Astron. Astrophys. 318, 631-638 (1997)

## 3. Magnitudes

### 3.1. Determination and accuracy of apparent magnitudes

A 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 , since most of the numbered asteroids included in the fits are brighter than this value. Table 4 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 and the standard deviations for the errors with regard to sign are also given.

Table 4. Mean apparent magnitude differences (ephemeris minus UESAC) for the numbered asteroids included in the data fit.

### 3.2. Statistics of apparent magnitudes

The 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 , for UESAC'92, UESAC'93 and PLS asteroids. The PLS numbers in the interval were corrected for incompleteness (van Houten et al. 1970). The somewhat peculiar V -magnitude intervals are a result of the fact that the PLS numbers were given as number of asteroids per half m -magnitude.

 Fig. 1. The logarithm of the cumulative number of asteroids per half-magnitude step for UESAC'92, UESAC'93 and PLS.

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 magnitudes

The 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 and the standard deviations for the errors with regard to sign are also given. For some numbered asteroids an orbit could not be calculated based on the UESAC observations; these asteroids have therefore been excluded from the error analysis. The errors with regard to sign are not significant.

Table 5. Mean absolute magnitude differences (ephemeris minus UESAC) for the observed numbered asteroids

### 3.4. Statistics of absolute magnitudes

The 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).

 Fig. 2. The logarithm of the cumulative number of asteroids per 0.25 magnitude for UESAC'92, UESAC'93 and PLS.

The linear parts of the curves can be represented by expressions of the form:

The expressions are based on points in the interval .

© European Southern Observatory (ESO) 1997

Online publication: July 8, 1998