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For reliable estimation of the accuracy of asteroid CCD observations we usually consider from ten or more various NUMBERED MINOR PLANETS (NMPs) observed during several nigths per month (more then 50 positions). We are sure that the errors of theory of NMP motion are more less then observational errors of their modern CCD observations. We have our EPOS Software package for exact asteroid ephemeris calculations with a full account for perturbation. It is important also that one night of observations ought to have three or more positions of the NMP for calculation of the "internal" accuracy (a symbol "int" in the Tables) and we use several close nights of observations of the same NMP for deriving the "external" accuracy (a symbol "ext" in the Tables).
The main idea of our method of estimation of an accuracy of asteroid observations is to use these (O-C) deviations when we calculate the mean value of (O-C) and its mean error for the considered NMP. The (O-C) values may be very different for various NMPs, but their mean error shows a reliability of "Atmosphere + Telescope + CCD matrix + Catalogue" system at the mean observational conditions. They can be considered as an indicator of accuracy of the CCD positional observations with given MPC code. We get a set of such mean errors derived from all NMPs observed at the given observatory during investigated observational period and then we calculate a total average value for this set of the "Mean error of single observation". This average value is an accuracy of the investigated CCD observations. Of course, we must have a lot of NMP observations in the set for each observatory under consideration.
Table 1.
Observations with normal values of the "Mean error of single observation"
-----------------------------------------------------------------------------
NMP Code Dynamical Time RA (O-C) DEC (O-C) V z
-----------------------------------------------------------------------------
3907 761 1998 08 24.383673 3 17 44.739 0.28 +30 46 00.84 -0.08 15.8 18
3907 761 1998 08 24.409133 3 17 46.152 0.28 +30 46 10.85 0.12 15.8 11
3907 761 1998 08 25.392523 3 18 40.107 0.33 +30 52 27.69 0.04 15.4 15
Total mean value of 3 observations 0.297+-0.017 0.027+-0.058
Mean error of single observation 0.029 0.101
===== =====
COMMENT. There are two neighbour nights of CCD observations. For any NUMBERED minor planet the (O-C) values must be zero if the errors of observations and the errors of its theory are absent. The errors of the theory for usual NUMBERED minor planet during several successive nights are very small, more less then observational errors in this conditions. Therefore, the range of these values due to observational errors may be a good characteristic of the accuracy of observational data. The real meanings of (O-C) may be different but we are investigating namely the range of these values during several close nights, or "Mean error of single observation" in this and other Tables.
Table 2. Observations with the large values of the "Mean error of single observation" ----------------------------------------------------------------------------- NMP Code Dynamical Time RA (O-C) DEC (O-C) V z ----------------------------------------------------------------------------- 3955 761 1998 10 16.163935 0 52 43.326 2.34 + 3 26 20.94 1.62 15.4 27 3955 761 1998 10 16.194495 0 52 41.796 2.68 + 3 26 17.64 1.68 15.2 24 3955 761 1998 10 17.165035 0 51 52.843 5.76 + 3 24 29.44 -0.82 15.5 26 3955 761 1998 10 17.181125 0 51 52.129 7.22 + 3 24 25.54 -3.00 15.2 25 Total mean value of 4 observations 4.500 -0.130 Mean error of single observation 2.378 2.240COMMENT. The large values of (O-C)s may be due to errors of the theory of NMP motion (old orbital unimprovement elements). We take into account not values but their range during one night observations. There are very large (O-C) ranges of RA & DEC for two close nights. Observations are only responsible for these (O-C) changings (from 2.3 in the first night to 7.2 arcsec in the next night for RA and from 1.6 to -3.0 arcsec for DEC).
