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Planetary Formation I: Core Accretion and Migration

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Planetary Formation: The Nebular HypothesisProtoplanetary Disk Structure and Evolution→→Multi-Planet System Architecture and Orbital Stability AnalysisPlanetary Formation II: Gravitational Instability and Direct Collapse+1 more
planet-formation core-accretion migration

Core Idea

Core accretion is the dominant theory of planetary formation, in which kilometer-sized planetesimals accumulate through collisions to form planetary cores. Planets migrate inward and outward through gravitational interactions with the protoplanetary disk, explaining why giant planets are found at various orbital distances rather than being segregated by their formation distance from the star.

Explainer

You already know that protoplanetary disks are rotating structures of gas and dust surrounding young stars, with temperature and composition varying by distance from the star. The core accretion model explains how the raw material in these disks assembles into planets through a sequence of stages that span millions of years, starting from microscopic dust grains and ending with worlds the size of Jupiter.

The process begins with dust coagulation: micron-sized grains of silicate and ice collide gently in the disk and stick together through electrostatic and surface forces, growing into millimeter- and centimeter-sized aggregates. This early phase is straightforward, but a major theoretical challenge arises at the meter scale — the so-called meter-size barrier. Objects around a meter across experience strong aerodynamic drag from the surrounding gas, causing them to spiral inward toward the star on timescales of only a few hundred years, faster than they can grow by further collisions. The leading solution involves streaming instabilities, where particles concentrate into dense clumps through collective interactions with the gas, bypassing the problematic size range and jumping directly to kilometer-scale planetesimals.

Once planetesimals reach roughly a kilometer across, gravity takes over as the dominant growth mechanism. Larger bodies have stronger gravitational fields, so they sweep up more material than smaller ones — a process called runaway accretion. The biggest planetesimals grow fastest, quickly outpacing their neighbors. Eventually, a few dominant bodies — planetary embryos — have consumed or scattered most of the nearby material, and growth transitions to oligarchic accretion, where a handful of similarly sized embryos compete for the remaining planetesimals in their feeding zones. For rocky planets like Earth, this oligarchic stage produces Mars-sized embryos that later undergo giant impacts over tens of millions of years, gradually assembling into the final terrestrial planets.

Gas giants require an additional step. Beyond the snow line — the distance from the star where water ice condenses, roughly 3 AU in our solar system — solid cores can grow larger because ice adds to the available solid material. When a core reaches approximately 10 Earth masses (the critical core mass), its gravity becomes strong enough to capture and retain hydrogen and helium gas from the surrounding disk. Gas accretion begins slowly but accelerates dramatically in a process called runaway gas accretion, allowing a planet to balloon from a rocky core to a gas giant of hundreds of Earth masses in as little as a hundred thousand years. This must happen before the disk dissipates — typically within 3–10 million years — which sets a tight deadline for giant planet formation.

Planetary migration resolves a puzzle that the basic core accretion model cannot: why hot Jupiters orbit closer to their stars than Mercury orbits the Sun, far inside the snow line where they could not have formed. A forming planet exchanges angular momentum with the gas disk through gravitational torques. Type I migration affects lower-mass planets embedded in the disk and can move them inward (or occasionally outward) over millions of years. Type II migration occurs when a planet grows massive enough to open a gap in the disk; it then migrates locked to the disk's own viscous evolution. Migration explains the wide diversity of observed exoplanet architectures — from hot Jupiters to compact multi-planet systems — as outcomes of the same physical process operating under different disk conditions and timescales.

