Orbit Fit and Astrometric record for 13XM40

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: 13XM40    
# Created Tue Dec  7 02:12:25 2021
# Orbit generated from Bernstein formalism
# Fitting      7 observations of      7
# Arc:   5.00y
# First observation: 2013/12/02
#  Last observation: 2018/12/01
Preliminary a, adot, b, bdot, g, gdot:
   0.000055   0.026917  -0.000093   0.001741   0.026782   0.000000
# Chi-squared of fit:     1.81 DOF:      8 RMS:  0.09
# Min/Max residuals:    -0.11    0.16
# Exact a, adot, b, bdot, g, gdot:
  1.688010E-05  2.689253E-02  1.564320E-06  1.674291E-03  2.584662E-02  1.464831E-03
# Covariance matrix:
  5.0696E-13 -3.0975E-13  1.2918E-14 -9.0074E-15 -7.0664E-14 -1.5546E-12
 -3.0975E-13  1.8813E-12 -2.8949E-14 -3.5668E-14 -8.2471E-13  1.3688E-11
  1.2918E-14 -2.8949E-14  4.7824E-13 -1.1738E-13 -9.9012E-14 -2.5595E-13
 -9.0074E-15 -3.5668E-14 -1.1738E-13  5.7822E-14  1.6429E-13 -2.1278E-13
 -7.0664E-14 -8.2471E-13 -9.9012E-14  1.6429E-13  2.2181E-12 -5.4862E-12
 -1.5546E-12  1.3688E-11 -2.5595E-13 -2.1278E-13 -5.4862E-12  1.0228E-10
#      lat0       lon0       xBary       yBary       zBary        JD0
  -47.078380   -7.329664   -0.959561   -0.159669   -0.148693  2456628.679478
# Heliocentric elements and errors
Epoch:              2456620.5000  =  2013/11/24
Mean Anomaly:           43.38378 +/-     0.075
Argument of Peri:      222.18032 +/-     0.101
Long of Asc Node:       77.91945 +/-     0.001
Inclination:            47.02840 +/-     0.000
Eccentricity:         0.10471349 +/-    0.0004
Semi-Major Axis:     41.78548201 +/-    0.0147
Time of Perihelion: 2444731.0578 +/-      19.5
Perihelion:          37.40997848 +/-    0.0224
Aphelion:            46.16098553 +/-    0.0244
Period (y)              270.1135 +/-      0.14
# Ecliptic coordinates at JD0 (AU and AU/d)
Ecliptic X           26.47047597 +/-    0.0015
Ecliptic Y           -2.43451251 +/-    0.0002
Ecliptic Z          -28.33200448 +/-    0.0016
Ecliptic XDOT         0.00059090 +/-    0.0000
Ecliptic YDOT         0.00279333 +/-    0.0000
Ecliptic ZDOT         0.00000729 +/-    0.0000
# Distances at JD0 (AU)
Heliocenter to KBO   38.84990897 +/-    0.0016
Geocenter to KBO     38.68977884 +/-    0.0022
# Hcoef:  7.88

The following table shows the complete astrometric record for 13XM40. 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 (13XM40) followed by the observatory code and reference code for the source of the astrometry.

2013 12  02.17870  01 09 34.290  -44 56 39.26  24.2r 13XM40    W84  C~52S3      
2013 12  06.17764  01 09 19.647  -44 52 56.31  24.5g 13XM40    W84  C~52S3      
2013 12  29.11479  01 08 34.737  -44 27 02.51  23.4r 13XM40    W84  C~52S3      
2016 10  06.07523  01 34 59.934  -42 13 30.39  23.9r 13XM40    W84  C~52S3      
2017 10  17.32598  01 39 52.524  -41 14 56.61  23.2r 13XM40    W84  C~52S3      
2018 11  08.25100  01 43 25.728  -40 12 24.12  24.1r 13XM40    W84  C~52S3      
2018 12  01.21567  01 41 19.441  -40 01 42.02  24.4g 13XM40    W84  C~52S3      

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    -0.09       0.00    -0.11
     2   0.0109     -4.97     0.16     271.80     0.12
     3   0.0737    460.40    -0.08    1829.83    -0.04
     4   2.8443  19208.74     0.04   -1861.36     0.14
     5   3.8745  24013.28    -0.03   -1161.60    -0.11
     6   4.9338  28334.76     0.01     214.81    -0.08
     7   4.9967  27611.02    -0.01    1643.62     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.

13XM40    quality flag:3

Type:       SCATEXTD  SCATEXTD  SCATEXTD

axisobj        42.048    42.094    42.001
ecceobj         0.110     0.111     0.108
incobj         47.056    47.056    47.056
qmin           36.598    36.518    36.624
qmax           47.478    47.585    47.316
amean          41.897    41.945    41.849
amin           41.570    41.619    41.509
amax           42.247    42.307    42.197
emean           0.109     0.110     0.107
emin            0.094     0.095     0.094
emax            0.124     0.126     0.122
imean          45.606    45.605    45.607
imin           45.374    45.343    45.362
imax           45.835    45.838    45.837
excite_mean     0.723     0.723     0.723
fracstop        1.000     1.000     1.000
cjmean          2.359     2.359     2.359

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       181.1     181.9     181.5
kozaiamp        180.0     180.0     179.9