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: 20FR40 # Created Sun Nov 24 02:11:01 2024 # Orbit generated by ELGB # -->Covariance matrix from a Bernstein fit # Fitting 15 observations of 15 # Arc: 21.06y # First observation: 2001/03/17 # Last observation: 2022/04/09 # Chi-squared of fit: 7.79 DOF: 24 RMS: 0.13 # Min/Max residuals: -0.30 0.31 # Exact a, adot, b, bdot, g, gdot: 1.455355E-05 1.973832E-02 1.977435E-07 4.199148E-05 2.072590E-02 9.473046E-03 # Covariance matrix: 7.0554E-13 -1.6168E-13 2.9419E-15 -3.6154E-16 -1.8884E-14 -3.6754E-13 -1.6168E-13 1.8943E-13 7.3035E-14 -2.2359E-15 6.2390E-13 5.1022E-13 2.9419E-15 7.3035E-14 4.7255E-13 -2.3874E-14 3.8630E-13 2.0197E-13 -3.6154E-16 -2.2359E-15 -2.3874E-14 1.6712E-15 -1.2509E-14 -6.2000E-15 -1.8884E-14 6.2390E-13 3.8630E-13 -1.2509E-14 3.1893E-12 1.7226E-12 -3.6754E-13 5.1022E-13 2.0197E-13 -6.2000E-15 1.7226E-12 1.3868E-12 # lat0 lon0 xBary yBary zBary JD0 15.910443 160.514032 -0.288133 0.262054 -0.919901 2451986.021622 # Heliocentric elements and errors Epoch: 2451986.5000 = 2001/03/18 Mean Anomaly: 22.62711 +/- 0.018 Argument of Peri: 12.15992 +/- 0.023 Long of Asc Node: 71.33372 +/- 0.000 Inclination: 15.60582 +/- 0.000 Eccentricity: 0.56441338 +/- 0.0001 Semi-Major Axis: 81.05135089 +/- 0.0452 Time of Perihelion: 2435234.5491 +/- 19.4 Perihelion: 35.30488381 +/- 0.0229 Aphelion: 126.79781797 +/- 0.0716 Period (y) 729.7071 +/- 0.61 # Ecliptic coordinates at JD0 (AU and AU/d) Ecliptic X -44.73684811 +/- 0.0038 Ecliptic Y 15.53004013 +/- 0.0013 Ecliptic Z 13.22669477 +/- 0.0011 Ecliptic XDOT -0.00201117 +/- 0.0000 Ecliptic YDOT -0.00205414 +/- 0.0000 Ecliptic ZDOT 0.00034857 +/- 0.0000 # Distances at JD0 (AU) Heliocenter to KBO 49.16785880 +/- 0.0035 Geocenter to KBO 48.24850340 +/- 0.0042 # Hcoef: 7.76
The following table shows the complete astrometric record for 20FR40. 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 (20FR40) followed by the observatory code and reference code for the source of the astrometry.
2001 03 17.520879 11 13 47.92 +22 16 44.9 24.7V 20FR40 568 C~5fv2 2001 03 17.577882 11 13 47.67 +22 16 45.9 24.2r 20FR40 568 C~5fv2 2006 05 27.348208 11 31 41.00 +20 04 43.3 24.8r 20FR40 568 C~5fv2 2006 05 27.355327 11 31 40.99 +20 04 43.3 24.6r 20FR40 568 C~5fv2 2006 05 27.362415 11 31 40.98 +20 04 43.2 24.6r 20FR40 568 C~5fv2 2020 03 24.37555 12 21 49.504 +14 10 29.07 25.4r 20FR40 568 C~5fv2 2020 03 24.54004 12 21 48.924 +14 10 32.41 25.5r 20FR40 568 C~5fv2 2021 03 17.30517 12 25 06.661 +13 44 33.36 25.5r 20FR40 304 C~5fv2 2021 04 12.16540 12 23 39.163 +13 52 39.64 25.6r 20FR40 304 C~5fv2 2021 04 12.23223 12 23 38.947 +13 52 40.72 25.4r 20FR40 304 C~5fv2 2021 04 13.18383 12 23 35.840 +13 52 54.23 25.4r 20FR40 304 C~5fv2 2022 03 07.31777 12 28 28.268 +13 17 31.77 25.2G 20FR40 304 C~5fv2 2022 03 07.38402 12 28 28.042 +13 17 33.36 25.5G 20FR40 304 C~5fv2 2022 04 08.18797 12 26 42.212 +13 28 36.41 25.5r 20FR40 304 C~5fv2 2022 04 09.14018 12 26 39.048 +13 28 51.56 25.4r 20FR40 304 C~5fv2
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 -0.07
2 0.0002 0.00 -0.10 0.00 -0.16
3 5.1932 0.00 0.06 0.00 0.03
4 5.1932 0.00 -0.01 0.00 0.14
5 5.1933 0.00 -0.09 0.00 0.16
6 19.0195 0.00 0.31 0.00 0.04
7 19.0199 0.00 0.27 0.00 -0.01
8 19.9994 0.00 0.15 0.00 -0.08
9 20.0702 0.00 -0.12 0.00 -0.13
10 20.0704 0.00 -0.02 0.00 -0.00
11 20.0730 0.00 -0.10 0.00 0.13
12 20.9714 0.00 -0.07 0.00 0.02
13 20.9716 0.00 -0.30 0.00 0.01
14 21.0586 0.00 0.06 0.00 -0.06
15 21.0612 0.00 -0.07 0.00 -0.05
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.
20FR40 quality flag:3 Type: SCATNEAR SCATNEAR SCATNEAR axisobj 80.388 80.389 80.387 ecceobj 0.562 0.562 0.562 incobj 15.606 15.606 15.606 qmin 34.061 33.629 34.016 qmax 130.607 131.187 134.100 amean 79.951 79.931 81.676 amin 78.069 76.165 79.235 amax 82.716 83.167 84.478 emean 0.559 0.564 0.568 emin 0.541 0.536 0.551 emax 0.579 0.580 0.587 imean 13.940 13.049 14.110 imin 12.860 11.657 12.849 imax 15.276 14.436 15.610 excite_mean 0.609 0.607 0.618 fracstop 1.000 1.000 1.000 cjmean 2.998 2.998 2.997 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 141.5 140.4 146.6 kozaiamp 180.0 180.0 179.9