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Astron. Astrophys. 318, 631-638 (1997) 3. Magnitudes3.1. Determination and accuracy of apparent magnitudesA complete description of the apparent magnitude calculation can be found in L95; here we present the main features. The apparent magnitudes were estimated by assigning one of eight brightness classes to each object while performing the astrometric measurements. A linear data fit between the magnitude estimates and the ephemeris V -magnitudes of the observed numbered objects was used to derive magnitudes for all the UESAC objects. This analysis was performed separately for the 1992 and 1993 objects. The magnitudes were corrected for trailing using the trail-correction equation: (Tancredi and Lindgren 1994) where l is the trail length, d the size of the seeing disk and erf the error function. We define the mean errors for the V -magnitudes as the mean
difference between the magnitudes of the numbered asteroids derived
from the above analysis and the corresponding ephemeris values. These
errors are only valid for Table 4. Mean apparent magnitude differences (ephemeris minus UESAC) for the numbered asteroids included in the data fit. 3.2. Statistics of apparent magnitudesThe following statistics are based on the UESAC March magnitudes;
the magnitudes for the unlinked April positions are not included. A
mean magnitude was used for each discrete object, so no asteroid
should therefore appear more than once in the statistics. The PLS
numbers are based on asteroids with a determined orbit. Since the
regions investigated by PLS and UESAC differ both in size and centre
coordinates, the PLS numbers (van Houten et al. 1970) have been
multiplied by a factor of 1.08 (L95). The PLS m -magnitudes
(International Photometric Magnitude System) were transformed to
V -magnitudes (L95). Fig. 1 shows the cumulative number of
asteroids per half magnitude step, starting from
The linear parts of the curves can be represented by expressions of the form: The expressions are based on points in the interval
3.3. Determination and accuracy of absolute magnitudesThe calculation of the absolute magnitudes was done according to the HG -system (Bowell et al. 1989); a thorough description can be found in L95. We define the mean errors for the absolute magnitudes as the mean
differences between the H -magnitudes of the observed numbered
asteroids and the corresponding EMP/MPC H -magnitudes (EMP =
Efemeridy Malykh Planet/Ephemerides of Minor Planets, MPC =
Minor Planet Circulars). Table 5 gives the mean
differences (ephemeris minus UESAC) for the 1992 and 1993 observing
campaigns separately. The number of numbered asteroids included in the
analysis is Table 5. Mean absolute magnitude differences (ephemeris minus UESAC) for the observed numbered asteroids 3.4. Statistics of absolute magnitudesThe statistics in this section are based on H -magnitudes for UESAC and PLS asteroids with determined orbits. Fig. 2 shows the logarithm of the cumulative numbers of absolute magnitudes per 0.25-magnitude step in UESAC'92, UESAC'93 and PLS. The PLS H -magnitudes are taken from EMP/MPC files and not from the values given in van Houten et al. (1970). As a result of differences in the survey coverage the PLS numbers have been multiplied by 0.90 (L95).
The linear parts of the curves can be represented by expressions of the form: The expressions are based on points in the interval
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