(4183) Cuno

Updated 2001 February 8.

Orbit, abs. magnitude:

Apollo, q = 0.722 AU, a = 1.983 AU, i = 6.8 deg, H = 14.4

Rotation period, amplitude:

P = 3.5596 hr, ampl. < 0.1 to 0.84 mag

Observations:

Contributing stations:
Ondrejov Observatory
Thornton Observatory, R. Koff
Badlands Observatory, R. Dyvig
River Oaks Observatory, B. Holliday
Manchester, J. Saxton

This Apollo asteroid has been observed on four nights during 2000 October 21.1-26.9 and ten nights during November 28.0 to December 17.4. An analysis of the data revealed a lightcurve with the synodic period of (3.5596 +/- 0.001) h. Six representative composite lightcurves are presented in Fig. 1. Most of the lightcurves contain very strong signals in the 1st harmonic, that is quite unusual. Moreover, the lightcurve evolved a lot during the 57-day interval. The unusual shape and the evolution of the lightcurve is apparent from Fig. 2 as well as from their parameters listed in the following Table. The Table contains also Ondrejov data from 1997 October 22-23 and data derived from a sparse lightcurve by Bembrick et al. (2000) taken on 1998 June 19.

Date

Lpab (deg)

Bpab (deg) Phase (deg) Amplitude (mag) 2*A1 (mag) 2*A2 (mag) Dif.Max (mag)
1997 Oct. 22 36 +9 7 < 0.1 < 0.1 < 0.1 < 0.1
1998 June 19 230 -14 58 (0.70) (0.04) (0.46) (0.18)
2000 Oct. 22 74 +9 34 0.46 0.44 0.12 0.34
2000 Nov. 28 96 +10 38 0.83 0.69 0.27 0.47
2000 Dec. 4 102 +11 42 0.84 0.56 0.39 0.36
2000 Dec. 8 107 +11 46 0.81 0.44 0.45 0.26
2000 Dec. 15 120 +12 59 0.75 0.24 0.51 0.07
2000 Dec. 17 126 +12 66 0.69 0.17 0.54 0.06

Analysis and Interpretation:

Rotation Period:

The complex shape and evolution of the lightcurve during 2000 October 21 to December 17 don't allow a direct application of methods of period determinations like that of Harris et al. (1989). We used a few different approaches to obtain a confident solution and we adopted a period of 3.5596 h that resulted from a method using extrema of the second harmonics of the best fit Fourier series to the individual lightcurves; the extrema were assumed to occur at a same rotation phase of the asteroid and the period has been estimated by minimizing a sum of square residuals of the observed extrema's rotation phases. The same method has been successfully used in a few past similar cases, e.g., for (2063) Bacchus (Pravec et al. 1998). A formal error of the adopted synodic period solution is 0.0003 h but our experiments showed that a realistic error is somewhat greater and we estimate it to be about 0.001 h. An a priori uncertainty of the difference between the synodic and sidereal periods of rotation caused by the motion of the PAB is 0.0013 h (see Pravec et al. 1996, Eq. 4). Thus, we conclude that a sidereal period of Cuno's rotation is (3.5596 +/- 0.002) h.

The First Harmonics:

The quite strong signal in the first harmonic of some of the lighcturves (see the amplitudes 2*A1 in the Table above) is probably caused by a large deviation of the asteroid's shape from a symmetric figure. A large hemispheric albedo difference is not plausible since in such case we would expect a relatively slow evolution of the amplitude of the first harmonic. In other words, the fact that we saw the major change from the dominance of the first harmonic on November 28 to the much more symmetric lightcurve on December 15, while the PAB moved by only 24 degrees during that interval, indicates that a smaller scale shape feature was the cause of the strong first harmonic, not a hemispheric scale albedo difference.

