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

## 5. Orbital elements

The orbital elements for the new UESAC asteroids were calculated at the Minor Planet Center. When dealing with observed arcs of less than seven days, it was often necessary to make some assumption about the orbit in order to get convergence.

For previously observed asteroids, numbered and unnumbered, we have used orbital elements from EMP/MPC files. Elements for all observed numbered and un-numbered asteroids have been included, even if only one or two UESAC positions were available. We divide the elements in three categories: 1) one-opposition elements based on arc-lengths, T, days; 2) one-opposition elements based on days; 3) multi-opposition elements, including the elements for the observed numbered asteroids. The numbers of asteroids in each category are given in Table 7.

Table 7. Number of asteroids in each orbital element category.

### 5.1. Accuracy of the orbital elements

We define the mean error for the one-opposition elements as the mean difference between the elements for the observed numbered asteroids (calculated with UESAC observations) and the elements published in EMP/MPC. Since the element accuracy is dependent on the arc-length covered by the observations we perform the error analysis separately for the element categories 1) and 2). Orbits could be calculated for 159 observed numbered asteroids based on UESAC observations with days. The average differences, EMP/MPC minus survey, at the epoch 1992 March 19.0 TDT (standard epoch in the EMP and MPC versions we used) are:

Orbits could be calculated for 124 observed numbered asteroids based on UESAC observations with time-arcs days. In some cases the arc-lengths were too short to yield reasonable orbits; these asteroids were excluded from the error analysis. No attempt was made to obtain e -assumed orbits. The average differences, EMP/MPC minus survey, at the epoch 1992 March 19.0 TDT are:

### 5.2. Statistics of semimajor axes

The distribution of the semimajor axes for the numbered asteroids show gaps at the points were the asteroid orbital period is commensurable with that of Jupiter's mean distance. This is also true for the UESAC and PLS asteroids; see Fig. 4.

 Fig. 4. Histograms of the semimajor axis for UESAC, PLS and 5297 numbered EMP/MPC asteroids.

The distribution of the semimajor axes for the numbered asteroids does not indicate any great differences between the number of asteroids located in the inner and outer belt. It is important, however, to include only asteroids with sizes larger than a certain completeness threshold. This threshold is obviously higher in the outer belt because the larger heliocentric distances prevents observations of small objects. The thresholds cannot be very well determined since the diameter information for the numbered asteroids is limited. Accurate diameters are not needed in principle; it is more important that all diameters are determined in the same manner and that the diameter distribution is correct. A completeness threshold which is valid for UESAC and PLS asteroids was established. A conservative estimate, based on the deflection from linearity in the diagram (Fig. 3), is 15 km for UESAC and 10 km for PLS. In Fig. 6 all UESAC and PLS asteroids with model-diameters larger than two different sets of thresholds are included. This result tells us that the outer main-belt asteroids are more numerous. We can rule out the possibility that the outer main-belt asteroids are generally larger (a situation which can produce a similar effect) since the result does not change significantly with different thresholds. Also the large numbered asteroids show the same pattern. For main-belt asteroids with absolute magnitudes up to essentially all have been found. This is shown in Fig. 5. However, the majority of the asteroids in the UESAC and PLS surveys have absolute magnitudes above . A possible explanation for the smaller number of asteroids in the inner part of the asteroid belt is that here the mechanism for transforming the orbits into planetcrossing ones is more efficient.

 Fig. 5. Histogram of the semimajor axis for 5297 numbered EMP/MPC asteroids, .
 Fig. 6. Histograms of the semimajor axis for UESAC and PLS asteroids larger than different completness thresholds.

### 5.3. Eccentricities and inclinations

Fig. 7 presents the eccentricities for the UESAC, PLS and 5297 numbered EMP/MPC asteroids (UPE hereafter). The PLS data seem to be slightly biased towards greater eccentricities which may be a result of the larger fraction of PLS asteroids with longitudes of perihelion () aligned with that of Jupiter.

 Fig. 7. Histograms of the eccentricities for UESAC, PLS and 5297 numbered EMP/MPC asteroids.

Fig. 8 presents the inclinations for UPE. The abundance of asteroids with high inclinations is lower for the UESAC and PLS asteroids. This was an expected result since both UESAC and PLS were focusing on a small region of sky close to the ecliptic.

 Fig. 8. Histograms of the inclinations for UESAC, PLS and 5297 numbered EMP/MPC asteroids.

### 5.4. True anomaly and longitude of the perihelion ()

Fig. 9 shows the true anomaly, f, at the mean epoch of the observations for UESAC and PLS. The major part of the PLS asteroids were observed close to perihelion ()

 Fig. 9. True anomaly at the mean epoch of the observations for UESAC'92, UESAC'93 and PLS asteroids.

while the true anomalies for the UESAC asteroids have a much wider distribution. Fig. 10 displays the deviation from Jupiter's longitude of perihelion for UPE. The numbered and PLS asteroids show a clear alignment with Jupiter's perihelion; this is seen to a much lesser degree for the UESAC asteroids. In both campaigns, the ecliptic longitude of the central UESAC region was close to the direction of Jupiter's aphelion. The result is a lower abundance of asteroids aligned with Jupiter since a substantial part of the observed UESAC asteroids are close to perihelion and can thus not have their longitude of perihelia aligned with Jupiters. If we instead plot the deviation from Jupiters longitude of perihelion only for asteroids with diameters large enough to ensure that we have completeness we get the result shown in Fig. 11. Neither asteroids in PLS or UESAC show any alignment with Jupiters longitude of perihelion. For the numbered EMP/MPC asteroids larger than 50 km (adopted completness threshold for the found main-belt asteroids) the alignment can still be seen, although it is less prominent. Could the difference between the larger EMP/MPC asteroids and the UESAC and PLS asteroids larger than the completness thresholds, most of them smaller than , be a difference between large more primordial bodies and small collisional fragments ?

 Fig. 10. Deviation from Jupiter's longitude of perihelion, , for UESAC, PLS and 5297 numbered EMP/MPC asteroids.
 Fig. 11. Deviation from Jupiter's longitude of perihelion, , for UESAC, PLS and 5297 numbered EMP/MPC asteroids larger than certain completeness thresholds.

© European Southern Observatory (ESO) 1997

Online publication: July 8, 1998