT 0.00105129 +/- 0.0000
# Distances at JD0 (AU)
Heliocenter to KBO 38.04972460 +/- 0.0003
Geocenter to KBO 37.06066473 +/- 0.0004
# Hcoef: 7.87
The following table shows the complete astrometric record for 13HR156. 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 (13HR156) followed by the observatory code and reference code for the source of the astrometry.
2013 04 17.46393 14 21 35.303 -12 54 32.32 23.5r 13HR156 568 C~1XRb 2013 04 19.44191 14 21 25.567 -12 53 30.58 23.3r 13HR156 568 C~1XRb 2013 04 19.49245 14 21 25.307 -12 53 29.02 23.5r 13HR156 568 C~1XRb 2013 04 19.54534 14 21 25.052 -12 53 26.84 13HR156 568 C~1XRb 2013 05 11.47819 14 19 36.179 -12 42 06.01 23.7r 13HR156 568 C~1XRb 2013 05 12.48047 14 19 31.354 -12 41 35.91 23.6r 13HR156 568 C~1XRb 2013 06 12.37556 14 17 24.283 -12 28 12.50 13HR156 568 C~1XRb 2013 06 12.42048 14 17 24.135 -12 28 11.43 23.7r 13HR156 568 C~1XRb 2013 07 04.33511 14 16 34.059 -12 22 20.20 24.0r 13HR156 568 C~1XRb 2013 07 06.34313 14 16 31.601 -12 21 59.09 23.0r 13HR156 568 C~1XRb 2013 08 02.25851 14 16 36.442 -12 20 37.47 24.0r 13HR156 568 C~1XRb 2013 08 05.25929 14 16 41.392 -12 20 51.47 23.9r 13HR156 568 C~1XRb 2014 02 02.65078 14 31 40.877 -13 16 52.66 23.8r 13HR156 568 C~1XRb 2014 02 02.65647 14 31 40.891 -13 16 52.47 23.7r 13HR156 568 C~1XRb 2014 02 03.59530 14 31 41.607 -13 16 47.80 23.8r 13HR156 568 C~1XRb 2014 02 24.59345 14 31 33.538 -13 13 08.04 23.7r 13HR156 568 C~1XRb 2014 02 24.60122 14 31 33.527 -13 13 07.81 23.7r 13HR156 568 C~1XRb 2014 02 25.58427 14 31 32.048 -13 12 52.35 23.8r 13HR156 568 C~1XRb 2014 02 28.53222 14 31 27.044 -13 12 03.02 23.7r 13HR156 568 C~1XRb 2014 04 04.42723 14 29 33.148 -12 58 11.57 23.5r 13HR156 568 C~1XRb 2014 04 04.46649 14 29 32.971 -12 58 10.39 23.4r 13HR156 568 C~1XRb 2014 04 05.42266 14 29 28.744 -12 57 42.95 23.3r 13HR156 568 C~1XRb 2014 05 22.43816 14 25 41.428 -12 34 17.43 23.5r 13HR156 568 C~1XRb 2014 05 25.37427 14 25 28.324 -12 32 58.11 23.9r 13HR156 568 C~1XRb 2014 05 25.37889 14 25 28.299 -12 32 57.71 23.5r 13HR156 568 C~1XRb 2014 05 25.38376 14 25 28.297 -12 32 57.77 24.0r 13HR156 568 C~1XRb 2014 05 25.40152 14 25 28.192 -12 32 57.32 23.7r 13HR156 568 C~1XRb 2014 06 26.34216 14 23 38.893 -12 21 43.83 23.8r 13HR156 568 C~1XRb 2014 07 18.30511 14 23 11.990 -12 18 19.59 23.5r 13HR156 568 C~1XRb 2015 01 26.64799 14 38 14.752 -13 13 22.13 23.7r 13HR156 568 C~1XRb 2016 05 29.36402 14 38 52.426 -12 24 03.93 24.0w 13HR156 568 C~2KOG 2016 06 05.34911 14 38 23.209 -12 21 21.97 23.7w 13HR156 568 C~2KOG 2017 05 26.32046 14 45 55.804 -12 21 00.04 23.9r 13HR156 568 C~2KOG 2017 05 26.38561 14 45 55.508 -12 20 58.39 23.7r 13HR156 568 C~2KOG
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 0.00 0.00 -0.13
2 0.0054 -154.68 0.14 12.22 -0.06
3 0.0056 -158.79 0.07 12.47 -0.10
4 0.0057 -163.02 ( 0.06) 13.32 ( 0.44)
5 0.0657 -1890.47 -0.12 139.07 -0.07
6 0.0685 -1967.03 -0.06 144.49 -0.03
7 0.1531 -3988.23 0.09 295.12 0.02
8 0.1532 -3990.63 0.02 295.42 0.13
9 0.2132 -4799.23 0.03 386.24 -0.08
10 0.2187 -4840.21 0.09 394.33 0.18
11 0.2924 -4800.04 -0.04 494.77 0.15
12 0.3006 -4726.90 -0.28 505.39 -0.13
13 0.7972 8817.20 -0.05 1558.67 -0.00
14 0.7972 8817.34 0.04 1558.91 0.20
15 0.7998 8825.80 -0.09 1566.64 0.18
16 0.8573 8644.48 0.10 1738.25 -0.03
17 0.8573 8644.25 0.08 1738.42 0.08
18 0.8600 8618.84 0.10 1746.29 0.01
19 0.8681 8533.80 0.02 1770.10 0.08
20 0.9636 6689.69 -0.06 2032.94 -0.04
21 0.9637 6686.86 -0.08 2033.23 0.01
22 0.9663 6619.49 0.10 2039.67 -0.17
23 1.0951 3017.26 -0.10 2311.35 -0.17
24 1.1031 2810.05 0.08 2324.95 -0.02
25 1.1031 2809.58 -0.07 2325.21 0.22
26 1.1031 2809.57 0.27 2325.14 0.14
27 1.1032 2807.97 -0.08 2325.07 -0.00
28 1.1906 1075.25 -0.01 2447.83 -0.04
29 1.2508 636.16 -0.03 2513.94 -0.02
30 1.7774 14233.99 -0.28 3557.14 -0.33
31 3.1154 13845.57 0.03 6549.40 -0.03
32 3.1345 13386.20 0.11 6570.82 -0.08
33 4.1064 19742.35 -0.06 8637.74 0.02
34 4.1066 19737.67 0.04 8638.00 0.10
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.
13HR156 quality flag:3 Type: SCATEXTD SCATEXTD SCATEXTD axisobj 45.451 45.467 45.434 ecceobj 0.184 0.184 0.184 incobj 20.470 20.470 20.470 qmin 36.199 36.365 36.213 qmax 55.784 55.650 55.774 amean 45.783 45.783 45.783 amin 45.399 45.374 45.389 amax 46.223 46.245 46.237 emean 0.193 0.193 0.192 emin 0.179 0.181 0.178 emax 0.207 0.204 0.207 imean 21.042 21.033 21.047 imin 20.611 20.706 20.616 imax 21.466 21.359 21.476 excite_mean 0.407 0.407 0.407 fracstop 1.000 1.000 1.000 cjmean 2.916 2.917 2.916 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 168.6 169.0 168.6 kozaiamp 180.0 180.0 180.0