Spin Vector Direction, Shape:

The lightcurve observed on 1997 October 22 and 23 showed an amplitude much lower than the other lightcurves taken in the other apparitions. Regardless of an actual shape of the asteroid and despite that it at least partly could be due to the smaller solar phase angles of that date, the small amplitude suggests that we saw the asteroid at an aspect closer to pole-on on 1997 October 22-23 than on any of the other dates. Although we cannot estimate exactly how far from pole-on it was, the uncertainty is likely a few tens degrees. The position of the PAB on 1997 October 22 and hence the tentative pole estimate is [36 deg, +9 deg] in equinox J2000. We have no constraint on if it was a north or south pole.

If the asteroid's figure could be approximated with a triaxial ellipsoid, it would be possible to estimate the asteroid's pole position and shape using an amplitude method (see, e.g., Magnusson et al. 1989). Since an ellipsoid is clearly a poor approximation of the shape of the asteroid (see the previous section), we doubt that the amplitude method could provide a meaningful estimate of the pole position and shape of the asteroid. Nevertheless, we checked if the amplitudes are consistent with the tentative pole estimate mentioned above and found that they suggest that the pole actually may be shifted to somewhat smaller ecliptic longitudes than the pole estimate given above. A pole around the longitude of about 10 degrees is suggested to have an aspect of the 1997 October 22 still not far from pole-on while the 1998 June 19 observations would be taken at a middle-latitude aspect that could cause the appreciable amplitude observed on that date. The decrease of the mean brightness (derived as the zero order of the best fit Fourier series) of the asteroid by 0.10 mag (after a reduction to the same phase angle) from 2000 October 21-23 to November 28 (see Fig. 2) is also consistent with the tentative pole position suggested above. The lightcurves taken in mid-December 2000 were taken at an aspect close to equator-on and their amplitudes corrected for a phase effect indicate that the equatorial profile is somewhat elongated with a/b about XXXX.

The mean, absolute R magnitude derived from the calibrated lightcurves of 2000 October 21-23 and November 28 assuming G=0.15 is Hr=14.14 and 14.24, respectively. Uncertainties of these estimates due to an uncertainty of G are greater than 0.3 mag. Considering that the mean V-R of asteroids is about 0.4 mag, these estimates are consistent with the absolute V magnitude H=14.4 from MPC 32296.



Fig. 1: Composite lightcurves from the 2000 apparition

The October and November lightcurves have been taken from Ondrejov Observatory, observers L. Sarounova and P. Kusnirak. The December 4.4 lightcurve has been taken by R. Dyvig from Badlands Observatory. The December 8.4 and 17.4 lightcurves have been taken by B. Holliday from River Oaks Observatory. The December 15.2 lightcurve has been taken by J. Saxton from Manchester. The curves are the best fit Fourier series of orders 3, 6, 8, 8, 7, and 7, respectively.


Fig. 2: Composite lightcurves

The curves representing the best fit Fourier series of five of the composite lightcurves from Fig. 1 plotted one over the other. The October and November lightcurves are calibrated and they are plotted on the absolute R magnitude scale (reduced to the solar phase angle of 38.0 deg assuming G=0.15). The December lightcurves are relative and they are plotted with their zeroth Fourier orders fixed at the value of the zeroth order of the November 28 lightcurve, to facilitate checking relative changes of the lightcurve shape.


Fig. 3: Individual lightcurves from 2000 November 30.4 to December 7.4

The lightcurves that also contributed but are not plotted in Fig. 1 are presented here. The curves are the Fourier fits to nearby lightcurves from Fig. 1.



References:

Bembrick, C., B. Pereghy, and T. Ainsworth 2000. A lightcurve for 4183 Cuno. Proc. XIX Natn. Aust. Conv. amat. Astrer. 1-4.

Pravec, P., L. Sarounova, and M. Wolf 1996. Lightcurves of 7 near-Earth asteroids. Icarus, 124 , 471-482.

Pravec, P., M. Wolf, and L. Sarounova 1998. Lightcurves of 26 near-Earth asteroids. Icarus, 136 , 124-153.

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