3955 699 1998 12 15.074492 0 32 36.715 0.73 + 4 27 42.71 0.67 16.3 19
3955 699 1998 12 15.094822 0 32 37.118 1.12 + 4 27 47.90 0.51 17
3955 699 1998 12 15.115212 0 32 37.521 1.49 + 4 27 53.90 1.13 17
-----------------------------------------------------------------------
NORMAL PLACE 3 obs. 15.094842 0 32 37.1184 1.113 + 4 27 48.172 0.770
+/-0.219 +/-0.186
Mean error of single observation 0.380 0.322
RA&DEC velocities and (O-C) 19.791 18.65 274.96 11.25
(per day) (per day)
Relative errors of velocities (%) 6.7 4.3
COMMENT. For each set of spheric coordinates (RA & DEC) obtained during one night we use a linear approximation to calculate a normal place with its accuracy and the first derivatives (dRA/dt & dDEC/dt), i.e the velocities of asteroid's motion (in time seconds per day for RA and arcseconds per day for DEC). The relative errors of these values may additionally characterise an accuracy of CCD observations.
Table 3. (O-C)s for the CCD observations made with MPC code 719
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NMP MPC Dynamical Time RA (O-C) DEC (O-C) V z
code (DT) (geocentr.) (geocentr.)
--------------------------------------------------------------------------------
1615 719 1999 01 23.295214 5 37 23.987 1.01 +21 19 44.10 2.29 15.2 34
1615 719 1999 01 23.359444 5 37 22.481 -0.21 +21 19 45.93 1.48 15.5 53
4150 719 1999 01 23.295214 5 36 58.694 0.79 +21 20 26.01 0.45 16.0 34
4150 719 1999 01 23.359444 5 36 56.569 0.38 +21 20 32.70 1.67 17.1 54
5945 719 1999 01 23.315254 8 20 36.813 0.34 +27 37 45.73 0.30 16.5 6
5945 719 1999 01 23.400954 8 20 30.592 0.61 +27 38 03.31 0.79 17.1 30
COMMENT. The observations with two positions per night do not give us to make a numerical estimation of CCD observations accuracy. The coincidence of the first and the second (O-C)s may show a quality of observations.
Table 4. Examples of typical errors of CCD observations (I - IV)
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NMP Code DT Geocentric positions and their (O-C) Mgn Z
------------------------------------------------------------------------------
I. CRUDE TIME ERROR (*):
31759 683 2001 12 18.369964 8 18 49.392 -0.24 + 3 28 44.53 1.01 18.2 32
31759 683 2001 12 18.381134 8 18 49.021 -1.33 + 3 28 43.62 -0.94 18.5 30
31759 683 2001 12 18.394534 8 18 48.365 -5.82* + 3 28 43.52 -2.29*18.4 29
NORMAL PLACE 3 obs. 18.381877 8 18 48.926 -2.463 + 3 28 43.89 -0.740
+-1.708 +-0.958
Mean error of single observation 2.958** 1.659**
RA&DEC velocities and (O-C) -42.016 -231.16 -39.91 -133.10
Relative errors of velocities (%) 57.9 142.8
COMMENT. The third position of the NMP 31759 have a crude error of UT registration
31759 704 2001 12 19.380534 8 18 21.828 0.98 + 3 30 24.25 0.11 18.0 30
31759 704 2001 12 19.396184 8 18 21.386 0.95 + 3 30 26.35 0.55 18.4 30
31759 704 2001 12 19.411874 8 18 20.924 0.65 + 3 30 27.15 -0.32 18.0 30
31759 704 2001 12 19.427554 8 18 20.481 0.64 + 3 30 28.76 -0.39 18.4 31
31759 704 2001 12 19.443894 8 18 20.010 0.48 + 3 30 30.86 -0.03 18.3 33
NORMAL PLACE 5 obs. 19.412008 8 18 20.926 +0.740!+ 3 30 27.48 -0.016!!
+-0.097 +-0.169
Mean error of single observation 0.216 0.377
RA&DEC velocities and (O-C) -28.724 -8.25 98.89 -7.62
Relative errors of velocities (%) 2.0 7.2
31759 608 2001 12 22.471034 8 16 47.719 -0.68 + 3 36 55.92 1.36 18.7 25
31759 608 2001 12 22.481174 8 16 47.399 -0.52 + 3 36 57.32 1.27 18.6 23
31759 608 2001 12 22.491744 8 16 47.050 -0.57 + 3 36 58.51 0.91 18.7 20
NORMAL PLACE 3 obs. 22.481317 8 16 47.389 -0.590!+ 3 36 57.25 +1.180!!
