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: 20MZ52
# Created Wed Nov 27 02:11:02 2024
# Orbit generated from Bernstein formalism
# Fitting 9 observations of 9
# Arc: 51.97d
# First observation: 2020/06/22
# Last observation: 2020/08/13
Preliminary a, adot, b, bdot, g, gdot:
-0.000001 0.022709 -0.000000 -0.004169 0.022294 0.000000
# WARNING MRQMIN stopped after 13 iterations -- oscilliatory solution
# WARNING Fitting with energy constraint
# WARNING MRQMIN stopped after 13 iterations -- oscilliatory solution
# Chi-squared of fit: 0.09 DOF: 13 RMS: 0.02
# Min/Max residuals: -0.03 0.02
# Exact a, adot, b, bdot, g, gdot:
1.350533E-05 1.843471E-02 -3.195254E-06 -4.205092E-03 2.162814E-02 2.397215E-03
# Covariance matrix:
1.8600E-11 2.5153E-08 -1.5475E-12 1.4180E-10 4.2205E-09 -1.2921E-08
2.5153E-08 3.5026E-05 -2.1630E-09 2.0117E-07 5.8604E-06 -2.4037E-05
-1.5475E-12 -2.1630E-09 3.9143E-13 -1.4392E-11 -3.6166E-10 1.5776E-09
1.4180E-10 2.0117E-07 -1.4392E-11 1.2202E-09 3.3546E-08 -1.8024E-07
4.2205E-09 5.8604E-06 -3.6166E-10 3.3546E-08 9.8103E-07 -3.8381E-06
-1.2921E-08 -2.4037E-05 1.5776E-09 -1.8024E-07 -3.8381E-06 8.4884E-05
# lat0 lon0 xBary yBary zBary JD0
2.024074 -71.860553 0.298972 0.033913 -0.963497 2459022.950281
# Heliocentric elements and errors
Epoch: 2459020.5000 = 2020/06/20
Mean Anomaly: 111.82379 +/- 178.297
Argument of Peri: 45.86469 +/- 142.391
Long of Asc Node: 116.45111 +/- 2.761
Inclination: 12.93026 +/- 3.983
Eccentricity: 0.13523960 +/- 0.5141
Semi-Major Axis: 44.33548063 +/- 14.5075
Time of Perihelion: 2425527.2509 +/- 50809.7
Perihelion: 38.33956811 +/- 26.0169
Aphelion: 50.33139316 +/- 28.1200
Period (y) 295.2129 +/- 144.90
# Ecliptic coordinates at JD0 (AU and AU/d)
Ecliptic X 14.40758114 +/- 0.6586
Ecliptic Y -44.92679890 +/- 2.0110
Ecliptic Z 1.63295825 +/- 0.0748
Ecliptic XDOT 0.00232593 +/- 0.0006
Ecliptic YDOT 0.00042432 +/- 0.0012
Ecliptic ZDOT -0.00052149 +/- 0.0000
# Distances at JD0 (AU)
Heliocenter to KBO 47.20870901 +/- 1.9243
Geocenter to KBO 46.23605799 +/- 2.1174
# Hcoef: 9.52
The following table shows the complete astrometric record for 20MZ52. 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 (20MZ52) followed by the observatory code and reference code for the source of the astrometry.
2020 06 22.44948 19 17 26.899 -20 12 15.23 26.2r 20MZ52 266 C~6c5f 2020 06 22.52092 19 17 26.584 -20 12 15.93 26.2r 20MZ52 266 C~6c5f 2020 06 22.59118 19 17 26.275 -20 12 16.60 26.2r 20MZ52 266 C~6c5f 2020 06 25.44823 19 17 13.797 -20 12 44.80 25.9r 20MZ52 266 C~6c5f 2020 06 25.52513 19 17 13.452 -20 12 45.56 25.9r 20MZ52 266 C~6c5f 2020 06 25.60088 19 17 13.113 -20 12 46.31 25.9r 20MZ52 266 C~6c5f 2020 08 13.24332 19 13 42.622 -20 21 28.61 26.4r 20MZ52 266 C~6c5f 2020 08 13.33331 19 13 42.286 -20 21 29.55 26.4r 20MZ52 266 C~6c5f 2020 08 13.42301 19 13 41.952 -20 21 30.47 26.4r 20MZ52 266 C~6c5f
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 -0.01 0.00 0.02
2 0.0002 -4.49 -0.00 -0.11 0.02
3 0.0004 -8.89 0.00 -0.20 0.02
4 0.0082 -186.72 0.01 -5.00 -0.02
5 0.0084 -191.63 0.01 -5.12 -0.02
6 0.0086 -196.46 0.00 -5.23 -0.03
7 0.1418 -3200.88 0.02 -141.18 -0.00
8 0.1421 -3205.69 -0.00 -141.51 0.00
9 0.1423 -3210.47 -0.01 -141.83 0.00
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.
20MZ52 quality flag:0 Type: ERR2LARGE ERR2LARGE ERR2LARGE axisobj 0.000 0.000 0.000 ecceobj -1.000 -1.000 -1.000 incobj -1.000 -1.000 -1.000 qmin 0.000 0.000 0.000 qmax 0.000 0.000 0.000 amean 0.000 0.000 0.000 amin 0.000 0.000 0.000 amax 0.000 0.000 0.000 emean 0.000 0.000 0.000 emin 0.000 0.000 0.000 emax 0.000 0.000 0.000 imean 0.000 0.000 0.000 imin 0.000 0.000 0.000 imax 0.000 0.000 0.000 excite_mean 0.000 0.000 0.000 fracstop 0.000 0.000 0.000 cjmean 0.000 0.000 0.000 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 0.0 0.0 0.0 kozaiamp 0.0 0.0 0.0