Questions: Thermal Evolution of Terrestrial Planets

Question 1

Mars has a diameter roughly half of Earth's. Which explanation best captures why Mars lost its global magnetic field billions of years ago while Earth's persists?

• A. Mars formed with far less radiogenic material, so its total initial heat was too small to sustain a dynamo
• B. Mars has a smaller volume-to-surface-area ratio, so it loses heat faster relative to its total heat content
• C. Mars has lower surface gravity, which allows internal heat to escape more easily through convection
• D. Mars rotates more slowly than Earth, reducing the dynamo effect regardless of internal temperature

Answer: (B)

The geometry of heat retention is the key insight. Heat content scales with volume (R³) while heat escapes through surface area (R²), so the timescale for cooling scales as R³/R² = R. Half the radius means the cooling timescale is roughly half as long — not because Mars has less total heat, but because it has less heat per unit of surface area to lose through. Radiogenic content (option A) matters too, but the dominant effect is geometric. Options C and D confuse secondary factors with the primary driver.

Question 2

A geologist proposes that Earth's mantle would remain convectively active for at least another billion years even if all radiogenic isotopes were instantly removed, because primordial heat alone is sufficient. What does the actual contribution of radiogenic heating suggest about this claim?

• A. The claim is roughly correct — primordial heat accounts for about 90% of Earth's current heat flux, and radiogenic decay is a minor supplement
• B. The claim is plausible but overstated — radiogenic heating contributes about 10–15% of current heat flux, making its removal a modest change
• C. The claim is significantly wrong — radiogenic heating currently contributes roughly half of Earth's total internal heat flux, and its removal would substantially reduce mantle convection
• D. The claim is entirely wrong — Earth's heat flux is now almost entirely radiogenic, and primordial heat has been completely dissipated

Answer: (C)

Radiogenic heating from U-238, Th-232, and K-40 contributes approximately half of Earth's current ~44 TW heat flux. Removing it would cut internal heat production roughly in half, dramatically slowing mantle convection and eventually ending plate tectonics. The common misconception is that 4.5 billion years of cooling would have exhausted primordial heat — it has not, but radiogenic heating is genuinely half the story today, not a footnote.

Question 3

Planetary cooling is self-accelerating — the hotter the interior, the faster it loses heat, so cooling speeds up over time.

• T. True
• F. False

Answer: False

Cooling is actually self-slowing, not self-accelerating. As a planet's interior cools, mantle viscosity increases, convection slows, and the lithosphere thickens — all of which reduce the rate of heat loss. Early in planetary history, when the interior is hottest and temperature gradients are steepest, heat loss is rapid. Over time, reduced convection efficiency and a thickening lid create a negative feedback that progressively decelerates cooling. This is why the Moon and Mars are now largely geologically dead — they exhausted the rapid early phase — while Earth continues to cool slowly.

Question 4

If two rocky planets of different sizes formed at the same time with identical initial temperatures, the smaller planet would cool to an inert state faster.

• T. True
• F. False

Answer: True

With identical initial temperatures, heat content scales as R³ while surface area (through which heat escapes) scales as R². The cooling timescale is proportional to their ratio, R. A smaller R means a shorter cooling timescale — the smaller planet has less heat to lose per unit of surface area through which it loses heat, so it reaches thermal equilibrium with space sooner. This is the fundamental geometric argument explaining why Earth remains active while the Moon and Mercury are geologically dead.

Question 5

Why does planet size (radius) have such a dominant effect on how long a planet remains geologically active, even when planets have similar compositions?

Model answer: Heat content scales with volume (R³) while the surface area through which heat escapes scales as R². The ratio — which sets the cooling timescale — scales linearly with radius R. A larger planet simply has more heat stored per unit of radiating surface, so it retains its thermal energy far longer. This is why Earth (R ≈ 6,371 km) still has a convecting mantle and active dynamo after 4.5 Gyr, while the Moon (R ≈ 1,737 km) cooled quickly into geologic inactivity.

The volume-to-surface-area ratio is the critical insight. Doubling the radius doubles the cooling timescale, not just slightly extends it. This same principle applies across scales — it's why a large potato takes much longer to cool than a small one, and why it governs thermal longevity across the entire terrestrial planet family.