Vertical instability and inclination excitation during planetary migration

G. Voyatzis, K. I. Antoniadou, K. Tsiganis

    Research output: Contribution to journalArticlepeer-review


    We consider a two-planet system migrating under the influence of dissipative forces that mimic the effects of gas-driven (Type II) migration. It has been shown that, in the planar case, migration leads to resonant capture after an evolution that forces the system to follow families of periodic orbits. Starting with planets that differ slightly from a coplanar configuration, capture can, also, occur and, additionally, excitation of planetary inclinations has been observed in some cases. We show that excitation of inclinations occurs, when the planar families of periodic orbits, which are followed during the initial stages of planetary migration, become vertically unstable. At these points, vertical critical orbits may give rise to generating stable families of 3D periodic orbits, which drive the evolution of the migrating planets to non-coplanar motion. We have computed and present here the vertical critical orbits of the 2/1 and 3/1 resonances, for various values of the planetary mass ratio. Moreover, we determine the limiting values of eccentricity for which the “inclination resonance” occurs.

    Original languageEnglish
    Pages (from-to)221-235
    Number of pages15
    JournalCelestial Mechanics & Dynamical Astronomy
    Issue number3-4
    Publication statusPublished - 1 Jan 2014


    • inclination excitation
    • periodic orbits
    • planetary systems
    • type II migration
    • vertical critical orbit
    • vertical stability


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