Dangers of Truncating the Disturbing Function In Small Body Solar System Dynamics

Planetary and satellite systems are replete with orbital resonant configurations that have been modeled by a variety of techniques. We highlight the dangers of models which attempt to trace numerically or analytically the orbital evolution of any two resonant bodies with a truncated disturbing function. Using a semianalytic model based on a traditional disturbing function expansion about zero eccentricities and inclinations, we pinpoint the nature and number of terms needed to model a typical Jovian asteroid and Kuiper Belt Object, and estimate the eccentricities at which convergence of disturbing function coefficients breaks down. We find the notion of 'order'to represent an inappropriate metric for accuracy in the orbital solution for these classes of objects, and deduce that even for dynamical configurations with 'massless' objects, including more than a few disturbing function terms is often necessary.