+-0.047 +-0.137
Mean error of single observation 0.082 0.238
RA&DEC velocities and (O-C) -32.341 5.07 124.93 -21.85
Relative errors of velocities (%) 1.0 14.9
COMMENT. Symbols (!) and (!!) may point out the errors connected with various reference star systems taken into consideration by astrometric reduction in two different observatories.
19713 704 2002 01 11.352004 9 36 47.506 -6.76 +10 49 43.97 5.80 18.2 26
19713 704 2002 01 11.367104 9 36 47.117 -6.02 +10 49 46.06 5.06 18.3 24
19713 704 2002 01 11.382204 9 36 46.679 -6.00 +10 49 49.76 5.92 18.9 22
19713 704 2002 01 11.397304 9 36 46.150 -7.30 +10 49 52.56 5.88 18.1 22
NORMAL PLACE 4 obs. 11.374654 9 36 46.863 -6.520 +10 49 48.09 5.665
+-0.314 +-0.203
Mean error of single observation 0.629 0.406
RA&DEC velocities and (O-C) -29.840 -10.64 194.99 7.32
Relative errors of velocities (%) 2.4 3.9
19713 704 2002 01 13.383044 9 35 46.539 0.71 +10 56 12.76 -1.24 17.8 22
19713 704 2002 01 13.398254 9 35 46.011 -0.03 +10 56 13.46 -3.61 18.9 23
19713 704 2002 01 13.413444 9 35 45.542 0.11 +10 56 15.37 -4.78 19.4 24
NORMAL PLACE 3 obs. 13.398247 9 35 46.030 0.263 +10 56 13.87 -3.210
+-0.227 +-1.041
Mean error of single observation 0.393 1.804
RA&DEC velocities and (O-C) -32.778 -20.14 85.88 116.42
Relative errors of velocities (%) 4.3 57.5
19713 704 2002 01 19.415624 9 32 17.813 -0.23 +11 18 35.70 -1.24 18.3 27
19713 704 2002 01 19.430774 9 32 17.294 0.51 +11 18 39.13 -1.49 18.3 31
19713 704 2002 01 19.445934 9 32 16.654 -0.52 +11 18 43.05 -1.23 18.9 34
NORMAL PLACE 3 obs. 19.430777 9 32 17.254 -0.080 +11 18 39.29 -1.320
+-0.307 +-0.085
Mean error of single observation 0.531 0.147
RA&DEC velocities and (O-C) -38.245 -9.95 242.56 0.50
Relative errors of velocities (%) 1.8 0.2
19713 644 2002 01 26.408114 9 27 34.965 0.19 +11 49 03.45 -0.12 17.5 24
19713 644 2002 01 26.418664 9 27 34.501 0.03 +11 49 06.16 -0.35 17.3 26
19713 644 2002 01 26.429074 9 27 34.076 0.36 +11 49 09.08 -0.33 17.3 28
NORMAL PLACE 3 obs. 26.418617 9 27 34.514 0.193 +11 49 06.23 -0.267
+-0.095 +-0.074
Mean error of single observation 0.165 0.127
RA&DEC velocities and (O-C) -42.454 8.47 268.49 -10.15
Relative errors of velocities (%) 1.3 3.6
IV. AN EXAMPLE OF POSSIBLE INFLUENCE OF ATMOSPHERIC TURBULENCE:
19480 644 2002 01 13.534954 10 17 33.722 0.19 - 0 25 09.12 -0.51 17.1 46
13.536094 33.684 -0.12 07.32 1.25 17.1 46
19480 644 2002 01 13.545524 10 17 33.558 0.15 - 0 25 09.02 -0.71 17.1 48
13.546674 33.520 -0.16 07.02 1.26 17.0 49
19480 644 2002 01 13.556384 10 17 33.403 0.33 - 0 25 08.52 -0.52 17.1 51
13.557534 33.355 -0.14 06.72 1.25 17.0 51
NORMAL PLACE 6 obs. 13.546194 10 17 33.540 0.042 - 0 25 07.95 0.337
+-0.085 +-0.411
Mean error of single observation 0.208 1.007
RA&DEC velocities and (O-C) -15.204 1.33 34.76 6.50
Relative errors of velocities (%) 0.6 23.0
COMMENT. A changing mark from (+) to (-) may be explaned by very short time interval between two neighbourhood exposures, near 0.001 day or 1.4 min, if atmospheric turbulence was large.
