Divergent migration of planets within a viscous circumstellar disk can engender resonance crossings and dramatic excitation of orbital eccentricities .
We provide quantitative criteria for the viability of this mechanism .
For the orbits of two bodies to diverge , a ring of viscous material must be shepherded between them .
As the ring diffuses in radius by virtue of its intrinsic viscosity , the two planets are wedged further apart .
The ring mass must be smaller than the planetary masses so that the crossing of an individual resonance lasts longer than the resonant libration period .
At the same time , the resonance crossing can not be of such long duration that the disk ’ s direct influence on the bodies ’ eccentricities interferes with the resonant interaction between the two planets .
This last criterion is robustly satisfied because resonant widths are typically tiny fractions of the orbital radius .
We evaluate our criteria not only for giant planets within gaseous protoplanetary disks , but also for shepherd moons that bracket narrow planetary rings in the solar system .
A shepherded ring of gas orbiting at a distance of 1 AU from a solar-type star and having a surface density of less than 500 { g } / { cm } ^ { 2 } , a dimensionless alpha viscosity of 0.1 , and a height-to-radius aspect ratio of 0.05 can drive two Jovian-mass planets through the 2:1 and higher-order resonances so that their eccentricities amplify to values of several tenths .
Because of the requirement that the disk mass in the vicinity of the planets be smaller than the planet masses , divergent resonance crossings may figure significantly into the orbital evolution of planets during the later stages of protoplanetary disk evolution , including the debris disk phase .