3 Discussion

In this section we present the first lightcurves in the literature for six asteroids. These are 1089 Tama, 1452 Hunnia, 2415 Ganesa, 9262, 1989 UR and 1998 FM5. Three minor planets in our programme (792, 1508, 1865) have been observed in one previous opposition. Therefore, no models can be derived for them, as modelling requires at least three well-observed oppositions. 1727 Mette have been observed in a third opposition in order to determine a model for its shape and rotation. Earlier measurements are summarized in Table 3. Based on these data, models are determined with an AM-method described in Michaowski (1993). The individual remarks are as follows.

792 Metcalfia

It was discovered by Metcalf in Taunton, on March 21, 1907. Previous measurements are from two nights in 1979, when Carlsson & Lagerkvist (1981) took 186 data points. They measured an amplitude of 0.64 mag and sinodic period of 9$.\!\!^{\rm h}$17.

  

Table 2: The comparison stars. The typical uncertainty in the magnitude values is as large as $\pm~0.2-0.3$ mag

In 1998, the observed amplitude in R was $0.76~\pm~0.02$ mag, while its period turned out to be 9$.\!\!^{\rm h}$$19~\pm~0$$.\!\!^{\rm h}$01. This result is based on 79 data points obtained on three nights. The newly obtained rotational period is in good agreement with the earlier determination of 9$.\!\!^{\rm h}$17 (Carlsson & Lagerkvist 1981). The zero phase of the presented composite diagram (Fig. 1) is JD 2451110.2050.

  

Figure 1: The composite R lightcurve of 792 (symbols: open squares - October 22; dotted circles - October 23; solid circles - October 26)

1089 Tama

It was discovered in 1927 by Oikawa. This asteroid is rather small; the assumed diameter is only $14.1~\pm~0.8$ km. The observed unfiltered amplitude is extremely low, only 0.025 mag, while the sinodical period is longer than 4 hours. The lightcurve is plotted in Fig. 2.

  

Figure 2: The unfiltered lightcurve of 1089 on April 4/5, 1998

1452 Hunnia

This asteroid was discovered by Kulin in 1938. No previous lightcurve has been found in the literature. 1452 was observed on February 28 and March 1, 1998 (Fig. 3). The unfiltered total amplitude was $\geq0.34~\pm~0.05$ mag.

The relative magnitudes were calculated in respect to the same comparison star, which enables a direct comparison of the lightcurves. Two minima of different magnitudes were observed. The brightness difference is most likely due to the fact that those minima were separated by a half of the rotation. Assuming this, a possible rotational period of $17\hbox{$.\!\!^{\rm h}$}2~\pm~0\hbox{$.\!\!^{\rm h}$}1$ can be derived, although the poor phase coverage does not exclude other probable values.

  

Figure 3: The unfiltered lightcurves of 1452 obtained on February 28 (top) and March 1 (bottom)

1508 Kemi

The minor planet was discovered by Alikoski in Turku, in 1938. Its diameter is 25.9 km. In 1995, 44 data points were measured by Holliday (1995). He determined two possible period of about $11\hbox{$.\!\!^{\rm h}$}36$ or $10\hbox{$.\!\!^{\rm h}$}21$. Our observations do not support these values, as they suggest a possible period of around 9$.\!\!^{\rm h}$$15~\pm~0$$.\!\!^{\rm h}$03. The amplitude was $0.52~\pm~0.01$ mag in R. Unfortunately the time span is fairly short, thus periods determined by Holliday (1995) cannot be either approved nor disapproved. The zero phase of the composite diagram (Fig. 4) is JD 2451113.3458.

  

Figure 4: The composite R lightcurve of 1508 (symbols: dotted circles - October 22; solid circles - October 26)

1604 Tombaugh

This asteroid has been discovered in Flagstaff, 1931, by Lampland. Its diameter is $33.8~\pm~2.0$ km. The minor planet was observed in 1975 (Lagerkvist 1978) and in 1984 (Binzel 1987). New measurements of this minor planet were carried out on January 4 and January 5, 1998. The unfiltered amplitude was $0.17~\pm~0.01$ mag, with 6$.\!\!^{\rm h}$$15~\pm~0$$.\!\!^{\rm h}$02 sinodic period. Lightcurves are plotted in Fig. 5.

  

Figure 5: Unfiltered lightcurve of 1604 (symbols: open squares - January 4; solid circles - January 5)

1727 Mette

This asteriod was discovered in 1965 by Andrews. Its diameter is about 20 kilometers. Previous observations were made in 1986 (Wisniewski & McMillan 1987) and in 1988 (Prokof'eva et al. 1992). Precise lightcurves were presented, so we could model this moderately faint asteroid (13.9 mag during our observing run). Earlier observations are summarized in Table 3.

 

Table 3: Earlier photometric observations in the literature for 1727

 

References: (1) - Wisniewski & McMillan (1987); (2) - Prokof'eva et al. (1992).

