4 Results

According to Zappalà & Knezevic (1984), the (AM) method for spin-vector determination allows us to obtain a preliminary indication of the rotational properties of the asteroid. One cannot derive the sense of rotation, and it is pratically impossible to distinguish between two pairs of opposite pole solutions, unless the choice takes into account one's stand on the smaller error or on the better fit with the theoretical plot. Notwithstanding this, we preferred to adopt the simple and fast (AM) method, particularly suitable in the case of a very large number of rotation axis and shape determinations.
Table 2 lists the average solar phase angle, the adopted maximum amplitude and the obtained values of the pole coordinates and of the axes ratios of the asteroids to which it was possible to apply the (AM) method. For many asteroids there are two pairs of solutions and it is usually difficult to reject one pair in favour of the other. When this occurs, the two solutions (the P₁ solution normally has a smaller error than the P₂ one) differ by about $180^{\circ}$ in ecliptic longitude. Since the data do not distinguish between prograde and retrograde rotation about the same axis, every tabulated solution has a symmetric one with equal probability, which is not reported in the table. The choice between the prograde or the retrograde reported solution was made according to the solution given by the computation program. For some asteroids we obtain errors of the order 1 or 2 degrees that, compared to the few data from which the solution was obtained, appear reasonably low.
A comparison between the values found by us and the ones by other authors, mainly computed by different methods, shows a certain agreement.

8 Flora

Even if the literature provides many lightcurves, we utilized one value of A by Ahmad (1954); van Houten et al. (1958); Veverka (1971), and Harris & Young (1989) and two by Di Martino et al. (1989), the only ones showing sure values of the amplitude and giving the magnitude V at the maximum of the lightcurve, necessary to apply the (AM) method. Among the existing solutions of this puzzling asteroid the values by Gehrels & Owings (1962), by Zappalà et al. (1983b) and Hollis et al. (1987) give partial solutions. A complete solution is given by Di Martino et al. (1989) and De Angelis (1995). All the solutions are in good agreement with that given by us.

10 Hygiea

To compute the pole coordinate and shape, 8 values of the amplitude, well distributed in longitude, were utilized. Our results are in agreement with the previous ones found by Michalowski et al. (1991); Erikson & Magnusson (1993) and Michalowski (1993), except for one solution, having the same longitude, but the $\beta_{0}$ value negative. Magnusson (1996) reports synthesis values, with an error of $\pm10^{\circ}$, that differ from ours by the sign of the latitude of the P₁ solution.

14 Irene

The available six values of the amplitude A present an absence in correspondence with the longitude of the maximum. The only solution found in literature comes from Bel'skaya et al. (1993) who reported only two values of the longitude with one that differs from the solution found by us.

19 Fortuna

The $(A-\lambda)$ plot of this asteroid too, even if with many determinations of the amplitude, presents few values at the maximum. Hansen (1977); Morrison (1977) and Lupishko et al. (1985) classify 19 Fortuna as a prograde asteroid. Our values of the pole coordinates and of the axes ratios substantially agree with the ones computed with different methods by Drummond et al. (1988, 1991); Magnusson (1990) and De Angelis (1995). Only our a/b value is a little greater than the other ones. This discrepancy probably results from the overestimated extrema of the theoretical $(A-\lambda)$ plot.

  

Table 2: Asteroids to which it was possible to apply the (A-M) method. In the columns from left to right, the name of the asteroids, the average solar phase angle, the adopted maximum amplitude, the coordinates of the pole and the axes ratios are reported. When the computation method gives two pairs of solutions, the P₁ solution normally has a smaller error than the P₂ one. According to the (AM) method that always gives pairs of opposite solutions, every tabulated solution has a symmetric solution with equal probability

69 Esperia

The five values found in literature are well distributed in longitude but show little variations in amplitude. Our pole coordinates differ from those by Velichko et al. (1989) and De Angelis & Mottola (1995), which are themselves in disagreement. The only existing axes ratio, reported by De Angelis & Mottola (1995), agrees with those found by us. Krugly & Velichko (1992) and Magnusson (1996) indicate that 69 Esperia is a prograde rotator.

115 Thyra

The four amplitude determinations, available for the $(A-\lambda)$ plot, are distributed in longitude only in an interval of $100^{\circ}$. The only value, among those found by us, that agrees with the existing ones published by Dotto et al. (1995), is a longitude value $\lambda_{0}$.

121 Hermione

The available A values of the amplitude are well distributed in longitude. The only value of our solution that agrees with those existing in the literature, reported by De Angelis (1995), is the value of the pole latitude $\beta_{0}$.

196 Philomela

The four amplitude determinations utilized to build the $(A-\lambda)$ plot provide well determined extrema and one solution. The existing determinations by Michalowski (1992, 1993); Licandro et al. (1994); De Angelis (1995) and Magnusson (1996), substantially agree with the values of our solution. Except for De Angelis (1995), the other authors obtained two pole solutions that differ by about $180^{\circ}$. The values of the axes ratios are also consistent with ours.

334 Chicago

The six lightcurves utilized to obtain the A values are not well distributed in longitude. We obtain two solutions that both differ from the one by Michalowski (1993), the only one found in the literature. The $\lambda_{0}$values of both solutions found by us are the only ones that agree with the solution by Michalowski (1993).

389 Industria

The $(A-\lambda)$ plot was built with only three determinations of the amplitude. The solution found by us is consistent with one of the two solutions published by Michalowski (1993).

624 Hektor

The A determinations taken from 10 lightcurves are well distributed in longitude. For this well studied asteroid, 11 authors reported pole coordinates and axes ratios values. We obtain two solutions substantially in agreement with those already published and whose mean value was reported by Magnusson (1996).

Of the other 19 objects no previous determination of rotation axis direction and shape has been found in the literature. To the greater part of these minor planets the (AM) method was applied at the minimum conditions of applicability: only with three amplitude determinations but well distributed in longitude. Nevertheless the use of the (AM) method in critical conditions of applicability does not necessarily mean that the results obtained are unreliable. Also to many of the presented asteroids, for which previous determinations exist in the literature, the (AM) method was applied with only three values of the amplitude, obtaining values in accordance with those already known.
The presented results are the first step in our research program. Even if they are in a preliminary form, we wish to publish them to permit their immediate use. The research continues with dedicated observational campaigns and search in the literature for new published data.

Acknowledgements

The authors would like to thank Ms. D. Recupero for editing this note. Special thanks are due to M. Di Martino and A. Cellino for the many and helpful discussions. The work was partially supported by grant ASI-92-RS-78 from the Italian Space Agency.