Editing Planetary migration (section)

===Planetesimal-driven migration===
The orbit of a planet can change due to gravitational encounters with a large number of planetesimals. <em>Planetesimal-driven migration</em> is the result of the accumulation of the transfers of angular momentum during encounters between the planetesimals and a planet. For individual encounters the amount of angular momentum exchanged and the direction of the change in the planet's orbit depends on the geometry of the encounter. For a large number of encounters the direction of the planet's migration depends on the average angular momentum of the planetesimals relative to the planet. If it is higher, for example a disk outside the planet's orbit, the planet migrates outward, if it is lower the planet migrates inward. The migration of a planet beginning with a similar angular momentum as the disk depends on potential sinks and sources of the planetesimals.<ref name="Levison_etal_2007" /> 

For a single planet system, planetesimals can only be lost (a sink) due to their ejection, which would cause the planet to migrate inward. In multiple planet systems the other planets can act as sinks or sources. Planetesimals can be removed from the planet's influence after encountering an adjacent planet or transferred to that planet's influence. These interactions cause the planet's orbits to diverge as the outer planet tends to remove planetesimals with larger momentum from the inner planet influence or add planetesimals with lower angular momentum, and vice versa. The planet's resonances, where the eccentricities of planetesimals are pumped up until they intersect with the planet, also act as a source. Finally, the planet's migration acts as both a sink and a source of new planetesimals creating a positive feedback that tends to continue its migration in the original direction.<ref name="Levison_etal_2007" /> 

Planetesimal-driven migration can be damped if planetesimals are lost to various sinks faster than new ones are encountered due to its sources. It may be sustained if the new planetesimals enter its influence faster than they are lost. If sustained migration is due to its migration only, it is called runaway migration. If it is due to the loss of planetesimals to another planet's influence, it is called forced migration.<ref name="Levison_etal_2007">{{cite book |last1=Levison |first1=H.F. |last2=Morbidelli |first2=A. |last3=Gomes |first3=R. |last4=Backman |first4=D. |title=Protostars and Planets V |chapter=Planet Migration in Planetesimal Disks |date=2007 |publisher=University of Arizona Press |pages=669–684 |chapter-url=http://www.lpi.usra.edu/books/PPV/8045.pdf |access-date=6 April 2017}}</ref> For a single planet orbiting in a planetesial disk the shorter timescales of the encounters with planetesimals with shorter period orbits results in more frequent encounters with the planetesimals with less angular momentum and the inward migration of the planet.<ref name="Kirsh_etal_2009">{{cite journal |last1=Kirsh |first1=David R. |last2=Duncan |first2=Martin |last3=Brasser |first3=Ramon |last4=Levison |first4=Harold F. |title=Simulations of planet migration driven by planetesimal scattering |journal=Icarus |date=2009 |volume=199 |issue=1 |pages=197–209 |doi=10.1016/j.icarus.2008.05.028 |bibcode=2009Icar..199..197K}}</ref> Planetesimal-driven migration in a gas disk, however, can be outward for a particular range of planetesimal sizes because of the removal of shorter period planetesimals due to gas drag.<ref name="Capobianco_eal_2011">{{cite journal |last1=Capobianco |first1=Christopher C. |last2=Duncan |first2=Martin |last3=Levison |first3=Harold F. |title=Planetesimal-driven planet migration in the presence of a gas disk |journal=Icarus |date=2011 |volume=211 |issue=1 |pages=819–831 |doi=10.1016/j.icarus.2010.09.001 |arxiv=1009.4525 |bibcode=2011Icar..211..819C|s2cid=118583564 }}</ref>