Lecture 04: Planetary Interiors and Differentiation

ASTR 120 Solar System

Learning Objectives

  1. Infer broad interior composition from mass, radius, and mean density while recognizing degeneracies.
  2. Explain differentiation as separation by density in a sufficiently warm or molten body.
  3. Connect heat flow, volcanism, gravity, and magnetic fields to interior structure and activity.

Connection to the Course

Orbital dynamics tells us where worlds are and how they interact. Interior physics tells us what those worlds are made of and whether they can drive volcanism, tectonics, magnetic fields, or subsurface oceans. Lectures 05 through 10 repeatedly use interior energy as the hidden cause behind visible surfaces and active moons.

Interior Inference

Planetary interiors are rarely sampled directly. Instead, scientists combine bulk properties and geophysical evidence. Mean density separates broad classes: metal-rich rocky planets are denser than ice-rich moons, and gas giants have low average densities despite massive interiors. Differentiation occurs when a body becomes warm enough for dense material, often metal, to sink and lighter silicates or ices to rise. Heating can come from accretional impacts, radioactive decay, differentiation itself, or tides.

Magnetic fields provide another clue. A global dynamo generally requires an electrically conducting fluid region, energy to drive motion, and rotation. Lack of a strong present field does not mean a body never had one; crustal magnetization can preserve evidence of an ancient dynamo.

Terms Developed in Context

These terms form the lecture's reasoning vocabulary. Each definition below extends the slide explorer by showing how the term is measured or modeled, how it connects to neighboring ideas, and where its use can fail.

Mean density
Mean density is a bulk boundary condition on any acceptable interior model. Large planets compress their interiors, so comparing raw densities without pressure effects can mislead. Combining density with moment-of-inertia, gravity, magnetic, seismic, or heat-flow evidence narrows the range of allowed layer structures.
Differentiation
Differentiation requires enough heat for materials to move relative to one another. Dense metal tends to sink while lower-density silicate or ice rises, releasing gravitational energy that can add further heating. The process connects formation energy, radioactive decay, magnetic dynamos, and surface volcanism.
Moment of inertia
The coefficient \(C\) is smaller when more mass is concentrated near the center. A uniform sphere has a larger normalized moment than a strongly differentiated planet. Spacecraft tracking, precession, and libration can constrain \(C\), providing information that mean density alone cannot supply.
Gravity field
Planetary gravity is expanded into harmonics that describe equatorial bulges and regional mass anomalies. Those coefficients respond to rotation, tides, topography, and internal layering. Interpreting them requires shape and rotation data, which is why gravity is most powerful when paired with imaging or altimetry.
Dynamo
A dynamo converts kinetic energy in a conducting fluid into magnetic energy. Cooling, compositional buoyancy, and rotation can support convection in a metallic core or conducting ocean. Crustal remanent magnetization can preserve evidence of an extinct field, linking present measurements to interior history.
Heat flow
Conductive heat flow relates the temperature gradient to thermal conductivity, while convection transports heat by moving material. Small worlds generally cool faster because surface area is large relative to volume, but tidal heating can overturn that trend. Heat flow therefore connects size, age, orbital forcing, and geologic activity.

Worked Quantitative Example: Density of an Icy Moon

For a spherical body, \(\rho=M/(4\pi R^3/3)\). Suppose a moon has \(M=1.08\times10^{23}\,\text{kg}\) and \(R=2.63\times10^6\,\text{m}\). Then

\[V=\frac{4\pi R^3}{3}\approx7.62\times10^{19}\,\text{m}^3,\qquad \rho\approx\frac{1.08\times10^{23}}{7.62\times10^{19}}\approx1.42\times10^3\,\text{kg m}^{-3}.\]

This is \(1.42\,\text{g cm}^{-3}\), far below typical silicate rock density, so substantial ice or low-density volatile material is implied. The calculation does not specify the thickness of each layer; gravity data, shape, magnetic induction, and surface geology are needed for that.

Observational Evidence

Mass can be inferred from orbital motion of moons or spacecraft tracking. Radius comes from imaging, occultations, radar, or shape models. Magnetic evidence comes from magnetometers, and heat flow may be inferred from volcanism, infrared emission, tectonic deformation, or plume activity. The strongest interior interpretations combine several of these, because mean density alone cannot distinguish a small dense core plus thick ice from a more mixed interior.

Common Misconceptions and Traps

Study-Ready Synthesis

Interior science converts remote measurements into physical models. Mass, radius, density, gravity, magnetism, and heat-flow evidence together constrain composition, layering, and energy. The central discipline is to say what each measurement rules out, what it leaves ambiguous, and what additional observation would discriminate among models.

Study Questions

  1. Why can two planets with the same mean density still have different interiors?
  2. What observations would strengthen a claim that a moon has a subsurface ocean?
  3. How can a body preserve evidence of an ancient magnetic field after its dynamo shuts down?

References