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D.P. Hamilton (U. Maryland)
Resonances are fundamental in orbital dynamics, and are responsible for a diverse set of Solar System phenomena including gaps, density waves, and bending waves in Saturn's rings; asteroids and satellites on tadpole and horseshoe orbits; gaps and enhancements in the asteroid belt and the delivery of meteoroids to Earth; tidal heating and volcanism on Io; the broad and dusty Saturnian E-ring; stable longitudes in the geopotential; the large vertical extent of the Jovian ring's diffuse halo; the high orbital eccentricities of Pluto and some Kuiper Belt objects; spin-locking of planetary satellites; and the dusty ring exterior to Earth's orbit.
The Solar System did not form in its current resonant-rich state though, rather it evolved slowly into this state under the influence of drag forces including planetary tides, planetary migration, Poynting-Robertson drag, plasma drag, and nebular drag. All of these forces act to drive objects from their initial non-resonant positions into resonant configurations where they can become permanently trapped.
Interestingly, the physics of resonance trapping is largely independent of the details of the resonant force, whether it is the gravity of an orbiting satellite, the gravity of a non-axisymmetric planet, or the Lorentz force from a spinning magnetic field (Hamilton 1994). Thus, the mathematical apparatus developed for satellite resonances may be applied to their more exotic non-gravitational counterparts and, conversely, the study of non-gravitational resonances can enhance our understanding of gravitational phenomena.
Most of these similarities are enforced by very simple physics, primarily orbital symmetries and the Jacobi Constant. In this talk, I will use these concepts to elucidate the main features of resonant dynamics and answer the following questions: Why do different resonances behave similarly? When can resonant trapping occur? Do equilibrium configurations exist and, if so, under what conditions are they stable?
I am grateful to both NSF and NASA for supporting this research.
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The author(s) of this abstract have provided an email address for comments about the abstract: hamilton@astro.umd.edu