The disturbing function in Solar System dynamics

The planetary disturbing function is the basis of much analytical work in S olar System dynamics and series expansions of it that were derived in the l ast century are still in common use today. However, most previous expansion s 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 fun ction in terms of the individual orbital elements of the two masses is pres ented. It allows the calculation, to any order, of the terms associated wit h any individual argument without the need for expanding the entire disturb ing function. The algorithm is used to generate a new expansion which is co mplete to fourth-order in the eccentricities and inclinations, and incorpor ates a consistent numbering system for each argument. The properties of the expansion for a selected argument are discussed, and the use of the expans ion is illustrated using the examples of the Titan-Hyperion 3:4 resonance a nd the possible Jupiter-Pallas 18:7 resonance. (C) 2000 Academic Press.