Unfiltered and R-band observations were taken by C. Hergenrother from Catalina Station around 1999 October 7.2, when the asteroid was at . The asteroid's airmass was in the range 2.6-2.9 during the observations. To reduce the unfiltered data, the night's R-band extinction coefficient of 0.092 mag/airmass was assumed. Because of the high airmass of the observations, some systematic error in the photometric reductions is to be expected. However, this error should be no larger than one hundredth of a magnitude.
The time distribution of the observations is shown in Fig. 3; first 31 points are unfiltered 15-sec exposures, followed by 22 R 30-sec points, and 42 unfiltered 10-sec exposures. The R measurements have been calibrated using the Landolt standards within the Johnson-Cousins system (Landolt 1992).
A formal analysis reveals that the period is min and the mean, absolute magnitude is . Shifts of the relative magnitude scales of the unfiltered data have been derived so as to minimize the sum of the squared residuals with respect to a fourth-order Fourier series. The mean, absolute magnitude has been derived from the zeroth-order coefficient of the best fit Fourier series, extrapolated to zero solar phase angle assuming and corrected for the mean asteroidal color index V-R = 0.4.
A composite lightcurve for 1999 SF10 is shown in Fig. 4. A curve representing the best fit fourth-order Fourier series to the unfiltered data is also plotted. The lightcurve is dominated by the second harmonic, and there is also a significant signal in the fourth harmonic. Since odd harmonics do not contain any significant signal, there is a possibility that the true period is half of the above mentioned period, min. In this case, Figure 4 would cover two rotation cycles. Considering, however, that a lightcurve with a single maximum/minimum pair of a high amplitude (see below) is unusual among asteroids, we believe the shorter period to be very unlikely.
The integration times of 10 to 30 seconds caused a smoothing of the lightcurve. The factors from Eq. 5 are f2=0.97 and f4=0.88 for sec; f2=0.93 and f4=0.75 for sec; f2=0.75 and f4=0.22 for sec. The true lightcurve has an amplitude greater by mag than the observed lightcurve in Fig. 4; the true amplitude is mag. However, the mean error of each coefficient of the best fit Fourier series is 0.01 mag, so an error of the measured peak-to-peak amplitude is about 0.04 mag. Thus, the smoothing of the lightcurve is only marginally significant with respect to the random noise.
The integration time of the R points, 30 seconds, is too long for a meaningful reconstruction of the lightcurve shape from them; the fourth harmonic is almost completely smoothed out in the R data. Thus the R points have been used in the period analysis (they helped to resolve a minor ambiguity in the period solution) but not for the lightcurve shape assessment.
We conclude that the lightcurve of 1999 SF10 is due to the object's fast rotation. An estimate of the mean diameter of 60 meters is made from the derived absolute magnitude and assuming a geometric albedo of 0.11 (see Pravec and Harris 1999). This diameter estimate can be in error by a factor of 2. Although the lightcurve amplitude suggests that the object is somewhat elongated, the elongation could be relatively small, considering the large phase angle at which the observations were made. Applying an approximate correction of the amplitude to zero solar phase angle (Zappalà et al. 1990), we estimate the equatorial axis ratio a/b to be .