Long-Term Evolution of Rotational States and Nongravitational Effects for Halley-like Cometary Nuclei

Abstract

We present the results of numerical simulations for the long-term evolution of rotational states of near-prolate cometary nuclei over many orbits under sublimation-induced torques. We derive plausible evolutionary paths for the rotational states and show that they strongly depend on the location of active areas on the nucleus. We conclude that for acceptable locations of active regions on the nucleus, the rotational state of the nucleus maintains nearly constant precessional angles and nongravitational forces over many orbits as suggested by observations of Comet P/Halley. In these cases, the strongest active area should be near cometographic midlatitudes when the equatorial plane is defined to contain the intermediate and small axes of inertia. A Halley-like nucleus with active areas and a near-commensurability (≈2) of precessional and rotational periods and an assumed density near 0.4 g cm -3 is capable of maintaining a consistent 4.1-day delay in the perihelion passage for each apparition as observations suggest. However, the exact amount of delay (or advance) depends on the precise details of the rotational state, including the direction of the rotational angular momentum vector, the details of the active areas such as locations, tilts, and strengths, the secular water production curve, and the mass (or density) of the nucleus. We predict a spin-up of the nucleus provided that the same set of active areas are present over many orbits. This spin-up is presumably the major cause for nuclear splittings.