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: 20VK40 # Created Thu Jul 3 01:11:52 2025 # Orbit generated from Bernstein formalism # Fitting 8 observations of 8 # Arc: 1.94d # First observation: 2020/11/09 # Last observation: 2020/11/11 # WARNING Fitting with energy constraint # WARNING and with gdot fixed = 0 # Chi-squared of fit: 0.68 DOF: 12 RMS: 0.05 # Min/Max residuals: -0.11 0.09 # Exact a, adot, b, bdot, g, gdot: 1.183233E-05 1.592888E-02 7.862337E-06 1.103218E-02 2.121040E-02 0.000000E+00 # Covariance matrix: 8.7714E-11 1.1483E-07 -2.9900E-13 -6.1761E-10 2.7867E-08 0.0000E+00 1.1483E-07 1.5134E-04 -3.9296E-10 -8.1310E-07 3.6673E-05 0.0000E+00 -2.9900E-13 -3.9296E-10 3.7327E-13 -1.1501E-10 -9.5311E-11 0.0000E+00 -6.1761E-10 -8.1310E-07 -1.1501E-10 7.7133E-08 -1.9710E-07 0.0000E+00 2.7867E-08 3.6673E-05 -9.5311E-11 -1.9710E-07 8.8909E-06 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 1.2557E-04 # lat0 lon0 xBary yBary zBary JD0 -0.240345 -0.777910 -0.739014 -0.002795 -0.660045 2459162.679571 # Heliocentric elements and errors Epoch: 2459160.5000 = 2020/11/07 Mean Anomaly: 46.21537 +/- 146.634 Argument of Peri: 311.58267 +/- 215.022 Long of Asc Node: 0.44329 +/- 0.388 Inclination: 34.64139 +/- 20.821 Eccentricity: 0.02111692 +/- 0.6053 Semi-Major Axis: 48.51601867 +/- 24.2542 Time of Perihelion: 2443314.8473 +/- 543872.0 Perihelion: 47.49150957 +/- 37.7638 Aphelion: 49.54052777 +/- 38.4161 Period (y) 337.9371 +/- 253.41 # Ecliptic coordinates at JD0 (AU and AU/d) Ecliptic X 47.81823905 +/- 6.6272 Ecliptic Y 0.08415851 +/- 0.0903 Ecliptic Z -0.19746801 +/- 0.0277 Ecliptic XDOT 0.00004102 +/- 0.0014 Ecliptic YDOT 0.00206112 +/- 0.0013 Ecliptic ZDOT 0.00142381 +/- 0.0002 # Distances at JD0 (AU) Heliocenter to KBO 47.81872084 +/- 6.6272 Geocenter to KBO 47.14668389 +/- 6.6279 # Hcoef: 6.91
The following table shows the complete astrometric record for 20VK40. 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 (20VK40) followed by the observatory code and reference code for the source of the astrometry.
2020 11 09.17877 23 57 31.65 -00 31 47.79 20VK40 W84 C~8vMD 2020 11 09.19335 23 57 31.61 -00 31 48.02 20VK40 W84 C~8vMD 2020 11 10.13934 23 57 29.09 -00 31 57.68 20VK40 W84 C~8vMD 2020 11 10.16116 23 57 29.03 -00 31 58.05 23.5i 20VK40 W84 C~8vMD 2020 11 10.16844 23 57 29.01 -00 31 58.09 20VK40 W84 C~8vMD 2020 11 10.17571 23 57 28.99 -00 31 58.18 20VK40 W84 C~8vMD 2020 11 10.18300 23 57 28.97 -00 31 58.33 20VK40 W84 C~8vMD 2020 11 11.11423 23 57 26.54 -00 32 07.38 20VK40 W84 C~8vMD
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 0.07
2 0.0000 -0.64 -0.02 0.03 0.00
3 0.0026 -39.16 0.07 6.20 0.07
4 0.0027 -40.14 -0.00 6.22 -0.06
5 0.0027 -40.43 0.01 6.30 -0.03
6 0.0027 -40.74 -0.01 6.34 -0.04
7 0.0027 -41.07 -0.04 6.32 -0.11
8 0.0053 -78.11 -0.01 12.51 0.09
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.