A Comparison of Lorentz, Planetary Gravitational, and Satellite Gravitational Resonances
Abstract
We consider a charged dust grain whose orbital motion is dominated by a planet's pointsource gravity, but perturbed by higherorder terms in the planet's gravity field as well as by the Lorentz force arising from an asymmetric planetary magnetic field. Perturbations to Keplerian orbits due to a nonspherical gravity field are expressed in the traditional way: in terms of a disturbing function which can be expanded in a series of spherical harmonics (W. M. Kaula, 1966, Theory of Satellite Geodesy, Blaisdell, Waltham, MA). In order to calculate the electromagnetic perturbation, we first write the Lorentz force in terms of the orbital elements and then substitute it into Gauss' perturbation equations. This procedure is analogous to the derivation of gravitational disturbing functions, except, since the Lorentz force has no associated potential, the perturbation of each orbital element must be calculated separately. We use our result to derive strengths of Lorentz resonances and elucidate their properties. In particular, we compare Lorentz resonances to two types of gravitational resonances: those arising from periodic tugs of a satellite and those due to the attraction of an arbitrarily shaped planet.
We find that Lorentz resonances share numerous properties with their gravitational counterparts and show, using simple physical arguments, that several of these patterns are fundamental, applying not only to our expansions, but to all quantities expressed in terms of orbital elements. Some of these patterns have been previously called "d'Alembert rules" for satellite resonances. Other similarities arise because, to firstorder in the perturbing force, the three problems share an integral of the motion. Yet there are also differences; for example, firstorder inclination resonances exist for perturbations arising from planetary gravity and from the Lorentz force, but not for those due to an orbiting satellite. Finally, we provide a heuristic treatment of a particle's orbital evolution under the influence of drag and resonant forces. Particles brought into meanmotion resonances experience either trapping or resonant "jumps," depending on the direction from which the resonance is approached. We show that this behavior does not depend on the details of the perturbing force but rather is fundamental to all meanmotion resonances.
 Publication:

Icarus
 Pub Date:
 June 1994
 DOI:
 10.1006/icar.1994.1089
 Bibcode:
 1994Icar..109..221H
 Keywords:

 Gravitational Effects;
 Interplanetary Dust;
 Lorentz Force;
 Orbital Resonances (Celestial Mechanics);
 Planetary Gravitation;
 Satellite Perturbation;
 Computerized Simulation;
 Disturbing Functions;
 Series Expansion;
 Spherical Harmonics;
 Astrophysics