The unfiltered amplitude of the light variation was $0.19~\pm~0.01$ mag, with rotational period of 3$.\!\!^{\rm h}$$22~\pm~0$$.\!\!^{\rm h}$02. We have to discuss this determination in details as the previous results for the period (2$.\!\!^{\rm h}$$637~\pm~0$$.\!\!^{\rm h}$004) significantly differ. The longer data sequence from 27 February is close to the cited period (2$.\!\!^{\rm h}$47 vs. 2$.\!\!^{\rm h}$637). The magnitude difference between the starting and ending points is quite high and a very sharp brightness decrease would be needed at the end of the light curve in order to match the phase diagram. Therefore, we accepted the above mentioned period value as it gives much smoother composite diagram as the shorter period does. The composite lightcurve is presented in Fig. 6 (the zero phase is JD 2450872.3320).

This asteroid has been observed in the third opposition, therefore its model could be derived. Based on earlier data, models are determined with an AM-method described in Michaowski (1993). Using the relation between the amplitude and the aspect, we fitted of the pole and the shape. Lacking a long-term lightcurve showing the phase dependence of the amplitude, the m parameter required for correcting the amplitude for zero solar phase (see Eq. (6) in Michaowski 1993) cannot be determined photometrically. Also 1727 was not classified in the IRAS taxonomic system, and consequently, the m parameter cannot be estimated by the approximate relations of Michaowski (1993). We have to note that we used V and unfiltered magnitudes simultaneously, thus our model has to be considered as an approximate one.

The obtained pole coordinates: $\lambda_{\rm p}=126/306~\pm~10^\circ$,$\beta_{\rm p}=56~\pm~15^\circ$. The axis ratios of the fitted ellipsoid: $a/b=1.9~\pm~0.1$, $b/c=1.6~\pm~0.1$.The observed amplitudes versus longitudes with the determined fit is presented in Fig. 7.

  

Figure 6: The composite unfiltered lightcurve of 1727 (symbols: open squares - February 26; solid circles - February 27)

  

Figure 7: The observed amplitudes vs. longitudes with the determined fit for 1727 Mette

1865 Cerberus

This asteroid has one of the largest observed amplitudes among all minor planets. Kohoutek discovered it, and the first photometry including 41 data points was discussed in Harris & Young (1989). Later, Wisniewski et al. (1997) presented the lightcurve of this asteroid. The amplitude is about 2 mag, which may imply a highly elongated shape.

We obtained 158 data points through R filter between October 23 and October 26, 1998. The amplitude in R was $2.3~\pm~0.1$ mag. The rotational period is 6$.\!\!^{\rm h}$$87~\pm~0$$.\!\!^{\rm h}$03 hours. The composite diagram is plotted in Fig. 8 (the zero phase is JD 2451113.5000). The individual lightcurve of October 26 has considerably smaller scatter ($\pm~0.05$) than that obtained on October 23.

  

Figure 8: The composite R lightcurve of 1865 (symbols: open squares - October 23; solid circles - October 26)

2415 Ganesa

It was discovered by Giclas in 1978. The assumed diameter is 26.2 km. The observed unfiltered amplitude is $0.15~\pm~0.01$ mag and the sinodical period is longer than 2.5 hours. We plotted its lightcurve in Fig. 9.

  

Figure 9: The unfiltered lightcurve of 2415 on April 4, 1998

9262

This asteroid with 20 km diameter showed an ambiguous light variation with $0.08~\pm~0.015$ R magnitude amplitude during the observing session. The lightcurve is presented in Fig. 10. The rotational period is longer than 6.3 hours, the quite symmetric lightcurve suggests a probable value of around 9 hours.

  

Figure 10: The R lightcurve of 9262 on October 22, 1998

1989 UR

The faintness of this asteroid did not allow us to obtain an accurate lightcurve. During the observations the scatter was comparable with the whole range of variations, which was caused by the unfavorable weather conditions. During the observations the asteroid has shown a 0.15 mag brightening in R, thus the period is suspected to be longer than 4 hours. The lightcurve is presented in Fig. 11.

  

Figure 11: The R lightcurve of 1989 UR on October 22/23, 1998

1998 FM5

It is an earth-grazing minor planet, which was discovered by the Near Earth Asteroid Tracking (NEAT) Team on March 24, 1998. The angular motion of this asteroid was quite fast, therefore the maximal exposure time was only 1 minute (even this short exposure did not prevent the trailed profile). The unfiltered amplitude of the light variation is $0.61~\pm~0.01$ mag, which is a common value among the earth-grazing asteroids. The sinodical period is longer than 2.8 hours. The lightcurve is presented in Fig. 12.

  

Figure 12: The unfiltered lightcurve of 1998 FM5 on April 3, 1998

Acknowledgements

This research was supported by the Szeged Observatory Foundation, OTKA Grant W015239 and Grant PFP 5191/1997. The warm hospitality of the staff of Konkoly Observatory and their provision of telescope time is gratefully acknowledged. The authors also acknowledge suggestions and careful reading of the manuscript by K. West. The anonymous referee has greatly improved the paper with his/her notes and suggestions. The NASA ADS Abstract Service was used to access references.