Icarus 157, 205–218 (2002) doi:10.1006/icar.2002.6829, available online at http://www.idealibrary.com on Evolution of Comet Nucleus Rotation A. I. Neishtadt Space Research Institute, Moscow, Russia D. J. Scheeres Department of Aerospace Engineering, The University of Michigan, Ann Arbor, Michigan 48109-2140 E-mail: scheeres@umich.edu V. V. Sidorenko Keldysh Institute of Applied Mathematics, Moscow, Russia and A. A. Vasiliev Space Research Institute, Moscow, Russia Received January 12, 2001; revised December 12, 2001 The secular evolution of comet nucleus rotation states subject to outgassing torques is studied. The dynamical model assumes that the nucleus inertia ellipsoid is axially symmetric. The outgassing torques acting on the surface are modeled using standard cometary activity formulae. The general rotational equations of motion are derived and separately averaged over the fast rotational dynam- ics terms and the comet orbit. Special cases where the averaging assumptions cannot be applied are evaluated separately. The mod- ification of the comet orbit due to comet outgassing is neglected. Resulting from this analysis is a system of secular differential equa- tions that describes the dynamics of the comet nucleus angular mo- mentum and rotation state. We find that the qualitative secular evolution of the rotation state is controlled by a single parameter that combines parameters related to the comet orbit and param- eters related to the nucleus surface geometry and activity. From this solution, we find qualitatively different evolutionary paths for comet nuclei whose entire surface is active, as compared to nuclei with only a single active region. For surface activity models between these extremes, we show that certain evolutionary paths are more likely than others. Additionally, our solution indicates that a comet nucleus’ rotational angular momentum will tend to increase over time, potentially contributing to the observed phenomenon of comet nucleus splitting. c  2002 Elsevier Science (USA) Key Words: comets; rotational dynamics. 1. INTRODUCTION Many phenomena studied in cometary physics cannot be ex- plained without some hypotheses on the possible nucleus ro- tation state (e.g., photometric and morphological properties of the inner coma). Additionally, these hypotheses are needed to constrain the mathematical models being developed to simu- late and analyze the navigation problems that arise in spacecraft missions to comets (Scheeres et al. 1998, Weeks 1995). Hence, it is important to understand the long-term dynamics of comet nucleus rotation. To date there is only limited information on the actual rotation states of active comets. In general, it is possible to evaluate the rotation period of a nucleus using Fourier analysis of lightcurves (Whipple 1982). More detailed understanding of the rotation state is possible if the comet has specific coma features such as jets (Samarasinha and A’Hearn 1991). For several comets, estimated rotation parameters were found in a less reliable way using additional assumptions on the properties of nongravita- tional forces perturbing their orbit motion (e.g., Whipple and Sekanina 1979). In the future, direct observations of comet nu- clei by comet-targeted missions will become an important source of information on their rotation. It is these future missions that have motivated this particular study. The first measurements of comet nucleus rotation were based on the spacecraft imaging of P/Halley from the “Giotto” and “Vega” spacecraft (Keller et al. 1987, Sagdeev et al. 1989). The 2.2-day spin period of the P/Halley nucleus (Keller et al. 1987) as well as the spin model of Sagdeev et al. (1989) has been questioned. Belton et al. (1991) proposed another model which satisfies a wide variety of space- and ground-based observations and which also is con- sistent with independent analysis by Samarasinha and A’Hearn (1991). Recent close-up views of Comet Borrelly should allow for the rotation state of this comet to be reliably estimated as well. 205 0019-1035/02 $35.00 c  2002 Elsevier Science (USA) All rights reserved.