Title: Statistical analysis of the ambiguities in the asteroid period determinations,
Abstract: Among asteroids there exist ambiguities in their rotation period
determinations. They are due to incomplete coverage of the rotation, noise
and/or aliases resulting from gaps between separate lightcurves. To help to
remove such uncertainties, basic characteristic of the lightcurves resulting
from constraints imposed by the asteroid shapes and geometries of observations
should be identified. We simulated light variations of asteroids which shapes
were modelled as Gaussian random spheres, with random orientations of spin
vectors and phase angles changed every $5^\circ$ from $0^\circ$ to $65^\circ$.
This produced 1.4 mln lightcurves. For each simulated lightcurve Fourier
analysis has been made and the harmonic of the highest amplitude was recorded.
From the statistical point of view, all lightcurves observed at phase angles
$\alpha < 30^\circ$, with peak-to-peak amplitudes $A>0.2$ mag are bimodal.
Second most frequently dominating harmonic is the first one, with the 3rd
harmonic following right after. For 1% of lightcurves with amplitudes $A < 0.1$
mag and phase angles $\alpha < 40^\circ$ 4th harmonic dominates.