Table 5. (O-C) residuals for CCD observations made by Blanco Telescope in 2000 ------------------------------------------------------------------------------ NMP Code DT Geocentric positions and their (O-C) Mgn Z ------------------------------------------------------------------------------ 355 807 2000 08 25.061526 21 13 18.279 -0.15 -19 41 42.75 -0.23 15.1 59 355 807 2000 08 25.124136 21 13 14.932 -0.63 -19 41 50.33 -0.06 50 355 807 2000 08 26.043236 21 12 26.676 -0.36 -19 43 41.43 -0.07 15.6 62 355 807 2000 08 26.110266 21 12 23.192 -0.23 -19 43 49.25 0.01 51 Total mean value of 4 observations -0.343+-.105 -0.088+-.051 Mean error of single observation 0.210 0.101 2884 807 2000 07 31.337196 22 38 57.746 -0.07 -11 27 37.89 0.33 16.1 45 2884 807 2000 07 31.417086 22 38 55.368 0.16 -11 27 53.99 0.38 62 2884 807 2000 08 27.133756 22 20 41.339 -0.59 -13 16 20.86 -0.03 16.2 48 2884 807 2000 08 27.205096 22 20 37.967 -0.62 -13 16 38.90 -0.06 43 Total mean value of 4 observations -0.280+-.194 0.155+-.116 Mean error of single observation 0.387 0.232 4434 807 2000 08 25.310056 23 42 57.209 0.18 - 1 36 09.34 -0.39 15.6 36 4434 807 2000 08 25.367456 23 42 55.384 0.12 - 1 36 34.27 -0.30 49 4434 807 2000 08 26.315236 23 42 24.641 -0.08 - 1 43 32.64 -0.42 16.1 37 4434 807 2000 08 26.387316 23 42 22.290 0.45 - 1 44 04.39 0.03 55 Total mean value of 4 observations 0.167+-.109 -0.270+-.103 Mean error of single observation 0.219 0.206 5219 807 2000 08 26.178286 22 14 05.649 -0.02 -14 03 05.14 0.19 16.9 44 5219 807 2000 08 26.232106 22 14 03.224 -0.13 -14 03 18.06 0.19 45 5219 807 2000 08 27.124556 22 13 23.170 -0.32 -14 06 51.30 0.02 16.6 49 5219 807 2000 08 27.194696 22 13 20.017 -0.48 -14 07 07.93 0.05 44 Total mean value of 4 observations -0.237+-.102 0.113+-.045 Mean error of single observation 0.204 0.090 10298 807 2000 08 26.984296 19 48 59.496 0.20 -21 43 14.48 -0.22 17.1 63 10298 807 2000 08 27.049606 19 48 58.031 0.29 -21 43 21.38 -0.17 53 10298 807 2000 08 27.986296 19 48 37.694 0.21 -21 44 58.64 -0.11 17.2 62 10298 807 2000 08 27.998716 19 48 37.435 0.21 -21 44 59.87 -0.08 60 Total mean value of 4 observations 0.227+-.021 -0.145+-.031 Mean error of single observation 0.042 0.062 15954 807 2000 07 29.236676 21 25 31.931 0.03 -19 58 27.83 -0.46 16.3 49 15954 807 2000 07 29.349856 21 25 26.565 0.04 -19 59 11.31 -0.42 63 15954 807 2000 08 01.279616 21 23 04.788 -0.35 -20 17 54.89 -0.54 16.2 53 15954 807 2000 08 01.356226 21 23 01.020 -0.31 -20 18 24.11 -0.51 67 Total mean value of 4 observations -0.147+-.106 -0.482+-.027 Mean error of single observation 