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: 21MZ22
# Created Tue Apr 1 01:11:25 2025
# Orbit generated from Bernstein formalism
# Fitting 9 observations of 9
# Arc: 79.96d
# First observation: 2021/06/17
# Last observation: 2021/09/05
Preliminary a, adot, b, bdot, g, gdot:
-0.000000 0.039264 -0.000004 -0.001453 0.027197 0.000000
# WARNING Fitting with energy constraint
# Chi-squared of fit: 0.02 DOF: 13 RMS: 0.01
# Min/Max residuals: -0.01 0.01
# Exact a, adot, b, bdot, g, gdot:
1.596350E-05 2.508032E-02 -9.964150E-07 -1.555278E-03 2.479739E-02 1.582013E-03
# Covariance matrix:
1.5427E-12 1.6663E-09 -4.1248E-13 1.2940E-11 2.7162E-10 -7.9070E-09
1.6663E-09 2.6476E-06 -6.5737E-10 2.0767E-08 4.2833E-07 -1.3155E-05
-4.1248E-13 -6.5737E-10 4.7295E-13 -6.8145E-12 -1.0633E-10 3.2697E-09
1.2940E-11 2.0767E-08 -6.8145E-12 1.8185E-10 3.3583E-09 -1.0348E-07
2.7162E-10 4.2833E-07 -1.0633E-10 3.3583E-09 6.9314E-08 -2.1245E-06
-7.9070E-09 -1.3155E-05 3.2697E-09 -1.0348E-07 -2.1245E-06 6.6157E-05
# lat0 lon0 xBary yBary zBary JD0
1.014566 -72.069717 0.382491 0.016369 -0.936418 2459382.936851
# Heliocentric elements and errors
Epoch: 2459380.5000 = 2021/06/15
Mean Anomaly: 28.79049 +/- 159.210
Argument of Peri: 129.45062 +/- 198.586
Long of Asc Node: 123.08107 +/- 1.006
Inclination: 3.66515 +/- 0.231
Eccentricity: 0.09803009 +/- 0.1184
Semi-Major Axis: 45.02512482 +/- 2.6193
Time of Perihelion: 2450555.2419 +/- 48797.1
Perihelion: 40.61130759 +/- 5.8326
Aphelion: 49.43894205 +/- 6.0588
Period (y) 302.1277 +/- 26.36
# Ecliptic coordinates at JD0 (AU and AU/d)
Ecliptic X 12.34577117 +/- 0.1318
Ecliptic Y -39.37575809 +/- 0.4073
Ecliptic Z 0.71408486 +/- 0.0076
Ecliptic XDOT 0.00269481 +/- 0.0001
Ecliptic YDOT 0.00069063 +/- 0.0009
Ecliptic ZDOT -0.00016878 +/- 0.0000
# Distances at JD0 (AU)
Heliocenter to KBO 41.27200393 +/- 0.3906
Geocenter to KBO 40.32683154 +/- 0.4282
# Hcoef: 8.86
The following table shows the complete astrometric record for 21MZ22. 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 (21MZ22) followed by the observatory code and reference code for the source of the astrometry.
2021 06 17.43605 19 17 07.821 -21 13 56.93 25.0r 21MZ22 266 C~6Ip5 2021 06 17.50053 19 17 07.513 -21 13 57.52 25.0r 21MZ22 266 C~6Ip5 2021 06 17.57953 19 17 07.135 -21 13 58.22 25.0r 21MZ22 266 C~6Ip5 2021 07 05.35106 19 15 39.245 -21 16 49.09 24.6r 21MZ22 266 C~6Ip5 2021 07 05.43951 19 15 38.785 -21 16 49.99 24.6r 21MZ22 266 C~6Ip5 2021 07 05.52517 19 15 38.339 -21 16 50.84 24.6r 21MZ22 266 C~6Ip5 2021 09 05.23105 19 11 17.068 -21 26 05.76 25.2r 21MZ22 266 C~6Ip5 2021 09 05.31314 19 11 16.868 -21 26 06.26 25.2r 21MZ22 266 C~6Ip5 2021 09 05.39641 19 11 16.667 -21 26 06.75 25.2r 21MZ22 266 C~6Ip5
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 0.00
2 0.0002 -4.35 0.00 -0.02 -0.00
3 0.0004 -9.68 -0.01 -0.02 -0.00
4 0.0490 -1250.14 -0.00 -9.45 -0.00
5 0.0493 -1256.63 0.00 -9.51 0.00
6 0.0495 -1262.92 0.00 -9.55 0.01
7 0.2185 -4954.57 0.01 -101.63 -0.00
8 0.2187 -4957.40 -0.00 -101.78 0.00
9 0.2189 -4960.25 -0.01 -101.92 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.
21MZ22 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