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Planetary dynamos

Electricity and magnetism · level 8, lesson 4 of 6

A question to start

Earth's core is liquid iron and it still makes a strong field. Mars's core is liquid too. So why did Mars's field die?

The idea

A planet's field comes from a dynamo: moving, electrically conducting fluid that keeps its own currents and field going. It needs three things.

  1. A conducting fluid: molten iron in the core.
  2. Motion: the iron must keep churning. In a planet, that comes from convection, driven by heat flowing out of the core into the mantle above.
  3. Spin: the planet's rotation twists the flows into the organized patterns that build a large field.

Take away any one, and the field decays. The key on Mars is the heat flow. A small planet holds less heat for its surface, so it cools faster. Once the core was losing heat too slowly to convect strongly, the churning stopped, even though the core stayed molten.

Dynamo Mars Earth
Mean radius 3,389.5 km 6,371.0 km
Core molten, about 1,800 km in radius liquid outer core round a solid inner core
Dynamo stopped a few hundred million years after Mars formed still running
Earth: the core churnsMars: molten, but still

Worked examples

1. Cooling time. Heat held goes as volume, \(R^3\); heat lost goes as surface, \(R^2\). So cooling time goes as \(R\): Mars would cool in about \(3389.5/6371 = 0.53\) of Earth's time, other things equal.

2. Surface for each cubic metre. A sphere has \(4\pi R^2/(\tfrac{4}{3}\pi R^3) = 3/R\) square metres of surface for each cubic metre. Mars: \(3/3.39\times10^6 = 8.9\times10^{-7}\); Earth: \(3/6.37\times10^6 = 4.7\times10^{-7}\). Mars has about 1.9 times as much.

3. Why the core is still molten. InSight found Mars's core has lighter elements mixed into the iron, lowering its melting point. Liquid is not enough; it has to move.

Try it

  1. Name the three things a dynamo needs.
  2. Where does the heat that drives the churning go?
  3. Why does a smaller planet cool faster?
  4. The Moon's radius is 1,737 km. Using the rule from example 1, how does its cooling time compare with Earth's?
Answers
  1. A conducting fluid, motion (convection), and spin.
  2. Out of the core, into the mantle and eventually to space.
  3. It has more surface for each unit of volume, so it loses its heat relatively faster.
  4. \(1737/6371 = 0.27\), about a quarter.

Common mistake

"A liquid iron core always makes a field." The iron must keep churning, driven by heat flowing out. A molten but still core makes no field.

Where it leads