0.211 0.053 16422 807 2000 07 30.257726 21 47 17.021 0.19 -10 47 42.75 -0.04 17.6 40 16422 807 2000 07 30.367456 21 47 11.849 0.27 -10 48 23.81 0.00 57 16422 807 2000 08 28.043556 21 21 23.581 0.15 -14 11 52.44 -0.13 17.9 58 16422 807 2000 08 28.104826 21 21 20.450 0.09 -14 12 17.99 -0.27 47 Total mean value of 4 observations 0.175+-.038 -0.110+-.060 Mean error of single observation 0.075 0.120 16655 807 2000 07 29.285356 22 17 44.429 0.06 -13 44 15.25 -0.11 17.7 43 16655 807 2000 07 29.393976 22 17 40.363 -0.05 -13 44 54.39 0.04 60 16655 807 2000 08 01.320356 22 15 44.976 -0.39 -14 03 01.62 -0.28 17.7 48 16655 807 2000 08 01.395346 22 15 41.893 -0.07 -14 03 29.85 0.01 63 Total mean value of 4 observations -0.113+-.097 -0.085+-.073 Mean error of single observation 0.194 0.145 17041 807 2000 07 29.269376 21 58 20.474 0.23 -17 30 40.32 -0.12 17.5 47 17041 807 2000 07 29.378016 21 58 15.242 0.34 -17 31 19.95 -0.20 62 17041 807 2000 08 28.048186 21 29 53.848 0.34 -20 20 28.36 -0.12 17.7 63 17041 807 2000 08 28.109696 21 29 50.407 0.10 -20 20 44.42 -0.31 53 Total mean value of 4 observations 0.253+-.057 -0.188+-.045 Mean error of single observation 0.114 0.090 18163 807 2000 08 26.033866 20 33 41.654 -0.04 -18 59 43.06 -0.09 18.0 58 18163 807 2000 08 26.099186 20 33 38.819 0.06 -19 00 01.14 -0.15 49 18163 807 2000 08 26.995616 20 33 00.348 -0.44 -19 04 05.46 0.02 17.9 65 18163 807 2000 08 27.061566 20 32 57.591 -0.03 -19 04 23.42 -0.15 53 Total mean value of 4 observations -0.112+-.111 -0.092+-.040 Mean error of single observation 0.223 0.080
Table 6. Accuracy of CCD observations made with MPC code 807
(Pulkovo method for estimation of external accuracy
with the use of Table 5 data)
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NMP j Date 2000 Mgn Z Errors
------------------------------------------------------
15954 4 29, 01 08 16.2 58 0.211" 0.053"
16655 4 29, 01 08 17.7 56 0.194 0.145
16422 4 30, 28 08 17.8 50 0.075 0.120
2884 4 31, 27 08 16.2 50 0.387 0.232
355 4 25, 26 08 15.3 56 0.210 0.101
4434 4 25, 26 08 15.8 46 0.219 0.206
5219 4 26, 27 08 16.8 45 0.204 0.090
18163 4 26, 27 08 18.0 55 0.223 0.080
10298 4 27, 28 08 17.2 60 0.042 0.062
17041 4 29, 28 08 17.6 56 0.114 0.090
======================================================
Total 10 40 9 nights 0.188" 0.118"
+/-0.030 0.019
COMMENT. It's a good accuracy for mass professional CCD observations. Our estimation contains an average influence of the system "Atmosphere + Telescope + CCD matrix + Image processing + Astrometric reduction + Star Catalog" in considered period of observations.