Practice Questions 5 questions

Prerequisite Chain

Understanding Zero → The Number Zero → Counting to Five → Counting to 10 → Counting to 20 → Counting a Set of Objects Up to 20 → Cardinality: The Last Number Counted → Matching Numerals to Quantities → Subitizing Small Quantities → Addition Within 10 → Number Bonds to 10 → Addition Within 20 → Doubles and Near Doubles → Doubles Facts Within 10 → Near Doubles Facts Within 20 → Mental Math Strategies for Addition → Mental Math: Adding and Subtracting Tens → Addition Within 100 → Repeated Addition as Multiplication → Multiplication as Equal Groups → Multiplication: Arrays → Basic Multiplication Facts (0s, 1s, 2s, 5s, 10s) → Multiplication Facts Within 100 → Division as Equal Sharing → Division as Grouping (Measurement Division) → Division: Grouping (Repeated Subtraction) Model → Division: Fair Sharing Model → Division as Equal Sharing → Division as Grouping → Basic Division Facts → Division Facts Within 100 → Multiplication and Division Fact Families → Relationship Between Multiplication and Division → Division Facts as Inverse of Multiplication → Remainders and Quotients in Division → Division Word Problems → Multi-Step Word Problems → Solving Multi-Step Word Problems → Multiplication Word Problems → Division Word Problems → Introduction to Long Division → Factors and Multiples → Prime and Composite Numbers → Equivalent Fractions → Relating Fractions and Decimals → Decimal Place Value → Integers and the Number Line → Comparing and Ordering Integers → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Dividing Integers → Unit Rates → Proportions → Percent Concept → Converting Between Fractions, Decimals, and Percents → Operations with Rational Numbers → Two-Step Equations → Solving Multi-Step Equations → Equations with Variables on Both Sides → Angle Pairs: Complementary, Supplementary, and Vertical → Parallel Lines and Transversals → Corresponding Angles → Alternate Interior Angles → Triangle Angle Sum Theorem → Exterior Angle Theorem → Triangle Inequality Theorem → Similar Triangles: AA Similarity → Similar Triangles: SSS and SAS Similarity → Proportions in Similar Triangles → Right Triangle Trigonometry Introduction → Sine, Cosine, and Tangent Ratios → Trigonometric Ratios Review → Radian Measure → Converting Between Degrees and Radians → The Unit Circle → Graphing Sine and Cosine → Graphing Tangent and Reciprocal Trigonometric Functions → Derivatives of Trigonometric Functions → Antiderivatives → Indefinite Integrals → Basic Integration Rules → Riemann Sums → Definite Integral Definition → Double Integrals: Definition and Setup → Iterated Integrals and Fubini's Theorem → Double Integrals over Rectangular Regions → Double Integrals over General Regions → Applications of Double Integrals: Area, Mass, and Moments → Triple Integrals in Cartesian Coordinates → Triple Integrals in Cylindrical and Spherical Coordinates → Change of Variables and the Jacobian Determinant → Applications of Triple Integrals: Volume and Mass → Vector Fields and Their Representations → Line Integrals of Vector Fields → Work and Circulation → Line Integrals of Scalar and Vector Functions → Fundamental Theorem for Line Integrals → Conservative Vector Fields → Conservative Vector Fields and Potential Functions → Curl and Divergence of Vector Fields → Curl and Divergence → Divergence Theorem → Electric Flux and Divergence Theorem → Gauss's Law: Integral Form and Meaning → Solving Problems with Gauss's Law → Conductors in Electrostatic Equilibrium → Capacitance and Capacitors → Dielectrics → Dielectric Constant and Relative Permittivity → Electric Field Inside Dielectric Materials → Dielectric Materials and Polarization → Dielectric Susceptibility and Permittivity → Energy Density in Electric Fields → Electric Current and Current Density → Electrical Resistance and Resistivity → Ohm's Law and Circuit Elements → Electromotive Force (EMF) and Batteries → Kirchhoff's Circuit Laws: Voltage and Current → DC Circuit Network Analysis Methods → Transient Response in RC Circuits → RC Circuits → LC and RLC Circuits → AC Circuits: Fundamentals → Impedance and Reactance → AC Power and Resonance → Electromagnetic Waves → Frequency-Dependent Permittivity and Dispersion → Electromagnetic Waves in Anisotropic Media → Birefringence and Dichroism → Wave Plates: Quarter-Wave and Half-Wave Plates → Circular and Elliptical Polarization Production → Polarization States: Linear, Circular, and Elliptical → Linear Superposition of Waves → Two-Source Interference Patterns → Path Difference and Constructive/Destructive Interference → Fringe Spacing in Interference Patterns → Young's Double-Slit Experiment and Analysis → Single-Slit Diffraction and Diffraction Patterns → Diffraction Limit and the Rayleigh Criterion → Fresnel Zones and Wavefront Propagation → Far-Field Diffraction and the Fraunhofer Approximation → Diffraction Gratings and the Grating Equation → Diffraction Gratings → Telescopes and Observing Methods → Stellar Properties: Luminosity, Temperature, and Size → Photometric Magnitude Systems and Color Indices → Stellar Spectral Classification → Nebulae and Star Formation → Planetary Formation: The Nebular Hypothesis → Protoplanetary Disk Structure and Evolution → Planetary Formation I: Core Accretion and Migration

Longest path: 153 steps · 1081 total prerequisite topics

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