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X.2. Information on new orbital elements

Since the last year's EMP, the number of newly numbered minor planets has increased by 30324. Elements of all numbered minor planets have been determined by IAA. The sets of elements are given for the standard epoch June 27.0, 2014. They were determined as a result of orbit improving on the base of all kinds of optical observations available in the catalog of observations of the Minor Planet Center on March 16, 2014 (radar observations have not been used at this stage). The brief information on the accuracy of each set of elements is given in the Table on p. 10-823. It contains the following data:

1) Number of planet.

2) The number of oppositions with observations used for determination of the orbit.

3) The time interval covered by the observations used for determination of the orbit.

4) The mean-root-square error of observations, expressed in arcsec, with respect to orbits fitted by the least squares.

When estimating these data it is necessary to take into consideration the following.

1) Corrections to the initial sets of elements were determined by the least square fit of weighted conditional equations. In so doing, the observations made before 1901 were assigned weight equal to 1/16, the observations made during the time interval from 1901 to 1950 were assigned weight equal to 1/9, the observations made during the time interval from 1951 to 1995 were assigned weight equal to 1/4, and at last the observations starting from 1996 were considered as having unit weight.

2) Observations of only standard accuracy were used for orbit improvement.

3) Observations in right ascension and in declination were considered as independent, so that conditional equation, e.g. in right ascension, could be excluded by "the three sigma; criterion" from solution whereas equation in declination could be used or vice versa.

4) Observation is considered as used, if both conditional equations in right ascension and in declination or at least one of them are used for finding solution.

5) The mean-root-square error of observations, given in column 4 of the Table was computed by the formula

σ= √[(∑((αo − αc)cosδ)2+∑(δo−δc)2)/(l+m+6)]

where 'l' is the number of equations in right ascension and 'm' is that of in declination.

Note that weights appearing in the conditional equations are not used in the above formula.

In the Table below the brief information on the accuracy of orbital elements which are publishing in EMP-2015 is correlated with corresponding information on the accuracy of orbital elements included in minor planet orbit file maintained by Minor Planet Center. For different intervals of σ value the Table gives number of sets of elements, determined with mean errors that fall in the indicated limits.


  Interval of σ     Number of sets     Percent                    Number of sets    Percent                              within interval     of the total              within interval     of the total                                            EMP orbits                                        MPC orbits               σ ≥ 1.0''        10                    0.003                               87                  0.02     0.9''≤ σ < 1.0''         21                   0.006                               35                  0.01     0.8''≤ σ < 0.9''         141                 0.04                                 84                  0.02     0.7''≤ σ < 0.8''         1379               0.38                                 417                0.12     0.6''≤ σ < 0.7''         24996             6.94                                 8413              2.34     0.5''≤ σ < 0.6''         137059         38.05                                 170889        47.44     0.4''≤ σ < 0.5''         112864         31.34                                 139758        38.80     0.3''≤ σ < 0.4''         80687           22.40                                 60244          16.73     0.2''≤ σ < 0.3''         32278             8.96                                 10461            2.90     0.1''≤ σ < 0.2''         1065               0.30                                 126                0.04               σ < 0.1''        14                    0.004                               0                    0.00  

These data show that quality of improvement of new sets is in general good. At least, 63.0% the EMP orbits have σ < 0.5'' , as compared with 58.5% of MPC orbits. True, in the more wide interval σ < 0.8" the MPC orbits and EMP orbits are presented approximately in equal amounts for the expense of more dense concentration of MPC orbits within interval 0.4" ≤ σ < 0.6".

The estimation of precision of new systems would not be complete without comparing the number of observations actually used for determining orbits. As the MPC orbits do not all were improved simultaneously with EMP orbits, only 383866 sets of elements were used for data comparison (for selected sets of elements process of improvement had started with the use of the same observations). From this number of orbits in 53253 cases the number of actually used observations was equal both for EMP and MPC orbits. In 314931 cases the number of observations used for determination of EMP orbits proves to be greater than that of used for MPC orbits and only in 15862 cases MPC orbits have been found from greater number of observations. It can be added that 5386 EMP orbits were determined on longer time interval at the expense of usage of more earlier observations.