Resonant and Secular Orbital Interations
Resonant and Secular Orbital Interations
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Date
2007-08-01
Authors
Zhang, Ke
Advisor
Hamilton, Douglas P
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Abstract
In stable solar systems, planets remain in nearly elliptical
orbits around their stars. Over longer timescales, however, their
orbital shapes and sizes change due to mutual gravitational
perturbations. Orbits of satellites around a planet vary for the same
reason. Because of their interactions, the orbits of planets and
satellites today are different from what they were earlier. In order
to determine their original orbits, which are critical constraints on
formation theories, it is crucial to understand how orbits evolve over
the age of the Solar System. Depending on their timescale, we
classify orbital interactions as either short-term (orbital
resonances) or long-term (secular evolution). My work involves
examples of both interaction types.
Resonant history of the small Neptunian satellites
In satellite systems, tidal migration brings satellite orbits in and
out of resonances. During a resonance passage, satellite orbits
change dramatically in a very short period of time. We investigate
the resonant history of the six small Neptunian moons. In this unique
system, the exotic orbit of the large captured Triton (with a
circular, retrograde, and highly tilted orbit) influences the
resonances among the small satellites very strongly. We derive an
analytical framework which can be applied to Neptune's satellites and
to similar systems. Our numerical simulations explain the current
orbital tilts of the small satellites as well as constrain key
physical parameters of both Neptune and its moons.
Secular orbital interactions during eccentricity damping
Long-term periodic changes of orbital shape and orientation occur when
two or more planets orbit the same star. The variations of orbital
elements are superpositions of the same number of fundamental modes as
the number of planets in the system. We investigate how this effect
interacts with other perturbations imposed by external disturbances,
such as the tides and relativistic effects. Through analytical
studies of a system consisting of two planets, we find that an
external perturbation exerted on one planet affects the other
indirectly. We formulate a general theory for how both orbits evolve
in response to an arbitrary externally-imposed slow change in
eccentricity.