Abstract
An ever-growing observational aggregate of extrasolar planets has revealed
that systems of planets that reside in or near mean-motion resonances are
relatively common. While the origin of such systems is attributed to
protoplanetary disk-driven migration, a qualitative description of the
dynamical evolution of resonant planets remains largely elusive. Aided by the
pioneering works of the last century, we formulate an approximate, integrable
theory for first-order resonant motion. We utilize the developed theory to
construct an intuitive, geometrical representation of resonances within the
context of the unrestricted three-body problem. Moreover, we derive a simple
analytical criterion for the appearance of secondary resonances between
resonant and secular motion. Subsequently, we demonstrate the onset of rapid
chaotic motion as a result of overlap among neighboring first-order mean-motion
resonances, as well as the appearance of slow chaos as a result of secular
modulation of the planetary orbits. Finally, we take advantage of the
integrable theory to analytically show that, in the adiabatic regime, divergent
encounters with first-order mean-motion resonances always lead to persistent
apsidal anti-alignment.
Users
Please
log in to take part in the discussion (add own reviews or comments).