Math 2.0

Astronomy and astrophysics Definition

Planetary migration

Builds on Kepler orbitAngular momentumTorqueAccretion diskOrbital resonance

Definition

Let a planet of mass mm orbit a star of mass M⋆≫mM_\star \gg m on a nearly circular Kepler orbit of semi-major axis a(t)a(t). The planet moves inside a gas disk or a population of small bodies. Its orbital angular momentum is L=mGM⋆aL = m \sqrt{G M_\star a}, where GG is the gravitational constant. Planetary migration is a systematic drift of a(t)a(t) over many orbits. It is caused by a net torque Γ\Gamma of the surrounding matter on the planet. Since dL/dt=ΓdL/dt = \Gamma, the drift rate is dadt=2a ΓL.\frac{da}{dt} = \frac{2 a \, \Gamma}{L}.

Remarks

Common types are distinguished by the mechanism.

  1. Type I: a low-mass planet in a gas disk feels the torques of the spiral waves it launches at Lindblad resonances, and the corotation torque. Its migration rate is proportional to the planet mass.
  2. Type II: a giant planet opens a gap in the disk and then drifts with the viscous evolution of the disk.
  3. Planetesimal-driven migration: the planet scatters many small bodies and recoils.

Example: if the net torque is Γ=−εL/τ\Gamma = -\varepsilon L/\tau for constants ε>0\varepsilon > 0 and τ>0\tau > 0, then da/dt=−2εa/τda/dt = -2\varepsilon a/\tau, so a(t)=a(0)e−2εt/τa(t) = a(0) e^{-2\varepsilon t/\tau} and the planet drifts inward.

Non-example: a planet whose semi-major axis only oscillates under the periodic pull of a neighbour, with no net change over many orbits, does not migrate.

Two migrating planets whose period ratio approaches a ratio of small integers can be captured into an orbital resonance.

Reading path

To understand this page from the ground up, read these 14 pages in order. The foundations come first.

Show the path as a graph
Accretion disk, concept, no evidence levelAccretion diskconceptCross product, concept, no evidence levelCross productconceptDerivative, concept, no evidence levelDerivativeconceptEuclidean space, object, no evidence levelEuclidean spaceobjectEuclidean vector, concept, no evidence levelEuclidean vectorconceptKepler orbit, concept, no evidence levelKepler orbitconceptOrbital resonance, concept, no evidence levelOrbital resonanceconceptOrdinary differential equation, concept, no evidence levelOrdinary differential…conceptTorque, concept, no evidence levelTorqueconceptVelocity, concept, no evidence levelVelocityconceptClassical mechanics, concept, no evidence levelClassical mechanicsconceptMomentum, concept, no evidence levelMomentumconceptAngular momentum, concept, no evidence levelAngular momentumconceptPlanetary migration, definition, no evidence levelPlanetary migrationdefinition
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Accretion disk concept
  2. Cross product concept
  3. Derivative concept
  4. Euclidean space object
  5. Euclidean vector concept
  6. Kepler orbit concept
  7. Orbital resonance concept
  8. Ordinary differential equation concept
  9. Torque concept
  10. Velocity concept
  11. Classical mechanics concept
  12. Momentum concept
  13. Angular momentum concept
  14. Planetary migration definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Planetary_migration
About this page
TagAJNHGHGDE2
URIm2://AJNHGHGDE2
Kinddefinition
WritingW0 stub
MSC85A04, 70F15
DefinesPlanetary migration
UsesKepler orbit, Angular momentum, Torque, Accretion disk, Orbital resonance
Changed3 November 2026

Markdown · JSON · Edit on GitHub

What this page needs for W1

  • an inventory row: the row of the inventory that the node accounts for (0 of 1)
  • a source with a locator (0 of 1)

The writing levels say how complete the text of a page is. They do not measure its truth.

What links here

No page links to this page yet.