The Diagnosis of Complex Rotation in the Lightcurve of 4179 Toutatis and Potential Applications to Other Asteroids and Bare Cometary Nuclei

The analysis of radar observations of the asteroid 4179 Toutatis by Hudson and Ostro (1995, Science270, 84–86) yielded a complex spin state. We revisit the visible lightcurve data on Toutatis (Spencer et al. 1995, Icarus117, 71–89) to explore the feasibility of using a rotational lightcurve to recover the signature of an excited spin state. For this, we apply Fourier transform and CLEAN algorithm (WindowCLEAN). WindowCLEAN yields clear and precise frequency signatures associated with the precession of the long axis about the total angular momentum vector and a combination of this precession and rotation about the long axis. For a long-axis mode state, our periodicities for Toutatis yield a mean long-axis precession period, Pφ, of 7.38 days and a rotation period around the long axis, Pψ, of 5.38 days, which compare well with the respective periods of 7.42 and 5.37 days derived by Ostro et al. (1999, Icarus137, 122–139) and represent an independent confirmation of these values. We explain why the dramatic change in the Earth–Toutatis–Sun geometry during the time that the lightcurve was obtained has little effect on the final results obtained. Using the Toutatis example as a guide, we discuss the capabilities as well as the limitations on deriving information about complex spin states from asteroidal lightcurves.