The disturbing function in Solar System dynamics

The planetary disturbing function is the basis of much analytical work in Solar System dynamics and series expansions of it that were derived in the last century are still in common use today. However, most previous expansions have the disadvantage of being in terms of the mutual inclination of the two masses. Also, several of the classical, high-order expansions contain a number of errors. A new algorithm for the derivation of the disturbing function in terms of the individual orbital elements of the two masses is presented. It allows the calculation, to any order, of the terms associated with any individual argument without the need for expanding the entire disturbing function. The algorithm is used to generate a new expansion which is complete to fourth-order in the eccentricities and inclinations, and incorporates a consistent numbering system for each argument. The properties of the expansion for a selected argument are discussed, and the use of the expansion is illustrated using the examples of the Titan-Hyperion 3:4 resonance and the possible Jupiter-Pallas 18:7 resonance. (C) 2000 Academic Press.