The "missing" 5%, the roughly 50 objects still lurking in the shadows, are thought to lie in resonant orbits
As an example, dynamical chains formed by linking heteroclinic connections and homoclinic orbits  are proposed for the analysis of fast resonance transitions between exterior and interior resonant orbits (in the Sun-Jupiter system)  or "loose" capture trajectories .
A preliminary solution (the sequence of resonant orbits and intercepted bodies) is defined by using two simple tools: the suboptimal solution of the [v.sub.[infinity]] leveraging problem proposed by Sims and Longuski  and the Tisserand graph .
The researchers think these comet swarms formed when a as-yet-undetected planet migrated outward, sweeping icy bodies into resonant orbits
. When the orbital periods of the comets matched the planet's in some simple ratio -- say, two orbits for every three of the planet -- the comets received a nudge from the planet at the same location each orbit.
One of the wonderful things about this system is that the exoplanets have resonant orbits: Their orbital periods are roughly integer ratios of one another, a setup that gravitationally links the planets together and can lead to tiny shifts in their positions--and the times of their transits.
Such resonant orbits arise when worlds migrate from their original locations, Gillon explains.
Sean Mills (University of Chicago) and colleagues show in the May 26th Nature that the planets circle their star in resonant orbits
, that is, orbits whose periods are multiples of one another.
Moreover, the team writes, "The detailed dynamics of a resonant system probe the system's formation." Planets in resonant orbits
probably didn't form that way but fell into the resonance and became stuck while migrating inward or outward early in the system's history.
The team's simulations show that an inwardly migrating Jupiter would have shepherded large numbers of asteroids into 3:2 resonant orbits
. The objects would remain stuck in this relationship even as Jupiter spiraled inward.
An earlier spasm of gravitational conflict tossed out one of the planets, leaving two survivors in highly eccentric resonant orbits
"It could even be that there are two planets" with differing orbital tilts "in resonant orbits
, so the relative inclination is maintained."
Asteroids with orbital periods commensurable with Jupiter's travel time around the Sun are treated to cyclical encounters that nudge them from those resonant orbits
. The gaps were first noticed in the middle of the 19th century by Daniel Kirkwood, an American mathematician.